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CHAPTER-WISE PREVIOUS YEARS' QUESTIONS, , SCIENCE, &, , MATHEMATICS, Class X (CBSE)

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Edition: 2019-20

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CHAPTER-WISE PREVIOUS YEARS' QUESTIONS, , SCIENCE

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Note: After attempting the questions, a student must refer to the stepwise solutions available on our, website www.aakash.ac.in and compare his/her solutions with the solutions given on our website., To get the text solution, students are required to sign in their account with their log in credentials.

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CHEMISTRY, Chapter - 1 : Chemical Reactions and Equations, 1., , Balance the following chemical equation:, Fe(s) + H2O(g)  Fe3O4(s) + H2(g), [2008]...[1M], , 2., , Why is respiration considered an exothermic, process?, , 3., , [2008]...[1M], , Balance the following chemical equation:, heat, Pb NO3 2 (s) ,  PbO(s)  NO2 (g)  O2 (g), , [2009]...[1M], 4., , Name a reducing agent that may be used to, obtain manganese from manganese dioxide., [2009]...[1M], , 5., , What change in the colour of iron nails and, copper sulphate solution you observe after, keeping the iron nails dipped in copper sulphate, solution for about 30 minutes?, , 6., , [2010]...[1M], , Give an example of a decomposition reaction., Describe an activity to illustrate such a reaction, by heating., , 9., , No chemical reaction takes place when granules, of a solid, A, are mixed with the powder of, another solid, B. However, when the mixture is, heated, a reaction takes place between its, components. One of the products, C, is a metal, and settles down in the molten state while the, other product, D floats over it. It was observed, that the reaction is highly exothermic., (i) Based on the given information make an, assumption about A and B and write a, chemical equation for the chemical reaction, indicating the conditions of reaction, physical, state of reactants and products and thermal, status of reaction., (ii) Mention any two types of reaction under, which above chemical reaction can be, classified., [2010]...[3M], , 10. Decomposition reactions require energy either in, the form of heat or light or electricity for breaking, down the reactants. Write one equation each for, decomposition reactions where energy is supplied, in the form of heat, light and electricity., , [2008]...[2M], [2018]...[3M], , 7., , (i) What is the colour of ferrous sulphate, crystals? How does this colour change after, heating?, (ii) Name the products formed on strongly, heating ferrous sulphate crystals. What type, of chemical reaction occurs in this change?, [2009]...[2M], , 8., , What happen when an aqueous solution of, , 11. 2 g of silver chloride is taken in a china dish and, the china dish is placed in sunlight for, sometime. What will be your observation in this, case? Write the chemical reaction involved in the, form of a balanced chemical equation. Identify, the type of chemical reaction., , [2019]...[3M], , 12. Identify the type of reactions taking place in each, of the following cases and write the balanced, chemical equation for the reactions., , sodium sulphate reacts with an aqueous solution, of barium chloride? State the physical conditions, of reactants in which the reaction between them, will not take place. Write the balanced chemical, equation for the reaction and name the type of, reaction., , [2010]...[2M], , (i) Zinc reacts with silver nitrate to produce zinc, nitrate and silver., (ii) Potassium iodide reacts with lead nitrate to, produce potassium nitrate and lead iodide., [2019]...[3M], , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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2, , Science, , Chapter-wise Previous Years' Questions (Class-10), , Chapter - 2 : Acids, Bases and Salts, 1., , How does the flow of acid rain water into a river, make the survival of aquatic life in the river, difficult?, [2008] ...[1M], , 2., , Fresh milk has a pH of 6. When it changes into, curd (yogurt), will its pH value increase or, decrease? Why?, [2009] ...[1M], , 6., , In an experiment to study the properties of, acetic acid, a student takes about 2 ml of, acetic acid in a dry test tube. He adds about 2, ml of water to it and shakes the test tube well., He is likely to observe that:, (a) The acetic acid dissolves readily in water., (b) The solution becomes light orange., , 3., , Which of the following observations is true about, dilute solution of acetic acid?, , (c) Water floats over the surface of acetic acid., (d) Acetic acid floats over the surface of water., , (a) It smells like vinegar and turns red litmus blue, (b) It smells like onion and turns blue litmus blue, , [2013] ...[1M], 7., , Write the chemical formula for washing soda., How may it be obtained from baking soda?, Name an industrial use of washing soda other, than washing clothes., [2008] ...[2M], , 8., , A compound which is prepared from gypsum has, the property of hardening when mixed with a, proper quantity of water. Identify the compound., Write the chemical equation for its preparation., For what purpose is it used in hospitals?, , (c) It smells like orange and turns red litmus blue, (d) It smells like vinegar and turns blue litmus red, [2012] ...[1M], 4., , A student adds 4 ml of acetic to a test tube, containing 4 ml of distilled water. He then shakes, the test tube and leaves it to settle. After about, 10 minutes he observes:, (a) A layer of water over the layer of acetic acid, (b) A layer of acetic acid over the layer of water, (c) A precipitate settling at the bottom of the, test tube, (d) A clear colourless solution, [2012] ...[1M], , 5., , A student prepared 20% sodium hydroxide, solution in a beaker containing water. The, observations noted by him are given below., (I) Sodium hydroxide is in the form of pellets., (II) It dissolves in water readily., (III) The beaker appears cold when touched from, outside., (IV) Red litmus paper turns blue when dipped, into the solution., The correct observations are:, , [2009] ...[2M], 9., , Blue litmus solution is added to two test tubes, A and B containing dilute HCl and NaOH, solution respectively. In which test tube a colour, change will be observed? State the colour, change and give its reason., [2019] ...[2M], , 10. What is observed when 2 mL of dilute, hydrochloric acid is added to 1 g of sodium, carbonate taken in a clean and dry test tube?, Write chemical equation for the reaction involved., [2019] ...[2M], 11. 2 mL of sodium hydroxide solution is added to, a few pieces of granulated zinc metal taken in, a test tube. When the contents are warmed, a, gas evolves which is bubbled through a soap, solution before testing. Write the equation of the, chemical reaction involved and the test to detect, the gas. Name the gas which will be evolved, when the same metal reacts with dilute solution, of a strong acid., [2018] ...[3M], 12. The pH of a salt used to make tasty and crispy, pakoras is 14. Identify the salt and write a, chemical equation for its formation. List its two, uses., [2018] ...[3M], , (a) (I), (II), and (III), (b) (II), (III) and (IV), (c) (III), (IV) and (I), (d) (I), (II) and (IV), [2013] ...[1M], , 13. Identify the acid and the base from which, sodium chloride is obtained. Which type of salt, is it? When is it called rock salt? How is rock, salt formed?, [2019] ...[3M], , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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Chapter-wise Previous Years' Questions (Class-10), , Science, , 3, , Chapter - 3 : Metals and Non-metals, 1., , A clean aluminium foil was placed in an aqueous, solution of zinc sulphate. When the aluminium, foil was taken out of the zinc sulphate solution, after 15 minutes, its surface was found to be, coated with a silvery grey deposit. From the, above observation it can be concluded that:, (a) Aluminium is more reactive than zinc, , (b) Why is it that non-metals do not displace, hydrogen from dilute acids? [2008] ...[3M], 6., , What is meant by 'rusting'? With labelled, diagrams, describe an activity to find out the, conditions under which iron rusts? [2009] ...[3M], , 7., , Write the electronic configuration of two elements, X and Y whose atomic numbers are 20 and 17, respectively. Write the molecular formula of the, compound formed when element X reacts with, element Y. Draw electron-dot structure of the, product and also state the nature of the bond, formed between both the elements., , (b) Zinc is more reactive than aluminium, (c) Zinc and aluminium both are equally reactive, (d) Zinc and aluminium both are non-reactive, [2011] ...[1M], 2., , Iron nails were dipped in an aqueous solution of, copper sulphate. After about 30 minutes, it was, observed that the colour of the solution changed, from, , [2017] ...[3M], 8., , (a) Colorless to light green, (b) Blue to light green, (c) Blue to colourless, (d) Green to blue, 3., , [2011] ...[1M], , The colours of aqueous solutions of CuSO4 and, FeSO4 as observed in the laboratory are :, , (c) Dark blue and dark green respectively, (d) Dark blue and pale green respectively, , [2010] ...[5M], , (b) Light blue and dark green respectively, , [2012] ...[1M], A student prepared an aqueous solution of, CuSO4 in beaker X and an aqueous solution of, FeSO4 in beaker Y. He then dropped some iron, pieces in beaker X and some zinc pieces in, beaker Y. After about 10 hours, he observed that, the solution in X and Y respectively appears:, (a) Blue and green, , 10. (i) Write the steps involved in the extraction of, pure metals in the middle of the activity, series from their carbonate ores., (ii) How is copper extracted from its sulphide, ore? Explain the various steps supported by, chemical equations. Draw labelled diagram, for the electrolytic refining of copper., , 11. (i) List in tabular form three chemical properties, on the basis of which we can differentiate, between a metal and a non-metal., , (c) Colourless and light blue, (d) Greenish and colourless, [2012] ...[1M], (a) What are amphoteric oxides? Choose the, amphoteric oxides from amongst the, following oxides :, Na2O, ZnO, Al2O3, CO2, H2O, , 9., , [2018] ...[5M], , (b) Colourless and pale green, , 5., , [2010] ...[5M], What is meant by refining of metals? Name the, most widely used method of refining impure, metals produced by various reduction processes., Describe with the help of a labelled diagram how, this method may be used for refining of copper., , (a) Pale green and light blue respectively, , 4., , Write the name and symbols of two most reactive, metals belonging to group-I of the periodic table., Explain by drawing electronic structure how, either one of the two metals reacts with a, halogen. With which name is the bond formed, between these elements known and what is the, class of the compound so formed known? State, any four physical properties of such compounds., , (ii) Give reasons for the following :, (a) Most metals conduct electricity well., (b) The reaction of iron (III) oxide [Fe2O3], with heated aluminium is used to join, cracked machine parts. [2019] ...[5M], , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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4, , Science, , Chapter-wise Previous Years' Questions (Class-10), , Chapter - 4 : Carbons and its Compounds, 1., , State two characteristic features of carbon which, when put together give rise to large number of, carbon compounds., [2010] ...[1M], , 2., , Draw the structure of Butanone molecule,, CH3COC2H5, [2011] ...[1M], , 3., , A student added acetic acid to test tubes I, II, III, and IV containing the labelled substances and, then brought a burning splinter near the mouth of, each test tube., , 7., , Hard water required for an experiment is not, available in a school laboratory. However,, following salts are available in the laboratory., Select the salts which may be dissolved in water, to make it hard for the experiment., 1. Calcium Sulphate, 2. Sodium Sulphate, 3. Calcium Chloride, 4. Potassium Sulphate, 5. Sodium Hydrogen Carbonate, 6. Magnesium Chloride, (a) 1, 2 and 4, (b) 1, 3 and 6, , I, , II, , III, , IV, , NaOH, , NaCl, , NaHCO 3, , Ca(OH)2, , The splinter would be extinguished when brought, near the mouth of test tube., , 4., , (c) 3, 5 and 6, (d) 2, 4 and 5, , [2011] ...[1M], , A student takes 2 ml acetic acid in a dry test, tube and adds a pinch of sodium hydrogen, carbonate to it. He makes the following, observations:, , Acetic acid reacts with solid sodium hydrogen, carbonate,, , (I) A colourless and odourless gas evolves with, a brisk effervescence., , (a) Slowly forming no gas, , (II) The gas turns lime water milky when passed, through it., , (a) I, , (b) II, , (c) III, , (d) IV, , 8., , (b) Vigorously with effervescence, , (III) The gas burns with an explosion when a, burning splinter is brought near it., , (c) Slowly without effervescence, (d) Vigorously without gas formation, , (IV) The gas extinguishes the burning splinter, which is brought near it., , [2011] ...[1M], 5., , Vapours of acetic acid smell:, , The correct observations are :, , (a) Pungent like vinegar, , (a) (I), (II) and (III), , (b) Sweet like rose, , (b) (II), (III) and (IV), (c) (III), (IV) and (I), , (c) Suffocating like sulphur dioxide, , (d) (IV), (I) and (II), , (d) Odorless like water, [2011] ...[1M], 6., , [2013] ...[1M], , A student takes Na2CO3 powder in a test tube, and pours some drops of acetic acid in it., He observes:, (a) No reaction in the test tube, , 9., , [2013] ...[1M], , In an experiment to study the properties of, ethanoic acid, a student takes about 3 mL of, ethanoic acid in a dry test tube. He adds an, equal amount of distilled water to it and shakes, the test tube well. After some time he is likely, to observe that, (A) a colloid is formed in the test tube, , (b) Colourless gas with pungent smell, , (B) the ethanoic acid dissolves readily in water, , (c) Bubbles of a colourless and odourless gas, , (C) the solution becomes light orange, , (d) White fumes with smell of vinegar, , (D) water floats over the surface of ethanoic acid, , [2012] ...[1M], , [2014] ...[1M], , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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Chapter-wise Previous Years' Questions (Class-10), , 10. We need 20% aqueous solution of sodium, hydroxide for the study of saponification reaction., When we open the lid of the bottle containing solid, sodium hydroxide we observe it in which form?, (A) Colourless transparent beads, , Science, , 5, , 14. While preparing soap a small quantity of, common salt is generally added to the reaction, mixture of vegetable oil and sodium hydroxide., Which one of the following may be the purpose, of adding common salt?, (A) To reduce the basic nature of the soap, , (B) Small white beads, , (B) To make the soap neutral, , (C) White pellets/flakes, , (C) To enhance the cleansing power of the soap, , (D) Fine white powder, , (D) To favour the precipitation of the soap, [2014] ...[1M], , [2015] ...[1M], , 11. While studying saponification reaction, a student, measures the temperature of the reaction, mixture and also finds its nature using blue/red, litmus paper. On the basis of his observations the, correct conclusion would be, , 15. A student takes about 4 ml of distilled water in, four test tubes marked P, Q, R and S. He then, dissolves in each test tube an equal amount of, one salt in one test tube, namely sodium, sulphate in P, potassium sulphate in Q, calcium, sulphate in R and magnesium sulphate in S., After that he adds an equal amount of soap, solution in each test tube. On shaking each of, these test tubes well, he observes a good, amount of lather (foam) in the test tube marked., , (A) the reaction is exothermic and the reaction, mixture is acidic, (B) the reaction is endothermic and the reaction, mixture is acidic, (C) the reaction is endothermic and the reaction, mixture is basic, , (A) P and Q, , (D) the reaction is exothermic and the reaction, mixture is basic, , (C) P, Q and S, , [2014] ...[1M], 12. In a locality, hard water, required for an, experiment, is not available. However, the, following salts are available in the school, laboratory :, , (D) P, R and S, , [2015] ...[1M], , 16. When you add sodium hydrogen carbonate to, acetic acid in a test tube, a gas liberates, immediately with brisk effervescence. Name this, gas. Describe the method of testing this gas., [2015] ...[1M], 17. Write the name and structure of an aldehyde with, four carbon atoms in its molecule. [2016] ...[1M], , 1. Sodium sulphate, 2. Calcium sulphate, , 18. Write the molecular formula of the 2nd and 3rd, member of the homologous series where the first, member is ethyne., [2017] ...[1M], , 3. Magnesium chloride, 4. Sodium chloride, 5. Calcium chloride, 6. Potassium sulphate, Which of the above salts may be dissolved in, water to obtain hard water for the experiment?, (A) 2, 3 and 5, (B) 1, 2 and 5, , 19. A student requires hard water for an experiment, in his laboratory which is not available in the, neighbouring area. In the laboratory there are, some salts, which when dissolved in distilled, water can convert it into hard water. Select from, the following groups of salts, a group, each salt, of which when dissolved in distilled water will, make it hard., (A) Sodium chloride, Potassium chloride, , (C) 1, 2, 4 and 6, (D) 3 and 5 only, , (B) Q and R, , (B) Sodium sulphate, Potassium sulphate, [2014] ...[1M], , (C) Sodium sulphate, Calcium sulphate, , 13. Write the number of covalent bonds in the, molecule of butane, C4H10., [2015] ...[1M], , (D) Calcium sulphate, Calcium chloride, [2017] ...[1M], , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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6, , Science, , Chapter-wise Previous Years' Questions (Class-10), , 20. Write the name and general formula of a chain, of hydrocarbons in which an addition reaction, with hydrogen is possible. State the essential, condition for an addition reaction. Stating this, condition, write a chemical equation giving the, name of the reactant and the product of the, reaction., [2015] ...[2M], 21. A student adds a spoon full of powdered sodium, hydrogen carbonate to a flask containing ethanoic, acid. List two main observations, he must note, in his note book, about the reaction that takes, place. Also write chemical equation for the, reaction., [2016] ...[2M], 22. Mention the essential material (chemicals) to, prepare soap in the laboratory. Describe in brief, the test of determining the nature (acidic/alkaline), of the reaction mixture of saponification reaction., [2017] ...[2M], 23. A compound 'X' on heating with excess conc., sulphuric acid at 443 K gives an unsaturated, compound 'Y'. 'X' also reacts with sodium metal, to evolve a colourless gas 'Z'. Identify 'X', 'Y' and, 'Z'. Write the equation of the chemical reaction of, formation of 'Y' and also write the role of, sulphuric acid in the reaction., [2018] ...[2M], 24. In three test tubes A, B and C, three different, liquids namely, distilled water, underground water, and distilled water in which a pinch of calcium, sulphate is dissolved, respectively are taken., Equal amount of soap solution is added to each, test tube and the contents are shaken. In which, test tube will the length of the foam (lather) be, longest? Justify your answer., [2019] ...[2M], 25. (i) Why are covalent compounds generally poor, conductors of electricity?, (ii) Name the following compound:, H, , H, , H—C—C—C—H, H, , O, , H, , (iii) Name the gas evolved when ethanoic acid is, added to sodium carbonate. How would you, prove the presence of this gas?, [2008] ...[3M], , 26. Give reasons for the following observations :, (i) The element carbon forms a very large, number of compounds., (ii) Air holes of a gas burner have to be adjusted, when the heated vessels get blackened by, the flame., (iii) Use of synthetic detergents causes pollution, of water., [2009] ...[3M], 27. Name the functional group of organic compounds, that can be hydrogenated. With the help of, suitable example, explain the process of, hydrogenation mentioning the conditions of the, reaction any one change in physical property, with the formation of the product. Name any one, natural source of organic compounds that are, hydrogenated., [2010] ...[3M], 28. Write chemical equations to show what happens, when:, (i) Ethanol is heated with concentrated, sulphuric acid at 443 K., (ii) Ethanol reacts with ethanoic acid in the, presence of an acid acting as a catalyst., (iii) An ester reacts with a base, , [2011] ...[3M], , 29. Complete the following equations:, (i) CH4 + O2 , Hot conc. H SO, , 2, 4, , (ii) C2H5 OH , , (iii) CH3COOH + NaOH , , [2012] ...[3M], , 30. Name the oxidising agent used for the conversion, of ethanol to ethanoic acid. Distinguish between, ethanol and ethanoic acid on the basis of, (i) Litmus test, (ii) Reaction with sodium carbonate [2013] ...[3M], 31. (i) Differentiate between alkanes and alkenes., Name and draw the structure of one member, of each., (ii) Alkanes generally burn with clean flame., Why?, [2013] ...[3M], 32. A carboxylic acid (molecular formula C2H4O2), reacts with an alcohol in the presence of an acid, catalyst to form a compound 'X'. The alcohol on, oxidation with alkaline KMnO 4 followed by, acidification gives the same carboxylic acid, C2H4O2., Write the name and structure of, (i) carboxylic acid,, (ii) alcohol and, (iii) the compound 'X'., , [2014] ...[3M], , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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Chapter-wise Previous Years' Questions (Class-10), , 33. Define the term 'structural' isomerism'. Explain, why propane cannot exhibit this property. Draw, the structures of possible isomers of butane,, C4H10, [2014] ...[3M], 34. List two tests for experimentally distinguishing, between an alcohol and a carboxylic acid and, describe how these tests are performed., [2015] ...[3M], 35. Write three different chemical reactions showing, the conversion of ethanoic acid to sodium, ethanoate. Write balanced chemical equation in, each case. Write the name of the reactants and, the products other than ethanoic acid and, sodium ethanoate in each case. [2016] ...[3M], 36. Distinguish between esterification and, saponification reactions with the help of the, chemical equations for each. State one use of, each (i) Esters, and (ii) Saponification process., [2017] ...[3M], 37. Write the structural formula of ethanol. What, happens when it is heated with excess of conc., H2SO4 at 443 K? Write the chemical equation for, the reaction stating the role of conc. H2SO4 in, this reaction., [2017] ...[3M], 38. (i) Why are most carbon compounds poor, conductors of electricity?, (ii) Write the name and structure of a saturated, compound in which the carbon atoms are, arranged in a ring. Give the number of single, bonds present in this compound., [2018] ...[3M], 39. (i) State two properties of carbon which lead to, a very large number of carbon compounds., (ii) Why does micelle formation take place when, soap is added to water? Why are micelles, not formed when soap is added to ethanol?, , Science, , 7, , 42. (i) Define the term 'isomers', (ii) Draw two possible isomers of the compound, with molecular formula C3H6O and write their, names., (iii) Give the electron dot structures of the above, two compounds, [2013] ...[5M], 43. Both soap and detergent are some type of salts., What is the difference between them? Describe, in brief the cleansing action of soap. Why do, soaps not form lather in hard water? List two, problems that arise due to the use of detergents, instead of soaps., [2015] ...[5M], 44. A carbon compound 'P' on heating with excess, conc. H2SO4 forms another carbon compound, 'Q' which on addition of hydrogen in the, presence of nickel catalyst forms a saturated, carbon compound 'R'. One molecule of 'R' on, combustion forms two molecules of carbon, dioxide and three molecules of water. Identify P,, Q and R and write chemical equations for the, reactions involved., [2016] ...[5M], 45. Why certain compounds are called, hydrocarbons? Write the general formula for, homologous series of alkanes, alkenes and, alkynes and also draw the structure of the first, member of each series. Write the name of the, reaction that converts alkenes into alkanes and, also write a chemical equation to show the, necessary conditions for the reaction to occur., [2017] ...[5M], 46. Write the chemical formula and name of the, compound which is the active ingredient of all, alcoholic drinks. List its two uses. Write, chemical equation and name of the product, formed when this compound reacts with, (i) Sodium metal, (ii) Hot concentrated sulphuric acid [2019] ...[5M], , [2011] ...[5M], 40. Explain isomerism. State any four characteristics, of isomers. Draw the structures of possible, isomers of butane, C4H10., [2011] ...[5M], 41. List in tabular form three physical and two, chemical properties on the basis of which, ethanol and ethanoic acid can be differentiated., [2012] ...[5M], , 47. What is methane? Draw its electron dot structure., Name the type of bonds formed in this compound., Why are such compounds :, (i) Poor conductors of electricity? and, (ii) Have low melting and boiling points? What, happens when this compound burns in, oxygen?, [2019] ...[5M], , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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8, , Science, , Chapter-wise Previous Years' Questions (Class-10), , Chapter - 5 : Periodic Classification of Elements, 1., , 2., , 3., , How many horizontal rows are there in the, Modern Periodic Table and what are they called?, , Based on the above information answer the, following questions:, , [2013] ...[1M], , (i) To which group or period of the periodic, table, do the listed elements belong?, , The atomic numbers of three elements A, B and, C are 12, 18 and 20 respectively. State, giving, reason, which two elements will show similar, properties., [2014] ...[1M], The electronic configuration of an element is 2,, 8, 4. State its:, (i) group and period in the Modern Periodic, Table., (ii) name and write its one physical property., [2019]..[1M], , 4., , How does the metallic character of elements, change along a period of the periodic table from, the left to the right and why?, [2011] ...[2M], , 5., , 6., , In the Modern Periodic Table, the element, calcium (atomic number = 20) is surrounded by, elements with atomic numbers 12, 19, 21 and, 38. Which of these elements has physical and, chemical properties resembling those of calcium, and why?, [2011] ...[2M], An element 'M' has atomic number 12., (i) Write its electronic configuration., (ii) State the group to which 'M' belongs., (iv) Write the formula of its oxide., [2012] ...[2M], , 8., , 9., , (iii) Which two of these elements could definitely, be metals?, (iv) Which one of the eight elements is most, likely to be found in gaseous state at room, temperature?, (v) If the number of electrons in the outermost, shell of element C and G be 3 and 7, respectively, write the formula of the, compound formed by the combination of C, and G., [2010] ...[3M], 10. The atomic number of an element is 16. Predict, (i) the number of valence electrons in its atom, (ii) its valency, (iii) its group number, (iv) whether it is a metal or a non-metal, (v) the nature of oxide formed by it, (vi) the formula of its chloride, , (iii) Is 'M' a metal or a non-metal?, , 7., , (ii) What would be the nature of compound, formed by a combination of elements B and, F?, , How can the valency of an element be, determined if its electronic configuration is, known? What will be the valency of an element, of atomic number 9?, [2012] ...[2M], How it can be proved that the basic structure of, the Modern Periodic Table is based on the, electronic configuration of atoms of different, elements?, [2019] ...[2M], Atoms of eight elements A, B, C, D, E, F, G and, H have the same number of electronic shells but, different number of electrons in their outermost, shell. It was found that elements A and G, combine to form an ionic compound. This, compound is added in a small amount to almost, all vegetable dishes during cooking. Oxides of, elements A and B are basic in nature while those, of E and F are acidic. The oxide of D is almost, neutral., , [2011] ...[3M], , 11. F, Cl and Br are elements each having seven, valence electrons. Which of these:, (i) has the largest atomic radius, (ii) is most reactive?, Justify your answer stating reason for each., [2012] ...[3M], 12. Given below are some elements of the modern, periodic table:, 4Be, 9F, 14Si, 19K, 20Ca, , (i) Select the element that has one electron in, the outermost shell and write its electronic, configuration., (ii) Select two elements that belong to the same, group. Give reasons for your answer., (iii) Select two elements that belong to the same, period. Which one of the two has bigger, atomic size?, [2013] ...[3M], , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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Chapter-wise Previous Years' Questions (Class-10), , Science, , 13. An element X (atomic number 17) reacts with an, element Y (atomic number 20) to form a compound., (i) Write the position of these elements in the, modern periodic table., (ii) Write the formula of the compound formed., Justify your answer in each case., [2013] ...[3M], 14. Study the following table in which positions of six, elements A, B, C, D, E, and F are shown as, they are in the Modern Periodic Table :, Group, , 1, , 2 3-12 13, , 14, , 15, , 16, , 17, , 18, , Period, 2, 3, , A, , C, , B, D, , E, , 9, , (ii) Which two elements amongst these belong, to the same group? Give reasons for your, answer., (iii) Which two elements amongst these belong, to the same period? Which one of the two, has bigger atomic radius?, [2015] ...[3M], 17. Taking the example of an element of atomic, number 16, explain how the electronic, configuration of the atom of an element relates to, its position in the Modern Periodic Table and how, valency of an element is calculated on the basis, of its atomic number., [2015] ...[3M], 18. The position of eight elements in the Modern, Periodic Table is given below where atomic, numbers of elements are given in the, parenthesis., , F, , On the basis of the above table, answer the, following questions:, (i) Name the element which forms only covalent, compounds., , Period No., 2, 3, 4, 5, , Li(3), Na(11), K(19), Rb(37), , Be(4), Mg(12), Ca(20), Sr(38), , (ii) Name the element which is a metal with, valency three., , (i) Write the electronic configuration of Ca., , (iii) Name the element which is a non-metal with, valency three., , (ii) Predict the number of valence electrons in, Rb., , (iv) Out of D and E, which is bigger in size and, why?, , (iii) What is the number of shells in Sr?, , (v) Write the common name for the family to, which the elements C and F belong., , (v) Which one of these elements has the largest, atom in size?, , [2014] ...[3M], , (vi) Arrange Be, Ca, Mg and Rb in the, increasing order of the size of their respective, atoms., [2016] ...[3M], , 15. The elements Be, Mg and Ca each having two, electrons in their outermost shells are in periods, 2, 3, and 4 respectively of the modern periodic, table. Answer the following questions, giving, justification in each case:, (i) Write the group to which these elements, belong., (ii) Name the least reactive element., (iii) Which of these elements has the largest, atomic radius., [2014] ...[3M], 16. Given below are some elements of the Modern, Periodic Table. Atomic number of the element is, given in parentheses., A (4), B (9), C (14), D (19), E (20), (i) Select the element that has one electron in, the outermost shell. Also, write the electronic, configuration of this element., , (iv) Predict whether K is a metal or a non-metal., , 19. An element 'X' belong to 3rd period and group 13, of the Modern Periodic Table., (i) Determine the valence electrons and the, valency of 'X'., (ii) Molecular formula of the compound formed, when 'X' reacts with an element 'Y' (atomic, number = 8)., (iii) Write the name and formula of the compound, formed when 'X' combines with chlorine., [2016] ...[3M], 20. An element 'X' has mass number 35 and number, of neutrons 18. Write atomic number and, electronic configuration of 'X'. Also write group, number, period number and valency of 'X'., [2016] ...[3M], , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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10, , Science, , Chapter-wise Previous Years' Questions (Class-10), , 21. What is periodicity in properties of elements with, reference to the Modern Periodic Table? Why do, all the elements of the same group have similar, properties? How does the tendency of elements, to gain electrons change as we move from left, to right in a period? State the reason of this, change?, [2017] ...[3M], 22. Based on the group valency of elements write the, molecular formula of the following compounds, giving justification for each :, (i) Oxide of first group elements., (ii) Halide of the elements of group thirteen, and, (iii) Compound formed when an element, A of, group 2 combines with an element, B of, group seventeen., [2019] ...[3M], 23. On the basis of Mendeleev's Periodic Table given, below, answer the questions that follow the, table :, Group, , Oxide, Hydride, , I, , II, , III, , IV, , V, , IV, , VII, , VIII, , R2 O, RH, , RO, RH 2, , R2O3, RH3, , RO2, RH4, , R 2O 5, RH3, , RO3, RH 2, , R 2O 7, RH, , RO4, , Group A, , , BA, , BA, , BA, , BA, , BA, , BA, , B, , 1, , H, 1.008, , 2, , Li, Be, B, C, N, O, F, 6.939 9.012 10.81 12.011 14.007 15.999 18.998, , 3, , Na, 22.99, , Second, series:, 6 First, series:, , [2008] ...[5M], 24. (i) Why do we classify elements?, (ii) What were the two criteria used by, Mendeleev in creating his Periodic Table?, (iii) Why did Mendeleev leave some gaps in his, Periodic Table?, (iv) In Mendeleev's Periodic Table, why was there, no mention of Noble gases like Helium, Neon, and Argon?, (v) Would you place the two isotopes of, chlorine, Cl-35 and Cl-37 in different slots, because of their different atomic masses or, in the same slot because their chemical, properties are the same? Justify your, answer., [2008] ...[5M], 25. (i) Which two criteria did Mendeleev use to, classify the elements in his periodic table?, (ii) State Mendeleev's periodic law., (iii) Why could no fixed position be given to, hydrogen in Mendeleev's periodic table?, , Mg, Al, Si, P, S, Cl, 24.31 29.98 28.09 30.974 32.06 35.453, , 4 First K, Ca, Sc, series: 39.102 40.08 44.96, Second Cu, series: 63.54, 5 First Rb, series: 85. 47, , Transition, series, , (v) Using atomic masses of Li, Na and K, find, the average atomic mass of Li and K and, compare it with the atomic mass of Na., State the conclusion drawn from this activity., , Zn, 65.37, Sr, 87.62, , Ti, V, Cr, Mn, 47.90 50.94 52.20 54.94, , Ga, Ge, 65.37 72.59, Y, Zr, 44.96 91.22, , As, 74.92, Nb, 50.94, , Se, 78.96, Mo, 52.20, , Fe, Co, Ni, 55.85 58.93 58.71, , Br, 79.909, Tc, Ru, Rh, Pd, 54.94, 101.07 102.91 106.4, , I, Te, Ag, Cd, In, Sn, Sb, 107.87 112.40 114.82 118.69 74.92 78.96 79.909, Cs, Ba, La, Hf, Ta, W, 132.90 137.34 138.91 178.49 180.95 183.85, , Os, 190.2, , Ir, 192.2, , Pt, 195.09, , Second Au, Hg, Tl, Pb, Bi, series: 196.97 200.59 201.37 207.19 208.98, , (i) Name the element which is in, (a) 1st group and 3rd period., (b) 7th group and 2nd period., (ii) Suggest the formula for the following, (a) Oxide of nitrogen, (b) Hydride of oxygen, (iii) In group VIII of the Periodic Table, why does, cobalt with atomic mass 58.93 appear before, nickel having atomic mass 58.71?, (iv) Besides gallium, which two other elements, have since been discovered for which, Mendeleev had left gaps in his Periodic, Table?, , (iv) How and why does the atomic size vary as, you go:, (a) From left to right along a period?, (b) Down a group?, , [2009] ...[5M], , 26. (i) Why did Mendeleev leave gaps in his, periodic table?, (ii) State any three limitations of Mendeleev's, classification., (iii) How do electronic configuration of atoms, change in a period with increase in atomic, number?, [2009] ...[5M], 27. (i) The Modern Periodic Table has been evolved, through the early attempts of Dobereiner,, Newland and Mendeleev. List one advantage, and one limitation of all the three attempts., (ii) Name the scientist who first of all showed, that atomic number of an element is a more, fundamental property than its atomic mass., (iii) State Modern Periodic law., , [2018] ...[5M], , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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BIOLOGY, Chapter - 6 : Life Processes, 1., , How do autotrophs obtain CO2 and N2 to make, their food?, [2008] ...[1M], , 2., , What will happen to a plant if its xylem is, removed?, [2009] ...[1M], , 3., , Name the green dot like structures in some cells, observed by a student when a leaf peel was, viewed under a microscope. What is this green, colour due to?, [2010] ...[1M], , 10. (a) Draw a diagram of excretory system in, human beings and label on it:, Aorta, vena cava, urinary bladder, urethra, (b) List two vital functions of the kidney., , 4., , Write one function each of the following, components of the transport system in human, beings:, (a) Blood vessels, (b) Blood platelets, , 5., , 6., , 7., , 11. Explain the process of digestion of food in, mouth, stomach and small intestine in human, body., [2010] ...[5M], 12. (a) List the three events that occur during the, process of photosynthesis. Explain the role, of stomata in this process., (b) Describe an experiment to show that, "sunlight is essential for photosynthesis.", , (c) Lymph, (d) Heart, , [2009] ...[5M], , [2010] ...[5M], , [2008] ...[2M], , Write two different ways in which glucose is, oxidized to provide energy in human body. Write, the products formed in each case. [2019]...[2M], In the experimental set up to show that "CO2 is, given out during respiration", name the, substance taken in the small test tube kept in, the conical flask. State its function and the, consequence of its use., [2019] ...[2M], How are oxygen and carbon dioxide transported, in human beings? How are lungs designed to, maximize the area for exchange of gases?, [2008] ...[3M], , 8., , Write three types of blood vessels. Give one, important feature of each., [2019] ...[3M], , 9., , (a) Draw a diagram of human alimentary canal, and label on it :, Oesophagus, Gall bladder, Liver and, Pancreas, (b) Explain the statement, 'Bile does not, contain any enzyme but it is essential for, digestion'., [2009] ...[5M], , 13. (a) Mention any two components of blood., (b) Trace the movement of oxygenated blood in, the body., (c) Write the function of valves present in, between atria and ventricles., (d) Write one structural difference between the, composition of artery and veins. [2018]...[5M], 14. (a) Define excretion., (b) Name the basic filtration unit present in the, kidney., (c) Draw excretory system in human beings, and label the following organs of excretory, system which perform following functions:, (i) Form urine, (ii) Is a long tube which collects urine from, kidney, (iii) Store urine until it is passed out., [2018] ...[5M], , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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12, , Science, , Chapter-wise Previous Years' Questions (Class-10), , Chapter - 7 : Control and Coordination, 7., , What are plant hormones? Name the plant, hormones responsible for the following ?, , 1., , Name two tissues that provide control and, coordination in multicellular animals.[2009]...[1M], , 2., , How is the spinal cord protected in the human, body?, [2010] ...[1M], , (i) Growth of stem, , What are 'nastic' and 'curvature' movements?, Give one example of each., [2009] ...[2M], , (iii) Inhibition of growth, , 3., 4., , What are hormones? Name the hormone, secreted by thyroid gland and state its function?, , (ii) Promotion of cell division, (iv) Elongation of cells, 8., , [2010] ...[2M], 5., , (b) Name the part of neuron:, (i) Where information is acquired., (ii) Through which information travels as an, electrical impulse., [2008] ...[5M], 9., , (a) What is, (i) Phototropism and, , Dendrite  a  b  End point of Neuron, , (ii) Geotropism?, , [2018] ...[2M], 6., , (a) Draw the structure of a neuron and label the, following on it :, Nucleus, Dendrite, Cell body and Axon, , (a) Name one gustatory receptor and one, olfactory receptor present in human beings., (b) Write a and b in the given flow chart of, neuron through which information travels as, an electrical impulse., , [2019] ...[3M], , With labelled diagrams describe an activity to, show that light and gravity change the direction, that plant parts grow in., , Name the hormones secreted by the following, endocrine glands and specify one function of, each:, , (b) Mention the role of each of the following, plant hormones:, , (a) Thyroid, (b) Pituitary, , (i) Auxin, , (c) Pancreas, , [2018] ...[3M], , (ii) Abscisic acid, , [2008] ...[5M], , Chapter - 8 : How do Organisms Reproduce?, 1., , What is the effect of DNA copying which is not, , The correct observation(s) is/are:, , perfectly accurate on the reproduction process?, , (a) d, a and c, , (b) c and d, , (c) b only, , (d) a and c, , [2008] ...[1M], , [2012] ...[1M], 2., , After observing the prepared slides of binary, fission in Amoeba and budding in yeast, the, following observations were reported :, a. Single cells of Amoeba and Yeast were, undergoing binary fission and budding, respectively., , 3., , A student after observing a slide showing, different stages of binary fission in Amoeba, draws the following diagrams. However these, diagrams are not in proper sequence., , (I), , (II), , (III), , b. Cytokinesis was observed in the Yeast cell., , The correct sequence is:, , c. Elongated nucleus was dividing to form two, daughter nuclei in Amoeba., , (a) I, V, IV, III, II, , d. A chain of buds were observed due to, , (c) I, III, IV, V, II, , reproduction in Amoeba., , (IV), , (V), , (b) I, V, III, IV, II, , (d) None of these, , [2011, 2013] ...[1M], , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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Chapter-wise Previous Years' Questions (Class-10), , 4., , Science, , In the figure, the parts marked A, B and C are, sequentially, A, , 13, , 6., , Name two simple organisms having the ability of, regeneration., [2015] ...[1M], , 7., , Students were asked to observe the permanent, slides showing different stages of budding in, yeast under high power of a microscope., [2015] ...[1M], (a) Which adjustment screw (coarse/fine) were, you asked to move to focus the slides?, , C, , B, (a) Plumule, Cotyledon and Radicle, , (b) Draw three diagrams in correct sequence, showing budding in yeast., 8., , (b) Radicle, Cotyledon and Plumule, (c) Radicle, Plumule and Cotyledon, (d) Plumule, Radicle and Cotyledon, [2013, 2014] ...[1], 5., , Select the correct statements for the process of, budding in yeast:, , A student was asked to observe and identify the, various parts of an embryo of a red kidney bean, seed. He identified the parts and listed them as, under :, I., , Tegmen, , II., , Testa, , III. Cotyledon, IV. Radicle, , I., , A bud arises from a particular region on a, parent body., , V. Plumule, , II., , A parent cell divides into two daughter cells;, here the parental identity is lost., , (A) I, II and III, , (B) II, III and IV, , (C) III, IV and V, , (D) I, III, IV and V, , III. Before detaching from the parent body a, bud may form another bud., IV. A bud when detached from the parent body, grows into a new individual., (a) II, III and IV, (b) I, II and III, , [2015] ...[1M], , The correctly identified parts among these are :, , 9., , List two functions of ovary of human female, reproductive system., [2016] ...[1M], , 10. A student while observing an embryo of a pea, seed in the laboratory listed various parts of the, embryo as given below:, Testa, Tegmen, Radicle, Plumule, Micropyle,, Cotyledon., , (c) III, IV and I, (d) None of the above, , [2013] ...[1], , OR, , On examining the list the teacher remarked that, only three parts are correct., , When you study a slide showing different stages, of budding in yeast, you observe the following, stages:, , Select three correct parts from the above list:, , I., , The bud may get separated from the parent, body and develop into a new individual., , (c) Cotyledon, Plumule, Testa, , II., , The body of the bud develops and gives rise, to another baby bud., , III. A bud comes out in any direction from the, body of the parent cell., , (a) Testa, Radicle, Cotyledon, (b) Tegmen, Radicle, Micropyle, (d) Radicle, Cotyledon, Plumule [2016] ...[1M], 11. With the help of diagrams show the different, stages of binary fission in Amoeba., [2010, 2017, 2018] ...[2M], , The proper sequence of the above stages is, , 12. List any four reasons for vegetative propagation, being practised in the growth of some type of, plants., [2011] ...[2M], , (A) II, I, III, IV, , 13. State the role of, , IV. Thus they may form a colony., , (B) II, III, I, IV, , i., , Seminal vesicle, , (C) III, II, l, IV, , ii., , Prostate gland in the human body., , (D) III, I, II, IV, , [2014] ...[1], , [2011] ...[2M], , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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14, , Science, , 14. Define the term puberty. List two changes, observed in girls at the time of puberty., [2012] ...[2M], 15. What is meant by asexual reproduction? List, any two of its different forms., [2012] ...[2], 16. A student is observing a permanent slide, showing sequentially the different stages of, asexual reproduction taking place in yeast., Name this process and draw diagrams, of what, he observes, in a proper sequence., [2012, 2016] ...[2M], 17. Mention two functions of the human testis., [2013] ...[2M], 18. Draw labelled diagrams to illustrate budding in, Hydra., [2014] ...[2M], OR, Draw a labelled diagram in proper sequence to, show budding in Hydra., [2019] ...[2M], 19. (a) Explain the terms :, (i) Implantation, (ii) Placenta, (b) What is the average duration of human, pregnancy?, [2009] ...[3M], 20. Write the full form of DNA. Name the part of the, cell where it is located. Explain its role in the, process of reproduction of the cell.[2010]...[3M], 21. What does HIV stand for? Is AIDS an infectious, disease? List any four modes of spreading AIDS., [2011] ...[3M], 22. Explain the meaning of sexually transmitted, diseases (STD's). Give two examples of STD's, each, caused due to, i. bacterial infection, ii. viral infection., State in brief how the spread of such, diseases may be prevented., [2008, 2012, 2013] ...[3M], 23. (a) Explain the process of regeneration in, Planaria., (b) How is regeneration different from, reproduction?, [2013] ...[3M], 24. Write one difference between asexual and sexual, mode of reproduction. Which species is likely to, have better chances of survival - the one, reproducing asexually or the one reproducing, sexually? Justify your answer., [2014] ...[3M], 25. What is the effect of DNA copying, which is not, perfectly accurate, on the reproduction process?, How does the amount of DNA remain constant, though each new generation is a combination of, DNA copies of two individuals?, [2014, 2018] ...[3M], , Chapter-wise Previous Years' Questions (Class-10), , 26. List any four methods of contraception used by, humans. State in brief two advantages of, adopting such preventive methods. [2015]...[3M], 27. (a) List two reasons for the appearance of, variations among the progeny formed by, sexual reproduction., (b), , A, B, , C, , D, , (i) Name the part marked 'A' in the, diagram., (ii) How does 'A'' reaches part 'B'?, (iii) State the importance of the part 'C', (iv) What happens to the part marked 'D', after fertilization is over? [2016] ...[3M], 28. Define reproduction. How does it help in, providing stability to the population of species?, [2016] ...[3M], 29. Explain the term "Regeneration" as used in, relation to reproduction of organisms. Describe, briefly how regeneration is carried out in, multicellular organisms like Hydra. [2016]...[3M], 30. List the two types of reproduction. Which one of, the two is responsible for bringing in more, variations in its progeny and how? [2017]...[3M], 31. List three techniques that have been developed, to prevent pregnancy. Which one of these, techniques is not meant for males? How does, the use of these techniques have a direct, impact on the health and prosperity of a family?, [2017] ...[3M], 32. What is vegetative propagation? State two, advantages and two disadvantages of this, method., [2017] ...[3M], 33. With the help of suitable diagrams, explain the, various steps of budding in Hydra., OR, What is binary fission in organisms? With the, help of suitable diagrams, describe the mode of, reproduction in Amoeba., [2011] ...[5M], 34. Define the terms pollination and fertilisation., Draw a diagram of a pistil showing pollen tube, growth into the ovule and label the following:, pollen grain, male gamete, female gamete and, ovary., , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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Chapter-wise Previous Years' Questions (Class-10), , OR, Describe in brief the role of :, (i) Testis, (ii) Seminal vesicle, (iii) Vas deferens,, (iv) Ureter, (v) Prostate gland in human male, reproductive system., [2012] ...[5M], 35. (a) Write the function of placenta in females., (b) List four ways of preventing pregnancy. State, two advantages of using such preventive, methods., [2013] ...[5M], 36. (a) Identify A, B and C in the given diagram and, write their functions., (b) Mention the role of gamete and zygote in, sexually reproducing organisms., [2013, 2015] ...[5M], A, , Science, , 15, , (b) What is pollination? State its significance., (c) How does fertilisation occur in flowers?, Name the parts of the flower that develop, into (i) seed, and (ii) fruit after fertilisation., [2014] ...[5M], 39. (a) Name the human male reproductive organ, that produces sperm and also secretes a, hormone. Write the functions of the secreted, hormone., (b) Name the parts of the human female, reproductive system where, (i) Fertilizations takes place, (ii) Implantation of the fertilized egg occurs., Explain how the embryo gets, nourishment inside the mother's body., , B, , [2015] ...[5M], 40. What is placenta? Describe its structure. State, its functions in case of a pregnant human, female., [2016] ...[5M], 41. (a) Write the functions of each of the following, parts in a human female reproductive, system:, , C, , 37. (a) Draw a sectional view of human female, reproductive system and label the part where, (i) eggs develop., (ii) fertilisation takes place., (iii) fertilised egg gets implanted., (b) Describe, in brief, the changes the uterus, undergoes, (i) to receive the zygote., (ii) if zygote is not formed., [2014] ...[5M], 38. (a) Name the parts labelled as A, B, C and D, in the diagram given below:, A, , (i) Ovary, (ii) Uterus, (iii) Fallopian tube, (b) Write the structure and functions of placenta, in a human female., [2017, 2018] ...[5M], 42. Define pollination. Explain the different types of, pollination. List two agents of pollination? How, does suitable pollination lead to fertilization?, [2019] ...[5M], OR, (a) Identify the given diagram. Name the parts, 1 to 5., , B, , 3, , 1, 2, , 4, C, D, , 5, , (b) What is contraception? List three, advantages of adopting contraceptive, measures., [2019] ...[5M], Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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16, , Science, , Chapter-wise Previous Years' Questions (Class-10), , Chapter - 9 : Heredity and Evolution, 1., , Study the different conclusions draw by students, of a class on the basis of observations of, preserved/available specimens of plants and, animals., I., II., , 4., , Potato and sweet potato are analogous, organs in plants and animals., , (A) Potato and sweet potato, , Wings of insects and wings of birds are, homologous organs in animals., , (B) Radish and carrot, (C) Okra and sweet potato, , III. Wings of insects and wings of bats are, analogous organs in animals., , (D) Potato and tomato, 5., , The correct conclusions are:, (A) I and II, , (a) Carrot and radish, , (B) II and IV, , (b) Potato and sweet potato, , (C) III and IV, (D) I and III, , (c) Potato and tomato, [2013] ...[1M], , Study the following statements:, , (d) Lady finger and potato, 6., , I., , Wings of birds and wings of bats are, homologous organs., , II., , Wings of birds and wings of insects are, modified forelimbs., , III. Wings of birds and wings of insects are, analogous organs., , The correct statements are, , (B) II and Ill, (C) III and IV, (D) I and IV, , [2014] ...[1M], , Which of the following pairs of two vegetables, represent the correct homologous structures?, (A) Sweet potato and potato, (B) Sweet potato and tomato, , What are fossils? What do they tell about the, process of evolution?, [2008] ...[2M], , 8., , Give one example each of characters that are, inherited and the ones that are acquired in, humans. Mention the difference between the, inherited and the acquired characters., [2010] ...[2M], A Mendelian experiment consisted of breeding, pea plants bearing violet flowers with pea plants, bearing white flowers. What will be the result in, F1 progeny?, [2018] ...[2M], , 10. Explain analogous organs and homologous, organs. Identify the analogous and homologous, organs amongst the following :, Wings of an insect, wings of a bat, forelimbs of, frog, forelimbs of a human, [2009] ...[3M], 11. Describe any three ways in which individuals, with a particular trait may increase in population., , (C) Carrot and potato, (D) Radish and carrot, , Why is variation important for a species?, , 7., , 9., , (A) I and II, , [2016] ...[1M], , [2017] ...[1M], , IV. Wings of birds and forelimbs of horse are, homologous organs., , 3., , [2015] ...[1M], , If you are asked to select a group of two, vegetables, out of the following, having, homologous structures which one would you, select?, , IV. Thorns of Citrus and tendrils of Cucurbita are, analogous organs in plants, , 2., , Given below is the list of vegetables available in, the market. Select from these the two vegetables, having homologous structures: Potato, sweet, potato, ginger, radish, tomato, carrot, okra, (Lady's finger)., , [2014] ...[1M], , [2011] ...[3M], , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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Chapter-wise Previous Years' Questions (Class-10), , 12. State the evidence we have for the origin of life, from inanimate matter., [2011] ...[3M], 13. Give an example of body characteristics used to, determine how close two species are in terms, of evolution and explain it., [2011] ...[3M], 14. Distinguish between homologous organs and, analogous organs. In which category would you, place wings of a bird and wings of bat? Justify, your answer giving a suitable reason., , Science, , 17, , 22. “Two areas of study namely ‘Evolution’ and, ‘Classification’ are inter-linked”. Justify this, statement., , [2016] ...[3M], , 23. How do Mendel's experiment show that traits are, inherited independently?, , [2016] ...[3M], , 24. How did Mendel's explain that it is possible that, a trait is inherited but not expressed in an, organism?, , [2017] ...[3M], , [2012] ...[3M], 15. Define the term 'evolution'. 'Evolution cannot be, equated with progress'. Justify this statement., , 25. What is an organic evolution? It cannot be, equated with progress. Explain with the help of, a suitable example., , [2017] ...[3M], , [2012] ...[3M], 16. A blue colour flower plant denoted by BB is, crossbred with a white colour flower plant, denoted by bb., , 26. Name the plant Mendel used for his experiment., , (a) State the colour of flower you expect in their, F1 generation plants., , tall and short plants? Write the ratio he obtained, , (b) What must be the percentage of white, flower plants in F2 generation if flowers of F1, plants are self-pollinated?, , 27. List two differences between acquired traits and, , (c) State the expected ratio of the genotypes, BB and Bb in the F2 progeny. [2012]...[3M], , [2019] ...[3M], , What type of progeny was obtained by Mendel, in F1 and F2 generations when he crossed the, in F2 generation plants., , [2019] ...[3M], , inherited traits by giving an example of each., , 28. 'The sex of a newborn child is a matter of, , 17. List three main factors responsible for the, speciation and briefly describe each one of, them., [2014] ...[3M], , chance and none of the parents may be, , 18. "A trait may be inherited, but may not be, expressed." Justify this statement with the help, of a suitable example., [2014] ...[3M], , determination of sex of a newborn. [2012]...[5M], , 19. What are chromosomes? Explain how in, sexually reproducing organisms the number of, chromosomes in the progeny is maintained., , considered responsible for it.' Justify this, statement with the help of flow chart showing, , 29. How do Mendel's experiments show that the, (a) Traits may be dominant or recessive, (b) Traits are inherited independently, , [2015] ...[3M], , [2015] ...[5M], , 20. Explain the following:, 30. Define evolution. How does it occur? Describe, , (a) Speciation, (b) Natural Selection, , how fossils provide us evidences in support of, [2015] ...[3M], , 21. Explain with an example for each, how the, following provides evidences in favour of evolution, in organisms:, , [2016] ...[5M], , 31. With the help of one example for each, distinguish, between the acquired traits and the inherited traits., Why are the traits/experiences acquired during, , (a) Homologous organs, , the entire lifetime of an individual not inherited in, , (b) Analogous organs, (c) Fossils, , evolution., , the next generation? Explain the reason of this, [2015] ...[3M], , fact with an example., , [2017] ...[5M], , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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PHYSICS, Chapter - 10 : Light : Reflection and Refraction, 1., , Draw the following diagram in your answer-book, and show the formation of image of the object,, AB with the help of suitable rays. [2008] ...[1M], , 7., , To find the focal length of a concave mirror, Sita, should choose which one of the following :, [2011] ...[1M], (a) A mirror holder and screen holder, (b) A screen holder and a scale, , A, C, , F, , (c) A mirror holder, a screen holder and a scale, , B, , (d) A screen, a mirror, holders for them and a, scale, 8., , 2., , Draw the given diagram in your answer book, and complete it for the path of ray of light, beyond the lens., [2009] ...[1M], , By using a convex lens, a student obtained a, sharp image of his classroom window grill on a, screen. In which direction should he move the, lens to focus a distant tree instead of the grill?, [2011, 2016, 2017] ...[1M], (a) Towards the screen, , O, 2F, , F, , F, , 3., , Why does a ray of light bend when it travels from, one medium into another?, [2009] ...[1M], , 4., , Explain why a ray of light passing through the, centre of curvature of a concave mirror gets, reflected along the same path., [2010] ...[1M], , 5., , What is the nature of the image formed by a, concave mirror if the magnification produced by, the mirror is +3?, [2010] ...[1M], , 6., , For a ray of light passing through a glass slab,, the lateral displacement was correctly measured, as :, [2011] ...[1M], B, , A, , (b) Away from the screen, , 2F, , (c) Very far away from the screen, (d) Behind the screen, 9., , To determine the focal length of a convex lens, by obtaining a sharp image of a distant object,, the following steps were suggested which are not, in proper sequence., [2011, 2012] ...[1M], I., , Hold the lens between the object and the, screen., , II., , Adjust the position of the lens to form a, sharp image., , III. Select a suitable distant object., IV. Measure the distance between the lens and, the screen., The correct sequence of steps to determine the, focal length of the lens is, , P, , R, , Q, C, , D, , (a) III, I, II, IV, , (b) III, I, IV, II, , (c) III, IV, II, I, , (d) I, II, III, IV, , 10. While tracing the path of a ray of light passing, through a rectangular glass slab a student, tabulated his observations as given below:, Sr., No., , i, , r, , e, , I, , 60°, , 40°, , 61°, , (b) PQ, , II, , 50°, , 36°, , 51°, , (c) CD, , III, , 40°, , 28°, , 39°, , (d) PR, , IV, , 30°, , 20°, , 31°, , (a) AB, , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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Chapter-wise Previous Years' Questions (Class-10), , Science, , The correct observation is [2012, 2013] ...[1M], (a) I, , (b) II, , (c) III, , (d) IV, , 19, , X, S, , 11. A student traces the path of a ray of white light, through a rectangular glass slab and marks the, angles of incidence (i), refraction (r) and, emergence (e) as shown., , 40 cm, , [2012, 2014] ...[1M], , (a) The device X is a convex lens of focal length, 20 cm, , i, , (b) The device X is a concave mirror of focal, length 40 cm, , r, , e, , Which angle or angles have not been marked, correctly?, (a) i only, , (b) i and r, , (c) r and e, , (d) i and e, , (c) The device X is a convex mirror of radius of, curvature 40 cm, (d) The device X is a convex lens of focal length, 40 cm., 15. Study the following ray diagrams : [2013] ...[1M], I., , 12. A student obtained a sharp image of the grills of, a window on a screen using a concave mirror., His teacher remarked that for getting better, results a well lit distance object (preferably the, Sun) should be focused on the screen. What, should be done for this purpose?, [2012, 2013] ...[1M], , F1, , F2, , F1, , F2, , II., , (a) Move the screen and the mirror towards the, object, (b) Move the screen and the mirror away from, the object, (c) Move the screen slightly away from the, mirror, , III., , (d) Move the mirror slightly towards the screen, 13. To determine focal length of a concave mirror a, student obtains the image of a well lit distant, object on a screen. To determine the focal, length of the given concave mirror he needs to, measure the distance between the [2012]...[1M], , F1, , F2, , F1, , F2, , IV., , (a) Cannot be determined, (b) Screen and the object, (c) Mirror and the object, (d) Mirror and the screen, 14. A student focussed the image of a distant object, using a device 'X' on a white screen 'S' as shown, in the figure. If the distance of the screen from, the device is 40 cm, select the correct, statement about the device., [2013, 2014, 2015, 2017] ...[1M], , The diagrams showing the correct path of the, ray after passing through the lens are :, (a) II and III only, , (b) I and II only, , (c) I, II and III, , (d) I, II and IV, , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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20, , Science, , Chapter-wise Previous Years' Questions (Class-10), , 16. Out of the five incident rays shown in the figure, find the three rays which are obeying the laws, of refraction and may be used for locating the, position of the image formed by a convex lens:, [2013, 2014] ...[1M], , (c) Is parallel to the refracted ray, , 2, , F2, , 3, , F1, , (a) Is parallel to the incident ray, (b) Perpendicular to the incident ray, , 1, , 2F1, , 18. In an experiment to trace the path of a ray of, light through a glass prism for different values of, angle of incidence a student would find that the, emergent ray :, [2013] ...[1M], , 2F2, , 4, 5, , (a) 1, 2 and 3, , (b) 2, 3 and 4, , (c) 3, 4 and 5, , (d) 1, 2 and 4, , 17. Select from the following the best set-up for, tracing the path of a ray of light through a, rectangular glass slab:, [2013] ...[1M], I., , (d) Bends at an angle to the direction of the, incident ray, 19. A student has obtained an image of a wellilluminated distant object on a screen to, determine the focal length, F 1 of the given, spherical mirror. The teacher then gave him, another mirror of focal length, F2 and asked him, to obtain a focussed image of the same object, on the same screen. The student found that in, order to focus the same object using the second, mirror, he has to move the mirror away from the, screen. From this observation, it may be, concluded that both the spherical mirrors given, to the student were (select the correct option), [2014] ...[1M], (A) Concave and F1 < F2, (B) Concave and F1 > F2, (C) Convex and F1 < F2, , II., , (D) Convex and F1 > F2, 20. A student is using a convex lens of focal length, 10 cm to study the image formation by a convex, lens for the various positions of the object. In, one of his observations, he may observe that, when the object is placed at a distance of 20 cm, from the lens, its image is formed at (select the, correct option), [2014] ...[1M], , III., , (A) 20 cm on the other side of the lens and is, of the same size, real and erect., (B) 40 cm on the other side of the lens and is, magnified, real and inverted., (C) 20 cm on the other side of the lens and is, of the same size, real and inverted., , IV., , (D) 20 cm on the other side of the lens and is, of the same size, virtual and erect., , (a) I, , (b) II, , (c) III, , (d) IV, , 21. Draw a ray diagram to show the path of the, reflected ray corresponding to an incident ray of, light parallel to the principal axis of a convex, mirror and show the angle of incidence and angle, of reflection on it., [2015] ...[1M], , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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Chapter-wise Previous Years' Questions (Class-10), , 22. A student traces the path of a ray of light, through a rectangular glass slab for the different, values of angle of incidence. He observes all, possible precautions at each step of the, experiment. At the end of the experiment, on, analyzing the measurements, which of the, following conclusions is he likely to draw?, [2015] ...[1M], (A) i = e < r, , (B) i – e < r, , (C) i > e > r, , (D) i = e > r, , 23. A student obtains a sharp image of the distant, window (W) of the school laboratory on the, screen (S) using the given concave mirror (M) to, determine its focal length. Which of the following, distances should he measure to get the focal, length of the mirror?, [2015] ...[1M], , Science, , 21, , (a) i is more than r, but nearly equal to e, (b) i is less than r, but nearly equal to e, (c) i is more than e, but nearly equal to r, (d) i is less than e, but nearly equal to r, 27. An object is placed at a distance of 15 cm from, a concave lens of focal length 30 cm. List four, characteristic (nature, position, etc.) of the, image formed by the lens., [2017] ...[1M], 28. Draw ray diagrams to represent the nature,, position and relative size of the image formed by, a convex lens for the object placed :, (a) at 2F1., (b) Between F1 and the optical centre O of lens., [2008] ...[2M], 29. What is the minimum number of rays required, for locating the image formed by a concave, mirror for an object? Draw a ray diagram to show, the formation of a virtual image by a concave, mirror., [2009] ...[2M], , (A) MW, , (B) MS, , (C) SW, , (D) MW – MS, , 24. A 4 cm tall object is placed on the principal axis, of a convex lens. The distance of the object, from the optical centre of the lens is 12 cm and, its sharp image is formed at a distance of 24 cm, from it on a screen on the other side of the, lens. If the object is now moved a little away, from the lens, in which way (towards the lens or, away from the lens) will he have to move the, screen to get a sharp image of the object on it, again?, How will the magnification of the image be, affected?, [2015] ...[1M], 25. To determine the approximate value of the focal, length of a given concave mirror, you focus the, image of a distant object formed by the mirror on, a screen. The image obtained on the screen, as, compared to the object is always.[2016] ...[1M], (A) Laterally inverted and diminished, (B) Inverted and diminished, (C) Erect and diminished, (D) Erect and highly diminished, 26. In your laboratory you trace the path of light, rays through a glass slab for different values of, angle of incidence (i) and in each case, measure the values of the corresponding angle, of refraction (r) and angle of emergence (e)., On the basis of your observations your correct, conclusion is, [2016] ...[1M], , 30. State any four characteristics of the image of the, objects formed by a plane mirror. [2011] ...[2M], 31. List four properties of the image formed by a, concave mirror when an object is placed, between the focus and pole of the mirror., [2012] ...[2M], 32. “A concave mirror of focal length 15 cm can form, a magnified, erect as well as inverted image of, an object placed in front of it.” Justify this, statement stating the position of the object with, respect to the pole of the mirror in both the, cases for obtaining the images. [2014] ...[2M], 33. An object of height 2.5 cm is placed at a, distance of 15 cm from the optical centre 'O' of, a convex lens of focal length 10 cm. Draw a ray, diagram to find the position and size of the, image formed. Mark optical 'O', principal focus F, and height of the image on the diagram., [2016, 2018] ...[2M], 34. The refractive indices of glass and water with, 3, 4, and, respectively. If, 2, 3, speed of light in glass 2 × 108 m/s, find the, speed of light in water., [2016] ...[2M], , respect to air are, , 35. If the image formed by a spherical mirror for all, positions of the object placed in front of it is, always erect and diminished, what type of mirror, is it? Draw a labelled ray diagram to support, your answer., [2018] ...[2M], , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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22, , Science, , Chapter-wise Previous Years' Questions (Class-10), , 36. List four precautions which a student should, observe while determining the focal length of a, given convex lens by obtaining image of a, distant object on a screen., [2019] ...[2M], 37. At what distance should an object be placed, from a convex lens of focal length 18 cm to, obtain an image at 24 cm from it on the other, side. What will be magnifications produced in, this case?, [2010] ...[3M], 38. An object is placed between infinity and the, pole of a convex mirror. Draw a ray diagram and, also state the position, the relative size and the, nature of the image formed., [2011] ...[3M], 39. What is the principle of reversibility of light?, Show that the incident ray of light is parallel to, the emergent ray of light when light falls, obliquely on a side of a rectangular glass slab., [2011, 2013] ...[3M], 40. State the type of mirror preferred as, [2012, 2013] ...[3M], (i) Rear view mirrors in vehicles, (ii) Shaving mirrors. Justify your answer giving, two reasons in each case, 41. The image of a candle flame placed at a, distance of 36 cm from a spherical lens is, formed on a screen placed at a distance of, 72 cm from the lens. Identify the type of lens, and calculate its focal length. If the height of the, flame is 2.5 cm, find the height of the image., , 44. An object of height 5 cm is placed perpendicular, to the principal axis of a concave lens of focal, length 10 cm. If the distance of the object from, the optical centre of the lens is 20 cm,, determine the position, nature and size of the, image formed using the lens formula., [2015] ...[3M], 45. The image formed by a spherical mirror is real,, inverted and is of magnification –2. If the image, is at a distance of 30 cm from the mirror, where, is the object placed? Find the focal length of the, mirror. List two characteristics of the image, formed if the object is moved 10 cm towards the, mirror., [2016] ...[3M], 46. “A lens can form a magnified erect image as well, as magnified inverted image of an object placed, in front of it”. State the nature of this lens and, draw ray diagrams to justify the above, statement. Mark the positions of O, F and 2F, in the diagram., [2017] ...[3M], 47. State the laws of refraction of light. Explain the, term 'absolute refractive of a medium' and write, an expression to relate it with the speed of light, in vacuum., [2018] ...[3M], 48. (a) Draw a ray diagram to show the formation of, image of an object placed between infinity, and the optical centre of a concave lens., (b) A concave lens of focal length 15 cm forms, an image 10 cm from the lens. Calculate, , [2012] ...[3M], , (i) The distance of the object from the lens., , 42. A student wants to project the image of a candle, flame on a screen 90 cm in front of a mirror by, keeping the flame at a distance of 15 cm from, its pole., [2014] ...[3M], , (ii) The magnification for the image formed., , (a) Suggest the type of mirror he should use, (b) Determine the linear magnification in this, case, (c) Find the distance between the object and its, image, (d) Draw ray diagram to show the image, formation in this case, 43. Draw a ray diagram to show the path of the, refracted ray in each of the following cases :, A ray of light incident on a concave lens is, [2014] ...[3M], , (iii) The nature of the image formed., [2011] ...[5M], 49. List the sign conventions for reflection of light by, spherical mirrors. Draw a diagram and apply, these conventions in the determination of focal, length of a spherical mirror which forms a three, times magnified real image of an object placed, 16 cm in front of it., [2012] ...[5M], 50. (a) Explain the following terms related to, spherical lenses :, [2014] ...[5M], (i) Optical centre, (ii) Centres of curvature, (iii) Principal axis, , (i) Passing through its optical centre., , (iv) Aperture, , (ii) Parallel to its principal axis., , (v) Principal focus, , (iii) Directed towards its principal focus., , (vi) Focal length, , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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Chapter-wise Previous Years' Questions (Class-10), , (b) A converging lens has focal length of, 12 cm. Calculate at what distance the, object should be placed from the lens so, that it forms an image at 48 cm on the other, side of the lens?, , Science, , 23, , 55. Analyse the following observation table showing, variation of image distance (v) with object, distance (u) in case of convex lens and answer, the questions that follow without doing any, calculations:, , 51. What is meant by power of a lens? Define its SI, unit. You have two lenses A and B of focal, lengths +10 cm and –10 cm, respectively. State, the nature and power of each lens. Which of the, two lenses will form a virtual and magnified, image of an object placed 8 cm from the lens?, Draw a ray diagram to justify your answer., [2015, 2018] ...[5M], 52. One half of a convex lens of focal length 10 cm, is covered with a black paper. Can such a lens, produce an image of a complete object placed, at a distance of 30 cm from the lens? Draw a, ray diagram to justify your answer. A 4 cm tall, object is placed perpendicular to its principal, axis of a convex lens of focal length 20 cm. The, distance of the object from the lens is 15 cm., Find the nature, position and the size of the, image., [2015] ...[5M], 53. It is desired to obtain an erect image of an object,, using concave mirror of focal length of 12 cm., (i) What should be the range of distance an, object placed in front of the mirror?, (ii) Will the image be smaller or larger than the, object? Draw ray diagram to show the, formation of image in this case., , S.No, , Object Distance, u (cm), , Image Distance, v (cm), , 1, 2, 3, 4, 5, 6, , – 100, – 60, – 40, – 30, – 25, – 15, , + 25, + 30, + 40, + 60, + 100, + 120, , (a) What is the focal length of the convex lens?, Give reason to justify your answer., (b) Write the serial number of the observation, which is not correct. On what basis have, your arrived at this conclusion?, (c) Select an appropriate scale and draw a ray, diagram for the observation at S. No. 2., Also find the approximate value of, magnification., , [2017] ...[5M], , 56. (a) If the image formed by a mirror for all, position of the object placed in front of it is, always diminished erect and virtual. State, the type of the mirror and also draw a ray, diagram to justify your answer. Write one, use of such mirrors are put to and why., , (iii) Where will the image of this object be, if it, is placed 24 cm in front of the mirror? Draw, ray diagram for this situation also justify, your answer., , (b) Define the radius of curvature of spherical, mirrors. Find the nature and focal length of, , Show the positions of pole, principal focus and, the centre of curvature in the above ray, diagrams., [2016] ...[5M], , 57. An object is placed at a distance of 60 cm from, a concave lens of focal length 30 cm., , 54. (a) Define focal length of a divergent lens., (b) A divergent lens of focal length 30 cm forms, the image of an object of size 6 cm on the, same side as the object at a distance of 15, cm from its optical center. Use lens formula, to determine the distance of the object from, the lens and the size of the image formed., (c) Draw a ray diagram to show the formation of, image in the above situation. [2016] ...[5M], , a spherical mirror whose radius of curvature, is +24 cm., [2017] ...[5M], , [2019] ...[5M], (a) Use lens formula to find the distance of the, image from the lens., (b) List four characteristics of the image (nature,, position, size, erect/inverted) formed by the, lens in this case., (c) Draw ray diagram to justify your answer of, part (b)., , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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24, , Science, , Chapter-wise Previous Years' Questions (Class-10), , Chapter - 11 : Human Eye and Colourful World, 1., , Why does sky look blue on a clear day?, , 4., , [2009] ...[1M], 2., , In the following ray diagram the correctly marked, angles are:, [2016] ...[1M], , In the following diagram, the path of a ray of, light passing through a glass prism is shown:, , A, D, , [2014] ...[1M], i, , P, Y, , T, , e, , r, , Q, R, , X, , 5., , (A) i and e, , (B) A and D, , (C) i, e and D, , (D) r, A and D, , Study the following ray diagram:, , In this diagram the angle of incidence, the angle, of emergence and the angle of deviation, respectively are (select the correct option) :, , z, , (A) X, R and T, , y, , p, q, , (B) Y, Q and T, x, , (C) X, Q and P, (D) Y, Q and P, 3., , In this diagram, the angle of incidence, the, angle of emergence and the angle of deviation, respectively have been represented by, , Study the following diagrams in which the path, of a ray of light passing through a glass prism, as traced by four students P, Q, R and S is, shown:, [2014] ...[1M], , P, , Q, , [2017] ...[1M], (B) x, q, z, , (C) p, y, z, , (D) p, z, y, , The student who has traced the path correctly, is, , A student very cautiously traces the path of a, ray through a glass slab for different values of the, angle of incidence (i). He then measures the, corresponding values of the angle of refraction, (r) and the angle of emergence (e) for every, value of the angle of incidence. On analysing, these measurement of angles, his conclusion, would be., [2017] ...[1M], , (A) P, , (A) i > r > e, , (B) Q, , (B) i = e > r, , (C) R, , (C) i < r < e, , (D) S, , (D) i = e < r, , R, , S, , 6., , (A) y, p, z, , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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Chapter-wise Previous Years' Questions (Class-10), , 7., , Science, , A triangular glass prism. After passing through, the prism it produces a spectrum XY on a, screen., [2010] ...[2M], , 25, , 16. State the difference in colours of the Sun, observed during sunrise/sunset and noon. Give, explanation for each., [2013] ...[3M], OR, With the help of scattering of light, explain the, reason for the difference in colours of the Sun as, it appears during sunset/sunrise and noon., , Y, X, , [2015] ...[3M], (a) State the colour seen at X and Y., (b) Why do different colours of white light bend, through different angles with respect to the, incident beam of light?, 8., , 17. A narrow beam PQ of white light is passing, through a glass prism ABC as shown in the, diagram., [2014] ...[3M], A, , Explain with the help of a diagram, how we are, able to observe the sunrise about two minutes, before the Sun gets above the horizon., Q, , [2011] ...[2M], 9., , Draw a diagram to show dispersion of white light, by a glass prism. What is the cause of this, dispersion?, [2011] ...[2M], , 10. When we place a glass prism in the path of a, narrow beam of white light, a spectrum is, obtained. What happens when a second, identical prism is placed in an inverted position, with respect to the first prism? Draw a labelled, ray diagram to illustrate it., [2012] ...[2M], 11. A star at times appears bright and at times, fainter. What is this effect called? State the, reason for this effect., [2012] ...[2M], 12. Define the term power of accommodation. Write, the modification in the curvature of the eye lens, which enables us to see the nearby objects, clearly?, [2019] ...[2M], 13. What is hypermetropia? State the two causes of, hypermetropia. With the help of ray diagrams,, show :, (i) The eye-defect hypermetropia, (ii) Correction of hypermetropia by using a lens, [2009] ...[3M], 14. At what distance should an object be placed, from a convex lens of focal length 18 cm to, obtain an image at 24 cm from it on the other, side. What will be magnification produced in this, case?, [2010] ...[3M], 15. (a) What is meant by the, accommodation of an eye?, , power, , of, , (b) A person with a myopic eye cannot see, objects beyond 1.2 m directly. What should, be the type of the corrective lens used?, What would be its power?, [2011] ...[3M], , D, , P, B, , C F, , Trace it on your answer sheet and show the path, of the emergent beam as observed on the, screen DE., (i) Write the name and cause of the, phenomenon observed., (ii) Where else in nature is this phenomenon, observed?, (iii) Based on this observation, state the, conclusion which can be drawn about the, constituents of white light., 18. Write the importance of ciliary muscles in the, human eye. Name the defect of vision that, arises due to gradual weakening of the ciliary, muscles. What types of lenses are required by, the person suffering from this defect to see the, objects clearly?, Akshay, sitting in the last row in his class,, could not see clearly the words write on the, blackboard. When the teacher noticed it, he, announced if any student sitting in the front row, could volunteer to exchange his seat with, Akshay. Salman immediately agreed to, exchange his seat with Akshay. He could now, see the words written on the blackboard clearly., The teacher thought it fit to send the message, to Akshay's parents advising them to get his, eyesight checked. In the context of the above, event, answer the following questions:, , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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26, , Science, , Chapter-wise Previous Years' Questions (Class-10), , (a) Which defect of vision is Akshay suffering, from? Which type of lens is used to correct, this defect?, (b) State the values displayed by the teacher, and Salman., (c) In your opinion, in what way can Akshay, express his gratitude towards the teacher, and Salman?, [2015] ...[3M], 19. Describe an activity to show that colours of white, light splitted by a glass prism can be, recombined to get white light by another, identical glass prism. Also draw ray diagram to, show the recombination of the spectrum of white, light., [2016] ...[3M], 20. What is "dispersion of white light"? Draw a, labelled diagram to illustrate the recombination, of the spectrum of white light. Why it is, essential that the two prisms used for the, purpose should be identical and placed in an, inverted position with respect to each other?, [2017] ...[3M], 21. Trace the sequence of events which occur when, a bright light is focussed on your eyes., , 25. What is atmospheric refraction? Use this, phenomenon to explain the following natural, events:, (a) Twinkling of stars, (b) Advanced sunrise and delayed sunset., Draw diagrams to illustrate your answers., [2016] ...[5M], 26. (a) A student suffering from myopia is not able, to see distinctly the object placed beyond, 5 m. List two possible reasons due to which, this defect of vision may have arisen. With, the help of ray diagrams explain., (i) Why the student is unable to see, distinctly the objects placed beyond 5, cm from his eyes., (ii) The type of the corrective lens used to, restore proper vision and how this defect, is corrected by the use of this lens., (b) If in this case, the numerical value of the, focal length of the corrective lens is 5 m., Find the power of the lens as per the new, Cartesian sign convention., [2017] ...[5M], , [2019] ...[3M], 22. What is a rainbow? Draw a labelled diagram to, show the formation of a rainbow. [2019] ...[3M], 23. (a) Give reasons for the following :, (i) Colour of the clear sky is blue., (ii) The sun can be seen about two minutes, before actual sunrise., (iii) We cannot see an object clearly if it is, placed very close to the eyes., (b) What is Presbyopia? Write two causes of, this defect., [2008] ...[5M], 24. (a) What is meant by dispersion of white light?, Describe the formation of rainbow in the sky, with the help of a diagram., (b) What is hypermetropia? Draw ray diagrams, to show the image formation of an object, by :, (i) Hypermetropic eye, (ii) Correction made with a suitable lens for, hypermetropic eye., [2008] ...[5M], , 27. (a) A student is unable to see clearly the words, written on the black board placed at a, distance of approximately 3 m from him., Name the defect of vision of the boy is, suffering from. State the possible causes of, this defect and explain the method of, correcting it., (b) Why do stars twinkle? Explain.[2018]...[5M], 28. (a) Write the function of each of the following, parts of human eye:, (i) Cornea, (ii) Iris, (iii) Crystalline lens, (iv) Ciliary muscles, (b) Why does the Sun appear reddish early in, the morning? Will this phenomenon be, observed by an astronaut on the Moon?, Give reason to justify your answer., [2018] ...[5M], , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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Chapter-wise Previous Years' Questions (Class-10), , Science, , 27, , Chapter - 12 : Electricity, 1., , Out of 60 W and 40 W lamps, which one has, a higher electrical resistance when in use?, , 8., , to the electric supply at 220 V., , [2008] ...[1M], 2., , 3., , [2019] ...[1M], , (b) Calculate the current drawn from the electric, supply., , Why are the coils of electric toasters made of, an alloy rather than a pure metal?, , (c) Calculate the total energy consumed by the, two lamps together when they operate for, one hour., , [2008] ...[2M], 4., , A piece of wire of resistance 20  is drawn out, so that its length is increased to twice its, original length. Calculate the resistance of the, wire in the new situation., , 5., , [2009] ...[2M], , The values of current (I) flowing through a given, resistor of resistance (R), for the corresponding, values of potential difference (V) across the, resistor are as given below :, V(volts), , 0.5, , 1.0, , 1.5, , 2.0, , 2.5, , 3.0, , 4.0, , 5.0, , I (amperes), , 0.1, , 0.2, , 0.3, , 0.4, , 0.5, , 0.6, , 0.8, , 1.0, , Plot a graph between current (I) and potential, difference (V) and determine the resistance (R), of the resistor., [2018] ...[2M], 6., , While studying the dependence of potential, difference (V) across a resistor on the current (I), passing through it, in order to determine the, resistance of the resistor, a student took 5, readings for different values of current and, plotted a graph between V and I. He got a, straight line graph passing through the origin., What does the straight line signify? Write the, method of determining resistance of the resistor, using this graph., [2019] ...[2M], , 7., , [2008] ...[3M], , (a) Draw a circuit diagram to show the, connections, , What is the function of a galvanometer in a, circuit?, , Two lamps, one rated 60 W at 220 V and the, other 40 W at 220 V, are connected in parallel, , 9., , Two resistor, with resistances 5  and 10 , respectively are to be connected to a battery of, emf 6 V so as to obtain:, (a) How will you connect the resistances in, each case?, (i) Minimum current flowing, (ii) Maximum current flowing, (b) Calculate the strength of the total current in, the circuit in the two cases. [2009] ...[3M], , 10. (a) Write Joule's law of heating., (b) Two lamps, one rated 100 W ; 220 V, and, the other 60 W; 220 V, are connected in, parallel to electric mains supply. Find the, current drawn by two bulbs from the line, if, the supply voltage is 220 V. [2018] ...[3M], 11. (a) List the factors on which the resistance of, a conductor in the shape of a wire depends., (b) Why are metals good conductors of, electricity whereas glass is a bad conductor, of electricity? Give reason., , What would you suggest to a student if while, , (c) Why are alloys commonly used in electrical, heating devices? Give reason. [2018]...[3M], , performing an experiment he finds that the, pointer/ needle of the ammeter and voltmeter do, not coincide with the zero marks on the scales, , 12. Show how would you join three resistors, each, of resistance 9  so that the equivalent, , when circuit is open? No extra ammeter/, voltmeter is available in the laboratory, [2019] ...[2M], , resistance of the combination is, , [2018]...[3M], , (i) 13 , (ii) 6 , , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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28, , Science, , Chapter-wise Previous Years' Questions (Class-10), , (b) In an electric circuit two resistors of 12 , each are joined in parallel to a 6 V battery., Find the current drawn from the battery., , 13. Derive the expression for the heat produced due, to a current 'I' flowing for a time interval 't', through a resistor 'R' having a potential difference, 'V' across it ends. With which name is the, relation known? How much heat will an, instrument of 12 W produce in one minute if it, is connected to a battery of 12 V? [2010]...[5M], , [2019] ...[5M], 16. An electric lamp of resistance 20  and a, conductor of resistance 4  are connected to a, 6 V battery as shown in the circuit. Calculate :, , 14. Explain with the help of a labelled circuit, diagram how you will find the resistance of a, combination of three resistor, of resistance R1,, R2 and R3 joined in parallel. Also mention how, you will connect the ammeter and the voltmeter, in the circuit when measuring the current in the, circuit and the potential difference across one of, the three resistors of the combination., , [2019] ...[5M], , 4, I, +, , –, 6V, , [2010] ...[5M], , – A +, , K, , (a) the total resistance of the circuit,, 15. (a) With the help of a suitable circuit diagram, , (b) the current through the circuit,, , prove that the reciprocal of the equivalent, resistance of a group of resistances joined, in parallel is equal to the sum of the, reciprocals of the individual resistances., , (c) the potential difference across the (i) electric, lamp and (ii) conductor, and, (d) power of the lamp., , Chapter - 13 : Magnetic Effects of Electric Current, 1., , 2., , Why is a series arrangement not used for, connecting domestic electrical appliances in a, circuit?, [2008] ...[1M], , 3., , What is the function of a galvanometer in a, circuit?, [2019] ...[1M], , 4., , What is meant by the term, ‘magnetic field’?, Why does a compass needle show deflection, when brought near a bar magnet? [2008] ...[2M], , 5., , A coil of insulated wire is connected to a, galvanometer. What would be seen if a bar, , A charged particle enters at right angles into a, uniform magnetic field is shown. What should, be the nature of charge on the particle if it, begins to move in a direction pointing vertically, out of the page due to its interaction with the, magnetic field?, [2010] ...[1M], , magnet with its north pole towards one face of, the coil is, (i) Moved quickly towards it,, (ii) Moved quickly away from the coil and, (iii) Placed near its one face?, , Magnetic, field, , Name the phenomena involved., 6., , Charged Particle, , [2010] ...[2M], , (a) Distinguish between the terms' overloading', and 'short-circuiting' as used in domestic, circuits., , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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Chapter-wise Previous Years' Questions (Class-10), , (b) Why are the coils of electric toasters made, of any alloy rather than a pure metal?, , Science, , 9., , (a) State Fleming's left hand rule., (b) Write the principle of working of an electric, , [2008] ...[3M], 7., , 29, , motor., , (a) What is a magnetic field? How can the, direction of magnetic field lines at a placed, be determined?, , (c) Explain the function of the following parts of, an electric motor., , (b) State the rule for the direction of the, magnetic field produced around a current, carrying conductor. Draw sketch of the, pattern of field lines due to a current flowing, through a straight conductor. [2009] ...[5M], 8., , (a) What is a solenoid? Draw a sketch of the, pattern of field lines of the magnetic field, through and around a current carrying, solenoid., , (i) Armature, (ii) Brushes, (iii) Split ring, , [2018] ...[5M], , 10. What is a solenoid? Draw the pattern of, magnetic field lines of, , (b) Consider a circular loop of wire lying in the, plane of the table. Let the current pass, through the loop clockwise. Apply the right, hand rule to find out the direction of the, magnetic field inside and outside the loop., , (i) A current carrying solenoid and, (ii) A bar magnet., List two distinguishing features between the, , [2009, 2010] ...[5M], , two fields., , [2019] ...[5M], , Chapter - 14 : Sources of Energy, 1., , Which one of the following is a renewable, resource?, , 6., , What is biogas? Why is biogas considered an, ideal fuel for domestic use?[2009, 2010] ...[2M], , Natural gas, Petroleum, Ground water, Coal, 7., [2008] ...[1M], 2., , Write the energy conversion that takes place in, a hydropower plant., [2018] ...[1M], , 3., , Why is biogas considered an excellent fuel?, , Mention any four limitations in harnessing wind, energy on a large scale., , 8., , List any four disadvantages of using fossil fuels, for the production of energy., , [2019] ...[1M], 4., , List any four characteristics of biogas on, account of which it is considered an ideal fuel., , 9., , [2010] ...[2M], , [2011] ...[2M], , Give two examples for each of the following :, (a) Renewable sources or energy, (b) Non-renewable sources of energy, , [2008] ...[2M], [2011]...[2M], 5., , Discuss one limitation each for the extracting of, energy from :, [2008] ...[2M], (a) Winds, , (b) Tides, , 10. “Burning fossil fuels is a cause of global, warming”. Justify this statement. [2012] ...[2M], , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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BIOLOGY, Chapter - 15 : Our Environment, 1., , How is the increasing demand for energy, adversely affecting our environment?, , components., , [2010] ...[1M], 2., , 11. (a) What is an ecosystem? List its two main, , (b) We do not clean ponds or lakes, but an, , Select two non-biodegradable substances from, , aquarium needs to be cleaned regularly., , the following waste generated in a kitchen: Spoilt, , Explain., , [2009, 2013] ...[3M], , food, paper bags, milk bags, vegetable peels, tin, cans, used tea leaves solution, 3., , 4., , [2012] ...[1M], , 12. Explain the phenomenon of "biological, , Mention one negative effect of our affluent life, , magnification." How does it affect organisms, , style on the environment., , belonging to different trophic levels particularly, , [2013, 2014] ...[1M], , In a food chain of frog, grass, insect and snake,, assign trophic level to frog., , 5., , 13. “Energy flow in a food chain is unidirectional”., Justify this statement. Explain how the, , was available to the plants. How much energy, , pesticides enter a food chain and subsequently, , would be available to man in this chain?, , get into our body., , [2014] ...[3M], , [2017] ...[1M], 14. Differentiate between biodegradable and non-, , "Burning fossil fuels is a cause of global, warming." Justify this statement. [2012] ...[2M], , 7., , [2010] ...[3M], , In the following food chain, 20,000 J of energy, , Plants  Sheep  Man, 6., , [2016] ...[1M], , the tertiary consumers?, , biodegradable substances with the help of one, example each. List two changes in habit that, , We often observe domestic waste decomposing, , people must adopt to dispose non-biodegradable, , in the bylanes of residential colonies. Suggest, , waste, for saving the environment.[2015] ...[3M], , ways to make people realise that the improper, disposal of waste is harmful to the environment., [2013] ...[2M], , 15. The activities of man had adverse effects on all, forms of living organisms in the biosphere., Unlimited exploration of nature by man disturbed, , 8., , State, , with, , reason, , any, , two, , possible, , consequences of elimination of decomposers, from the Earth., 9., , [2014] ...[2M], , You being an environmentalist are interested in, contributing towards the conservation of nature, resources. List four activities that you can do on, your own., , [2017] ...[2M], , the delicate ecological balance between the living, and nonliving components of the biosphere. The, unfavorable conditions created by man himself, threatened the survival not only of himself but, also of the entire living organisms on the mother, earth. One of your classmates is an active, member of 'Eco club' of your school which is, , 10. How is ozone formed in the upper atmosphere?, , creating environmental awareness amongst the, , Why is damage to ozone layer a cause of, , school students, spreading the same in the, , concern to us? What causes this damage?, [2008] ...[3M], , society and also working hard for preventing, environmental degradation of the surroundings., , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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Chapter-wise Previous Years' Questions (Class-10), , Science, , (a) Why is it necessary to conserve our, , 31, , the second is to generate least garbage at, , environment?, , individual level., , (b) State the importance of green and blue dust-, , (a) Suggest two measures to manage the, , bins in the safe disposal of the household, , garbage we produce., , waste., (b) As an individual, what can we do to, (c) List two values exhibited by your classmate, , generate the least garbage? Give two, , who is an active member of Eco-club of your, school., , points., , [2016] ...[3M], (c) List two values the teacher instilled in his, , 16. Students in a school listened to the news read, , students in this episode., , [2018] ...[3M], , in the morning assembly that the mountain of, garbage in Delhi suddenly exploded and various, , 17. How can we help in reducing the problem of, waste disposal? Suggest any three methods., , vehicles got buried under it. Several people were, also injured and there was traffic jam all ground., , OR, , In the brain storming session the teacher also, discussed this issue and asked the students to, , Define an ecosystem. Draw a block diagram to, , find out a solution to the problem of garbage., , show the flow of energy in an ecosystem., , Finally they arrived at two main points - one is, [2017, 2019] ...[3M], , self management of the garbage we produce and, , Chapter - 16 : Sustainable Management of Natural Resources, , 1., , What are the advantages of water stored in the, ground?, , 2., , 6., , resources. List four activities that you can do on, , Every one of us can do something to reduce, , your own., , our consumption of various natural resources., List four such activities based on the 3-R, approach., , You being an environmentalist are interested in, contributing towards the conservation of natural, , [2012] ...[2M], , 7., , Why are coal and petroleum categorized as, natural resources? Give a reason as to why they, , [2013] ...[2M], , should be used judiciously., 3., , [2017] ...[2M], , [2017] ...[2M], , Why is sustainable management of natural, resources necessary? Out of the two - reuse, and recycle - which, in your opinion, is better to, practice? Give reason., , [2015] ...[2M], , 8., , (a) Water is an elixir of life, a very important, natural resource. Your science teacher, wants you to prepare a plan for a formative, assessment activity, "How to save water, the, , 4., , What is meant by bio-diversity? List two, , vital natural resource". Write any two ways, , advantages of conserving forests and wildlife., , that you will suggest to bring awareness in, , [2015] ...[2M], , your neighbourhood, on how to 'save water'., (b) Name and explain any one way by which, , 5., , List four stakeholders which may be helpful in, the conservation of forests., , [2016] ...[2M], , the underground water table does not go, down further., , [2017] ...[3M], , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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32, 9., , Science, , Chapter-wise Previous Years' Questions (Class-10), , What is a dam? Why do we seek to build large, dams? While building large dams, which three, main problems should particularly be addressed, to maintain peace among local people? Mention, them., [2018] ...[3M], , 10. What is water harvesting? List two main, advantages associated with water harvesting at, the community level. Write two causes for the, failure of sustained availability of groundwater., [2019] ...[3M], , ‰ ‰ ‰, , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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CHAPTER-WISE PREVIOUS YEARS' QUESTIONS, , MATHEMATICS

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Note: After attempting the questions, a student must refer to the stepwise solutions available on our, website www.aakash.ac.in and compare his/her solutions with the solutions given on our website., To get the text solution, students are required to sign in their account with their log in credentials.

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MATHEMATICS, Chapter - 1 : Real Numbers, 1., , Complete the missing entries in the following, factor tree:, [2008] ...[1M], , 2, , 7., , Find the HCF of 1260 and 7344 using Euclid's, algorithm., [2019] ...[2M], , 8., , Show that every positive odd integer is of the, form (4q + 1) or (4q + 3), where q is some, integer., [2019] ...[2M], , 9., , Use Euclid's Division Lemma to show that the, square of any positive integer is either of the, form 3m or (3m + 1) for some integer m., , 3, 7, 2., , 3., , Find the (HCF × LCM) for the numbers 100 and, 190., [2009] ...[1M], Has the rational number, , 441, 2 5 7, , 5 7 2, , a terminating, , [2008] ...[3M], 10. Prove that 3 , , [2009] ...[3M], , or a non-terminating decimal representation?, [2010] ...[1M], 4., , What is the HCF of smallest prime number and, the smallest composite number? [2018] ...[1M], , 5., , Find a rational number between, , 2 and, , 3., , [2019] ...[1M], 6., , Given that, , 2 is irrational, prove that  5  3 2 , , is an irrational number., , 2 is an irrational number., , 11. Prove that 2  3 5 is an irrational number., [2010] ...[3M], 12. Find HCF and LCM of 404 and 96 and verify that, HCF × LCM = Product of the two given, numbers., [2018] ...[3M], 13. Prove that, , 2 is an irrational number., [2019] ...[3M], , [2018] ...[2M], , Chapter - 2 : Polynomials, , 1., , If (x + a) is a factor of 2x2 + 2ax + 5x + 10,, find a., , 2., , 5., , Find all the zeroes of the polynomial, x3 + 3x2 – 2x – 6, if two of its zeroes are  2, and 2., [2009] ...[2M], , 6., , If two zeroes of the polynomial x3 – 4x2 – 3x + 12, are 3 and  3, then find its third zero., , [2008] ...[1M], , If 1 is a zero of the polynomial p(x) = ax2 – 3, (a – 1)x – 1, then find the value of a.[2009]...[1M], , 3., ,  +  = 6 and  = 4, then write the, polynomial., 4., , [2010] ...[2M], , If ,  are the zeroes of a polynomial, such that, [2010] ...[1M], , Find all the zeros of the polynomial, x4 + x3 – 34x2 – 4x + 120, if two of its zeros, are 2 and –2., , 7., , [2008] ...[2M], , Find all zeroes of the polynomial (2x4 – 9x3 +, 5x2 + 3x – 1) if two of its zeroes are  2  3 , , and  2  3  ., 8., , [2018] ...[3M], , Find the value of k such that the polynomial, x2 – (k + 6)x + 2(2k – 1) has sum of its zeros, equal to half of their product., [2019] ...[3M], , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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34, , Mathematics, , Chapter-wise Previous Years' Questions (Class-10), , Chapter - 3 : Pair of Linear Equations in Two Variables, 1., , Find the number of solutions of the following pair, of linear equations :, , 7., , fraction is 3 less than twice the denominator., , x + 2y – 8 = 0, , If each of the numerator and denominator is, , 2x + 4y = 16, 2., , [2009] ...[1M], , Find the value of k for which the following pair, of linear equations have infinitely many solutions, 2x + 3y = 7; (k – 1)x + (k + 2)y = 3k., , In figure, ABCD is a rectangle. Find the values, of x and y., [2018] ...[2M], D, , x +y, , 14 cm, , the fraction., 8., , 30 cm, , 9., , C, , B, , Find c if the system of equations, cx + 3y + (3 – c) = 0; 12x + cy – c = 0 has, infinitely many solutions?, [2019] ...[2M], , 5., , Represent the following pair of equations, graphically and write the coordinate of points, where the lines intersect y-axis., , A father's age is three times the sum of the, will be two times the sum of their ages. Find the, present age of the father., , [2019] ...[3M], , 1, when 2 is subtracted, 3, 1, from the numerator and it becomes, when 1, 2, is subtracted from the denominator. Find the, , 10. A fraction becomes, , fraction., , [2019] ...[3M], , 11. A peacock is sitting on the top of a pillar, which, , x + 3y = 6, , 6., , [2010] ...[3M], , ages of his two children. After 5 years his age, , 4., , 2x – 3y = 12, , Solve the following pair of equations, , 4, 6,  3 y  8,  4 y  5., x, x, , x–y, , A, , 1, . Find, 2, [2010] ...[3M], , decreased by 1, the fraction becomes, , [2010] ...[2M], 3., , The sum of numerator and denominator of a, , is 9 m high. From a point 27 in away from the, [2008] ...[3M], , bottom of the pillar, a snake is coming to its, , Solve for x and y, , hole at the base of the pillar. Seeing the snake, , ax by, ,  ab, b, a, , the peacock pounces on it. If their speeds are, , ax – by = 2ab, , equal, at what distance from the hole is the, snake caught ?, , [2009] ...[3M], , [2008] ...[6M], , Chapter - 4 : Quadratic Equations, 1., , Show that x = –3 is a solution of x2 + 6x + 9 = 0., [2008] ...[1M], , 2., , Find the discriminant of the quadratic equation, 3 3 x 2  10 x  3  0., [2009] ...[1M], , 3., , The root of the equation x2 – 3x – m (m + 3), = 0, where m is a constant, are [2011] ...[1M], , 4., , (A) 3, (C) 6, 5., , (A) m, m + 3, , (D) –m, –(m + 3), , 7, 2, (D) –3, (B) , , If the quadratic equation px 2  2 5 px  15  0, has two equal roots, then find the value of p., [2015] ...[1M], , (B) –m, m + 3, (C) m, – (m + 3), , If 1 is a root of the equations ay2 + ay + 3 = 0 and, y2 + y + b = 0, then ab equals, [2012]...[1M], , 6., , If x = 3 is one root of the quadratic equation, x2 – 2kx – 6 = 0, then find the value of k., [2018] ...[1M], , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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Chapter-wise Previous Years' Questions (Class-10), , Mathematics, , 7., , For what values of k, the roots of the equation, x2 + 4x + k = 0 are real?, [2019] ...[1M], , 8., , Find the value of k for which the roots of the, equation 3x2 – 10x + k = 0 are reciprocal of, each other., [2019] ...[1M], , 9., , Find the value of m so that the quadratic, equation mx(x – 7) + 49 = 0 has two equal, roots., [2011] ...[2M], , 10. Find the value(s) of k so that the quadratic, equation 3x2 – 2kx + 12 = 0 has equal roots., [2012] ...[2M], 11. Solve the following quadratic equation for, x : 4 3 x 2  5 x  2 3  0., [2013] ...[2M], 12. Solve the quadratic equation, for x., , 2x2, , a2, , + ax –, =0, [2014] ...[2M], , 13. Solve the following quadratic equation for x :, 4x2 + 4bx – (a2 – b2) = 0, , [2015] ...[2M], , 14. If –5 is a root of the quadratic equation 2x2 + px, – 15 = 0 and the quadratic equation p(x2 + x) +, k = 0 has equal roots, find the value of k., [2016] ...[2M], 15. Find the value of p, for which one root of the, quadratic equation px2 – 14x + 8 = 0 is 6 times, the other., [2017] ...[2M], 16. The sum of two numbers is 8. Determine the, numbers if the sum of their reciprocals is, , 8, ., 15, , [2009] ...[3M], 17. Find the roots of the following quadratic, equation : x 2  3 5 x  10  0., [2011] ...[3M], 18. Solve for x : 4x2 – 4ax + (a2 – b2) = 0., [2012] ...[3M], 19. Solve for x : 3 x 2  2 6 x  2  0. [2012] ...[3M], 20. For what value(s) of k, the roots of the quadratic, equation (k + 4)x 2 + (k + 1)x + 1 = 0 are, equal?, [2013] ...[3M], 21. Solve the equation, , 4, 5, 3, 3 , ; x  0,  ,, x, 2x  3, 2, , for x., , [2014] ...[3M], , 22. Solve of x :, 3 x 2  2 2x  2 3  0, , [2015] ...[3M], , 35, , 23. Solve for x, , 1, 1, 2, ,  , x  1, 2, 3,  x  1 x  2   x  2   x  3  3, [2016] ...[3M], 24. If ad  bc, then prove that the equation, (a2 + b2)x2 + 2(ac + bd)x + (c2 + d 2) = 0 has, no real roots., [2017] ...[3M], 25. A plane left 30 minutes late than its scheduled, time and in order to reach the destination, 1500 km away in time, it had to increase its, speed by 100 km/h from the usual speed. Find, its usual speed., [2018] ...[3M], 26. Sum of the areas of two squares is 400 cm2. If, the difference of their perimeters is 16 cm, find, the sides of the two squares., [2013] ...[4M], 27. Solve the following for x :, 1, 1 1 1, ,  , 2a  b  2 x 2a b 2 x, , [2013] ...[4M], , 28. The difference of two natural numbers is 5 and, the difference of their reciprocals is, numbers., , 1, . Find the, 10, [2014] ...[4M], , 29. Find the values of k for which the quadratic, equation (k + 4)x2 + (k + 1)x + 1 = 0 has equal, roots. Also, find the roots., [2014] ...[4M], 30. The diagonal of a rectangular field is 16 metres, more than the shorter side. If the longer side is 14, metres more than the shorter side, then find the, lengths of the sides of the field., [2015]...[4M], 31. A train travels at a certain average speed for a, distance of 54 km and then travels a distance of, 63 km at an average speed of 6 km/h more than, the first speed. If it takes 3 hours to complete, the total journey, what is its first speed?, [2015] ...[4M], 32. Solve for x :, , 1, 2, 4, , , ; x  1,  2,  4, x 1 x  2 x  4, [2016] ...[4M], 33. A motor-boat whose speed is 24 km/h in still, water takes 1 hour more to go 32 km upstream, than to return downstream to the same spot., Find the speed of the stream., [2016] ...[4M], , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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36, , Mathematics, , Chapter-wise Previous Years' Questions (Class-10), , 40. Solve the following equation for x:, , 34. Solve of x :, , 9x2 – 9(a + b)x + (2a2 + 5ab + 2b2) = 0, , 1, 3, 5, 1, , , , x   1, ,  4, x  1 5x  1 x  4, 5, [2017] ...[4M], , 1, 13, hours. If one tap takes 3 hours more than the, other to fill the tank, then how much time will, each tap take to fill the tank?, [2017] ...[4M], , 35. Two taps running together can fill a tank in 3, , 36. A motor-boat whose speed is 18 km/hr in still, water take 1 hr more to go 24 km upstream, than to return downstream to the same spot., Find the speed of the stream., [2018] ...[4M], 37. A train travels at a certain average speed for a, distance of 63 km and then travels a distance of, 72 km at an average speed of 6 km/hr more, than its original speed. It takes 3 hours to, complete total journey, what is the original, average speed?, [2018] ...[4M], 7, 38. Two water taps together can fill a tank in 1, 8, hours. The tap with longer diameter takes 2, hours less than the tap with smaller one to fill, the tank separately. Find the time in which each, tap can fill the tank separately. [2019] ...[4M], , 39. The difference of two numbers is 4. If the, difference of their reciprocals is, numbers., , 4, , find the two, 21, [2008] ...[6M], , [2009] ...[6M], 41. If (–5) is a root of the quadratic equation 2x2 +, px – 15 = 0 and the quadratic equation p(x2 +, x) + k = 0 has equal roots, then find the values, of p and k., [2009] ...[6M], 42. Three consecutive positive integers are such that, the sum of the square of the first and the, product of the other two is 46, find the integers., [2010] ...[6M], 43. The difference of squares of two numbers is 88., If the larger number is 5 less than twice the, smaller number, then find the two numbers., [2010] ...[6M], 44. A train travels 180 km at a uniform speed. If the, speed had been 9 km/hour more, it would have, taken 1 hour less for the same journey. Find the, speed of the train., [2011] ...[6M], 45. Find the roots of the equation, , 1, 1, 3, ,  1, x  , 5., 2x  3 x  5, 2, , [2011] ...[6M], , 46. A shopkeeper buys books of the `80. If he had, bought 4 more books for the same amount,, each book would have cost `1 less. Find the, number of books he bought., [2012] ...[6M], 47. The sum of two numbers is 9 and the sum of, 1, their reciprocals is . Find the numbers., 2, [2012] ...[6M], , Chapter - 5 : Arithmetic Progressions, 1., , The first term of an AP is p and its common, difference is q. Find its 10th term. [2008] ...[1M], , 5., , The sum of first 20 odd natural number is, [2012] ...[1M], , 4, If , a, 2 are three consecutive terms of an AP,, 5, then find the value of a., [2009] ...[1M], , (A) 100, , 3., , If the sum of first p terms of an AP, is ap2 + bp,, find its common difference., [2010] ...[1M], , (C) 400, , 4., , If the common difference of an AP is 3, then, a20 – a15 is, [2011] ...[1M], , 2., , (A) 5, (B) 3, , (B) 210, , (D) 420, 6., , The common difference of AP, 1 1  6q 1  12q, ,, ,, , ... is, 3q 3q, 3q, , [2013] ...[1M], , (C) 15, , (A) q, , (B) –q, , (D) 20, , (C) –2, , (D) 2, , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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Chapter-wise Previous Years' Questions (Class-10), , 7., , 8., , Mathematics, , The first three terms of an AP respectively are, 3y – 1, 3y + 5 and 5y + 1. The y equals, , terms of two AP's, 22. For what value of n are the, 63, 65, 67, ... and 3, 10, 17, ... equal?, , [2014] ...[1M], , [2008] ...[3M], , (A) –3, , (B) 4, , (C) 5, , (D) 2, , For what value of k will k + 9, 2k – 1 and, 2k + 7 are the consecutive terms of an AP?, [2016] ...[1M], , 9., , 37, , nth, , What is the common difference of an AP in, which a21 – a7 = 84?, [2017] ...[1M], , 10. In an AP, if the common difference (d) = – 4, and, the seventh term (a7) is 4, then find the first, term., [2018] ...[1M], , 23. If m times the mth term of an AP is equal to n, times its nth term, find the (m + n)th term of the, AP., [2008] ...[3M], 24. In an AP, the first term is 8, nth term is 33 and, sum to first n terms is 123. Find n and d, the, common difference., [2008] ...[3M], 25. The sum of first six terms of an arithmetic, progression is 42. The ratio of its 10th term to its, 30th term is 1 : 3. Calculate the first and the, thirteenth term of the AP.?, [2009] ...[3M], , 11. How many two digit numbers are divisible, by 3?, [2019] ...[1M], , 26. In an AP, the sum of first ten terms is –150 and, the sum of its next ten terms is –550. Find the, AP, [2010] ...[3M], , 12. Which term of the AP 3, 15, 27, 39, ... will be, 120 more than its 21st term? [2009, 2019]...[2M], , 27. Find an AP whose fourth term is 9 and the sum, of its sixth term and thirteenth term is 40., , 13. In an AP, the first term is 2, the last term is 29, and sum of the terms is 155. Find the common, difference of the AP, [2010] ...[2M], 14. Find how many two-digit numbers are divisible, by 6., [2011] ...[2M], 15. Find the sum of all three digit natural numbers,, which are multiples of 7., [2012] ...[2M], OR, , 16. The first and the last term of an AP are 5 and 45, respectively. If the sum of all its terms is 400, find, its common difference., [2014, 2017] ...[2M], 17. In an AP, if S5 + S7 = 167 and S10 = 235, then, find the AP, where Sn denotes the sum of its first, n terms., [2015] ...[2M], 18. The 4th term of an AP is zero. Prove that the 25th, term of the AP is three times its 11th term., [2016] ...[2M], term, , of, , the, , 28. The, term of an AP is 1 more than twice its, 8th term. If the 12th term of the AP is 47, then, find its nth term., [2012] ...[3M], 29. The sum of first n terms of an AP is 3n2 + 4n., Find the 25th term of this AP., [2013] ...[3M], 30. If the seventh term of an AP is, , How many three-digit natural numbers are, divisible by 7?, [2013] ...[2M], , 19. Which, , [2011] ...[3M], 16th, , progression, , 20,, , 1, 1, 3, 19 , 18 , 17 , ..... is the first negative term?, 4, 2, 4, [2017] ...[2M], , term is, , 1, , find its 63rd term., 7, , 1, and its ninth, 9, [2014] ...[3M], , 31. The 14th term of an AP is twice its 8th term. If, its 6th term is –8, then find the sum of its first, 20 terms., [2015] ...[3M], 32. If the ratio of the sum of first n terms of two AP's, is (7n + 1) : (4n + 27), find the ratio of their, [2016] ...[3M], mth terms., OR, If the ratio of the sum of the first n terms of two, AP's is (7n + 1) : (4n + 27), then find the ratio, of their 9th terms., [2017] ...[4M], , 20. Find the sum of first 8 multiples of 3. [2018]...[2M], , 33. The first and the last terms of an A.P. are 8 and, 350 respectively. If its common difference is 9,, how many terms are there and what is their, sum?, [2011] ...[4M], , 21. If Sn, the sum of first n terms of an AP is given, by Sn = 3n2 – 4n, find the nth term. [2019]...[2M], , 34. How many multiples of 4 lie between 10 and, 250? Also find their sum., [2011] ...[4M], , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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38, , Mathematics, , Chapter-wise Previous Years' Questions (Class-10), , 35. Sum of the first 20 terms of an AP is –240 and its, first term is 7. Find its 24th term. [2012] ...[4M], 36. Find the number of terms of the AP –12, –9,, –6, ... 12. If 1 is added to each term of this AP,, then find the sum of terms of the AP thus, obtained., [2013] ...[4M], , 39. The houses in a row numbered consecutively, from 1 to 49. Show that there exists a value of, X such that sum of numbers of houses, preceding the house numbered X is equal to, sum of the numbers of houses following X., [2016] ...[4M], , 37. In an AP of 50 terms, the sum of first 10 terms, is 210 and the sum of its last 15 terms is 2565., Find the AP., [2014] ...[4M], , 40. The sum of four consecutive numbers in an AP, is 32 and the ratio of the product of the first and, the last term to the product of two middle terms, is 7 : 15. Find the numbers., [2018] ...[4M], , 38. Find the 60th term of the AP 8, 10, 12 ..........,, if it has a total of 60 terms and hence find the, sum of its last 10 terms., [2015] ...[4M], , 41. If the sum of first four terms of an AP is 40 and, that of first 14 terms is 280. Find the sum of its, first n terms., [2019] ...[4M], , Chapter - 6 : Triangles, 1., , The lengths of the diagonals of a rhombus are, 30 cm and 40 cm. Find the side of the, rhombus., [2008] ...[1M], , 2., , In figure, PQ || BC and AP : PB = 1 : 2. Find, ar( APQ ), ., ar( ABC ), , [2008] ...[1M], , Given ABC ~ PQR, if, , 7., , ar( ABC ), [2018] ...[1M], ., ar( PQR ), In figure, DE || BC, AD = 1 cm and BD = 2 cm., What is the ratio of the ar(ABC) to the, ar(ADE)?, [2019] ...[1M], , A, P, , A, , Q, D, , 3., 4., , C, B, In LMN, L = 50° and N = 60°. If LMN ~, PQR, then find Q., [2009] ...[1M], , In below figure, S and T are points on the, sides PQ and PR respectively of PQR, such, that PT = 2 cm, TR = 4 cm and ST is parallel, to QR. Find the ratio of the areas of PST and, PQR., [2010] ...[1M], P, , B, , 9., , C, , H, , A, , C, , E is a point on the side AD produced of, parallelogram ABCD and BE intersects CD at F., Show that ABE ~ CFB., [2008] ...[2M], In figure, ABD is a right triangle, right-angled at, A and AC  BD. Prove that AB2 = BC.BD., [2009] ...[2M], D, , Q, R, In below figure, AHK is similar to ABC. If, AK = 10 cm, BC = 3.5 cm and HK = 7 cm, find, AC., [2010] ...[1M], , C, , E, , B, , 8., , T, , S, , 5., , AB 1,  , then find, PQ 3, , 6., , A, B, 10. In figure, AD  BC. Prove that AB 2 + CD 2, = BD2 + AC2., [2008] ...[3M], C, , K, , D, B, , A, , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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Chapter-wise Previous Years' Questions (Class-10), , 11. In figure, AD  BC and BD =, 2CA2 = 2AB2 + BC2, , 1, CD. Prove that, 3, [2009] ...[3M], , A, , B, , 17. If P and Q are the points on side CA and CB, respectively of ABC, right angled at C, prove, that (AQ2 + BP2) = (AB2 + PQ2) [2019] ...[3M], , 12. In figure, M is mid-point of side CD of a, parallelogram ABCD. The line BM is drawn, intersecting AC at L and AD produced at E., Prove that EL = 2BL., [2009] ...[3M], D, , A, , A, , B, , E, , D, , C, , 19. Prove that, in a right triangle, the square of the, hypotenuse is equal to the sum of the squares, of the other two sides., [2018, 2019] ...[4M], , M, L, C, , B, , 39, , 18. In an equilateral ABC, D is a point on side BC, 1, such that BD = BC. Prove that 9(AD) 2, 3, = 7(AB)2., [2018] ...[4M], , C, , D, , Mathematics, , 13. In below figure, ABC is a right triangle, right, angled at C, and D is the midpoint of BC. Prove, that AB2 = 4AD2 – 3AC2., [2010] ...[3M], A, , 20. If a line is drawn parallel to one side of a, triangle to intersect the other two sides in, distinct points, prove that the other two sides, are divided in the same ratio., Using the above, prove the following :, In figure, AB | | DE and BC | | EF. Prove that, [2008] ...[6M], AC | | DF., , B, , D, , C, , 14. Prove that the area of an equilateral triangle, described on one side of the square is equal to, half the area of the equilateral triangle described, on one of its diagonal., [2018] ...[3M], 15. If the area of two similar triangles are equal,, prove that they are congruent., [2018] ...[3M], 16. In figure, ACB = 90° and CD  AB, prove that, CD2 = BD × AD., [2019] ...[3M], C, , D, , A, O, , E, , B, C, , F, , 21. Prove that the ratio of the areas of two similar, triangles is equal to the square of the ratio of, their corresponding sides., Using the above, prove the following :, If the areas of two similar triangles are equal,, then prove that the triangles are congruent., , A, , D, , B, , [2010] ...[6M], , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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40, , Mathematics, , Chapter-wise Previous Years' Questions (Class-10), , Chapter - 7 : Coordinate Geometry, 1., , If P(2, p) is the mid-point of the line segment, joining the points A(6, –5) and B(–2, 11), find the, value of p., [2010] ...[1M], , 2., , If A(1, 2), B(4, 3) and C(6, 6) are the three, vertices of a parallelogram ABCD, find the, coordinates of the fourth vertex D.[2010] ...[1M], , 3., , 4., , 6., , 7., , 9., , If the points A(x, 2), B(–3, –4) and C(7, –5) are, collinear, then the value of x is, [2014] ...[1M], (A) –63, , (B) 63, , (C) 60, , (D) –60, , Find the distance of a point P(x, y) from the, origin., [2018] ...[1M], , a, If P  , 4  is the midpoint of the line-segment, 2 , joining the points A(–6, 5) and B(–2, 3), then the, value of a is, [2011] ...[1M], , 10. Find the coordinates of a point A, where AB is, diameter of a circle whose centre is (2, –3) and, B is the point (1, 4)., [2019] ...[1M], , (A) –8, , (B) 3, , 11. Find the value of k if the points (k, 3), (6, –2), and (–3, 4) are collinear., [2008] ...[2M], , (C) –4, , (D) 4, , If A and B are the points (–6, 7) and (–1, –5), respectively, then the distance 2AB is equal to, [2011] ...[1M], , 5., , 8., , (A) 13, , (B) 26, , (C) 169, , (D) 238, , The coordinates of the point P dividing the line, segment joining the points A(1, 3) and B(4, 6), in the ratio 2 : 1 are, [2012] ...[1M], (A) (2, 4), , (B) (3, 5), , (C) (4, 2), , (D) (5, 3), , (B) (6, –7), , (C) (6, 7), , (D) (–6, –7), , In below figure, the area of the triangle ABC (in, sq. units) is, [2013] ...[1M], y, , 3, 1, , B, –3 –2 –1, , –1, , 14. If a point A(0, 2) is equidistant from the points, B(3, p) and C(p, 5) then find the value of p., [2012] ...[2M], , 16. Find the relation between x and y if the points, A(x, y), B(–5, 7) and C(–4, 5) are collinear., [2015] ...[2M], 17. Let P and Q be the points of trisection of the, line segment joining the points A(2, –2), and, B(–7, 4) such that P is nearer to A. Find the, coordinates of P and Q., [2016] ...[2M], 18. Prove that the points (3, 0), (6, 4) and (–1, 3) are, the vertices of a right angled isosceles triangle., , 19. A line intersects the y-axis and x-axis at the, points P and Q respectively. If (2, –5) is the, mid-point of PQ, then find the coordinates of, P and Q., [2017] ...[2M], , A(1, 3), , 2, , x, , 13. Find the value of y for which the distance, between the points A(3, –1) and B(11, y) is 10, units., [2011] ...[2M], , [2016] ...[2M], , 5, 4, , [2009] ...[2M], , 15. The points A(4, 7), B(p, 3) and C(7, 3) are the, vertices of a right triangle, right-angled at B, find, the values of P., [2015] ...[2M], , If the coordinates of the one end of a diameter, of a circle are (2, 3) and the coordinates of its, centre are (–2, 5), then the coordinates of the, other end of the diameter are, [2012] ...[1M], (A) (–6, 7), , 12. If the points A(4, 3) and B(x, 5) are on the circle, with the centre O(2, 3), find the value of x., , 1, , 2, , 3, , C, , 4, , –2, , 5, , x, , 20. If the distances of P(x, y) from A(5, 1) and, B(–1, 5) are equal, then prove that 3x = 2y., [2017] ...[2M], , y, , (A) 15, , (B) 10, , (C) 7.5, , (D) 2.5, , 21. Find the ratio in which P(4, m) divides the line, segment joining the points A(2, 3) and B(6, –3)., Hence find m., [2018] ...[2M], , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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Chapter-wise Previous Years' Questions (Class-10), , Mathematics, , 41, , 22. Find the ratio in which the segment joining the, points (1, –3) and (4, 5) is divided by x-axis?, Also find the coordinates of this point on x-axis., , 34. Find the ratio in which the y-axis divides the line, segment joining the points (–4, –6) and (10, 12)., Also, find the coordinates of the point of division., , [2019] ...[2M], , [2013] ...[3M], , 23. If P divides the joining of A(–2, –2) and B(2, –4), , 35. Show that the points (–2, 3), (8, 3) and (6, 7) are, the vertices of a right triangle., [2013] ...[3M], , AP 3,  , find the coordinates of P., such that, AB 7, [2008] ...[3M], 24. The mid-points of the sides of a triangle are, (3, 4), (4, 6) and (5, 7). Find the coordinates of, the vertices of the triangle., [2008] ...[3M], 25. Find the ratio in which the point (2, y) divides the, line segment joining the points A(–2, 2) and, B(3, 7). Also find the value of y. [2009] ...[3M], 26. Find the area of the quadrilateral ABCD whose, vertices are A(–4, –2), B(–3, –6), C(3, –2) and, D(2, 3), [2009] ...[3M], 27. Point P divides the line segment joining the, AP 1,  ., AB 3, If P lies on the line 2x – y + k = 0, find the, value of k., [2010] ...[3M], , points A(2, 1) and B(5, –8) such that, , 28. If R(x, y) is a point on the line segment joining, the points P(a, b) and Q(b, a), then prove that, x + y = a + b., [2010] ...[3M], 29. Point P(x, 4) lies on the line segment joining the, points A(–5, 8) and B(4, –10). Find the ratio in, which point P divides the line segment AB. Also, find the value of x., [2011] ...[3M], 30. Find the area of quadrilateral ABCD, whose, vertices are A(–3, –1), B(–2, –4), C(4, –1) and, D(3, 4)., [2011] ...[3M], 31. Find the area of the triangle formed by joining, the midpoints of the sides of the triangle whose, vertices are A(2, 1), B(4, 3) and C(2, 5)., [2011] ...[3M], 32. A point P divides the line segment joining the, points A(3, –5) and B(–4, 8) such that, , AP K,  . If P lies on the line x + y = 0, then, PB 1, find the value of K., [2012] ...[3M], 33. If the vertices of triangle are (1, –3), (4, p) and, (–9, 7) and its area is 15 sq. units, find the, value(s) of p., [2012] ...[3M], , 36. If the point A(0, 2) is equidistant from the points, B(3, p) and C(p, 5), find P, also find the length, of AB., [2014] ...[3M], 37. If the points A(–2, 1), B(a, b) and C(4, –1), are collinear and a – b = 1, find the values of, a and b., [2014] ...[3M], 38. If the coordinates of points A and B are (–2, –2), and (2, –4) respectively, find the coordinates of P, such that AP , segment AB., , 3, AB, where P lies on the line, 7, [2015] ...[3M], , 39. If the point P(x, y) is equidistant from the points, A(a + b, b – a) and B(a – b, a + b). Prove that, bx = ay., [2016] ...[3M], , 24, 40. In what ratio does the point  , y  divide the,  11, , line segment joining the points P(2, –2) and, Q(3, 7)? Also find the value of y. [2017] ...[3M], 41. If A(–2, 1), B(a, 0), C(4, b) and D(1, 2) are the, vertices of a parallelogram ABCD, find the values, of a and b. Hence find the lengths of its sides., [2018] ...[3M], 42. If A(–5, 7), B(–4, –5), C(–1, –6) and D(4, 5) are, the vertices of quadrilateral, find the area of the, quadrilateral ABCD., [2018] ...[3M], 43. Find the point on y-axis which is equidistant, from the points (5, –2) and (–3, 2).[2019]...[3M], 44. The line segment joining the points A(2, 1) and, B(5, –8) is trisected at the points P and Q such, that P is nearer to A. If P also lies on the line, given by 2x – y + k = 0, find the value of k., [2019] ...[3M], 45. If the area of triangles ABC formed by A(x, y),, B(1, 2) and C(2, 1) is 6 square units, then prove, that x + y = 15., [2013] ...[4M], , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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42, , Mathematics, , Chapter-wise Previous Years' Questions (Class-10), , 46. Find the ratio in which the point P(x, 2) divides, the line segment joining the points A(12, 5) and, B(4, –3). Also find the value of x. [2014] ...[4M], , A(4, 6), , 47. Find the values of k so that the area of the, triangle with vertices (1, –1), (–4, 2k) and, (–k, –5) is 24 sq. units., [2015] ...[4M], 48. In figure, the vertices of ABC are A(4, 6),, B(1, 5) and C(7, 2). A line-segment DE is drawn, to intersect the sides AB and AC at D and E, AD AE 1, respectively such that, ,  . Calculate, AB AC 3, the area of ADE and compare it with area of, ABC., [2016] ...[4M], , D, , E, , B(1, 5), , C(7, 2), , 49. If the points A(k + 1, 2k), B(3k, 2k + 3) and, C(5k – 1, 5k) are collinear, then find the value, of k., [2017] ...[4M], , Chapter - 8 : Introduction to Trigonometry, 1., , If tan A , sec A., , 5, , find the value of (sin A + cos A), 12, [2008] ...[1M], , 2., , If sec2(1 + sin )(1 – sin ) = k, then find the, value of k., [2009] ...[1M], , 3., , If 3x = cosec and, , 3,  cot , find the value of, x, , , 1 , 3  x 2  2 ., x , , 4., , 11. Without using trigonometric tables, find the value, of the following expression, sec(90  ).cosec   tan (90  )cot ,  cos2 25  cos2 65, 3 tan27  tan63, , [2010] ...[2M], 12. Find the value of cosec 30° geometrically., , [2010] ...[1M], , What is the value of (cos267° – sin223°)?, [2018] ...[1M], , 5., , Find A if tan 2A = cot(A – 24°), , [2019] ...[1M], , 6., , Find the value of (sin233° + sin257°) [2019] ...[1M], , 7., , If sec 4A = cosec(A – 20°), where 4A is an, acute angle, find the value of A. [2008] ...[2M], , [2010] ...[2M], 13. Prove that : (1 + cot A + tan A)(sin A – cos A), = sin A tan A – cot A cos A., [2008] ...[3M], 14. Without using trigonometric tables, evaluate the, following :, , cos58 ,  cos38 cosec 52 , 2 ,  3, ,  sin32 ,  tan15 tan 60 tan75 , [2008] ...[3M], 15. Evaluate :, , 8., , 1, In a ABC, right-angled at C, if tanA , , find, 3, the value of sinA cos B + cosA sinB., , [2008] ...[2M], , 2, 2, 5, cosec 2 58  cot 58 tan32 – tan13, 3, 3, 3, tan37° tan45° tan53° tan77°, , [2009] ...[3M], , 16. Prove the following :, 9., , 15, , then evaluate, If cot  , 8, (2  2 sin )(1  sin ), ., (1  cos )(2  2cos ), , tan A, cot A, ,  1  tan A  cot A ., 1  cot A 1  tan A, , [2010] ...[3M], [2009] ...[2M], , 10. Find the value of tan 60°, geometrically., [2009] ...[2M], , 17. Prove the following :, , (cosec A  sin A)(sec A  cos A) , , 1, ., tan A  cot A, [2010] ...[3M], , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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Chapter-wise Previous Years' Questions (Class-10), , Mathematics, ,  4 sin   cos   1 , 18. If 4 tan = 3, evaluate , ,  4 sin   cos   1 , [2018] ...[3M], , 21. Prove that : (1 + cotA – cosecA) (1 + tanA +, secA) = 2., [2019] ...[3M], 22. Prove that, , 19. If tan2A = cot (A – 18°), where 2A is an angle,, find the value of A., [2018] ...[3M], 20. Prove that : (sin +, = 7 + tan2 + cot2., , cosec)2, , sec)2, , + (cos +, [2019] ...[3M], , 43, , 23. Prove that, , sin A  2sin3 A,  tan A [2018] ...[4M], 2cos3 A  cos A, , sin A  cos A  1, 1, , sin A  cosA  1 sec A  tan A, [2019] ...[4M], , Chapter - 9 : Some Applications of Trigonometry, 1., , 2., , A tower stands vertically on the ground. From a, point on the ground which is 25 m away from the, foot of the tower, the angle of elevation of the top, of the tower is found to be 45°. Then the height, (in meters) of the tower is, [2011] ...[1M], , 6., , A ladder leaning against a wall makes an angle, of 60º with the horizontal. If the foot of the, ladder is 2.5 m away from the wall, find the, length of the ladder., [2016] ...[1M], , (A) 25 2, , (B) 25 3, , 7., , If a tower 30 m high, casts a shadow 10 3 m, , (C) 25, , (D) 12.5, , The length of shadow of a tower on the plane, ground is 3 times the height of the tower. The, angle of elevation of Sun is, [2012] ...[1M], , 3., , 4., , (A) 45°, , (B) 30°, , (C) 60°, , (D) 90°, , The angle of depression of a car, standing on the, ground, from the top of a 75 m high tower, is, 30°. The distance of the car from the base of the, tower (in metre) is, [2013] ...[1M], (A) 25 3, , (B) 50 3, , (C) 75 3, , (D) 150, , A ladder makes an angle of 60º with the ground, when placed against a wall. If the foot of the, ladder is 2 m away from the wall, then the length, (in meters) is, [2014] ...[1M], (A), , 4, , (B) 4 3, , 3, , (C) 2 2, 5., , (D) 4, , long on the ground, then what is the angle of, elevation of the sun?, [2017] ...[1M], 8., , From the top of a vertical tower, the angles of, depression of two cars, in the same straight line, with the base of the tower, at an instant are, found to be 45° and 60°. If the cars are 100 m, in apart and are on the same side of the tower,, find the height of the tower. ( 3 = 1.73), [2011] ...[3M], , 9., , A kite is flying at a height of 45 m above the, ground. The string attached to the kite is, temporarily tied to a point on the ground. The, inclination of the string with the ground is 60°., Find the length of the string assuming that there, is no slack in the string., [2012] ...[3M], , 10. The horizontal distance between two poles is, 15 m. The angle of depression of the top of first, pole as seen from the top of second pole is 30°., If the height of the second pole is 24 m, find the, height of the first pole. [Use 3  1.732 ], , In the following figure, a tower AB is 20 m high, , [2013] ...[3M], , and BC, its shadow on the ground is 20 3 m, long. Find the Sun's altitude., [2015] ...[1M], , 11. Two ships are there in the sea on either side, of a light house in such a way that the ships, and the light house are in the same straight line., The angles of depression of two ships as, observed from the top of the light house are, 60º and 45º. If the height of the light house is, 200 m, find the distance between the two ships., Use 3  1.73 , [2014] ...[3M], , A, , , C, , B, , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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44, , Mathematics, , Chapter-wise Previous Years' Questions (Class-10), , 12. The angle of elevation of an aeroplane from, point A on the ground is 60º. After flight of 15, seconds, the angle of elevation changes to 30º., If the aeroplane is flying at a constant height of, 1500 3 m, find the speed of the plane in, km/hr., , [2015] ...[3M], , 19. An aeroplane is flying at a height of 300 m, above the ground. Flying at this height, the, angles of depression from the aeroplane of two, points on both banks of a river in opposite, directions are 45° and 30° respectively. Find the, width of the river. Use 3  1.732, [2017] ...[4M], , 13. A man standing on the deck of a ship, which is, 10 m above water level, observes the angle of, elevation of the top of a hill as 60º and the angle, of depression of the base of the hill as 30º. Find, the distance of the hill from the ship and the, height of the hill., [2016] ...[3M], 14. On a straight line passing through the foot of a, tower, two points C and D are at distances of, 4 m and 16 m from the foot respectively. If the, angles of elevation from C and D of the top of, the tower are complementary, then find the height, of the tower., [2017] ...[3M], 15. Two poles of equal heights are standing opposite, to each other on either side of the roads, which, is 80 m wide. From a point between them on, the road, the angles of elevation of the top of the, poles are 60º and 30º respectively. Find the, height of the poles and the distances of the, point from the poles., [2013] ...[4M], 16. The angles of elevation and depression of the top, and the bottom of a tower from the top of a, building, 60 m high, are 30° and 60° respectively., Find the difference between the heights of the, building and the tower and the distance between, them., [2014] ...[4M], 17. At a point A, 20 metres above the level of water, in a lake, the angle of elevation of a cloud is, 30º. The angle of depression of the reflection of, the cloud in the lake, at A is 60º. Find the, distance of the cloud from A., [2015] ...[4M], 18. The angle of elevation of the top Q of a vertical, tower PQ from a point X on the ground is 60º., From a point Y, 40 m vertically above X, the, angle of elevation of the top Q of tower is 45º., Find the height of the tower PQ and the distance, PX. Use 3  1.73 , , [2016] ...[4M], , 20. As observed from the top of a 100 m high light, house from the sea-level, the angles of, depression of two ships are 30° and 45°. If one, ship is exactly being the other on the same side, of the light house, find the distance between the, two ships. Use 3  1.732, [2018] ...[4M], 21. A man in a boat rowing away from a light house, 100 m high takes 2 minutes to change the angle, of elevation of the top of the light house from, 60° to 30°. Find the speed of the boat in metres, per minute. Use 3  1.732, , [2019] ...[4M], , 22. The angle of elevation of an aeroplane from a, point A on the ground is 60°. After a flight of, 30 seconds, the angle of elevation changes to, 30°. If the plane is flying at a constant height of, , 3600 3 m , then find the speed (in km/hour) of, the plane., , [2008] ...[6M], , 23. An aeroplane when flying at a height 3125 m, from the ground passes vertically below another, plane at that instant when the angles of elevation, of the two planes from the same point on the, ground are 30° and 60° respectively. Find the, distance between the two planes at that instant., [2009] ...[6M], 24. From the top of a 7 m high building, the angle, of elevation of the top of a tower is 60° and the, angle of depression of the foot of the tower is, 45°. Find the height of the tower. [2010] ...[6M], 25. The angle of elevation of the top of a vertical, tower from a point on the ground is 60°. From, another point 10 m vertically above the first, its, angle of elevation is 30°. Find the height of the, tower., [2011] ...[6M], 26. The angle of elevation of the top of a hill from the, foot of a tower is 60° and the angle of, depression from the top of the tower to the foot, of the hill is 30°. If the tower is 50 m high, find, the height of the hill., [2012] ...[6M], , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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Chapter-wise Previous Years' Questions (Class-10), , Mathematics, , 45, , Chapter - 10 : Circles, 1., , In figure, ABC is circumscribing a circle. Find, the length of BC., [2009, 2012] ...[1M], A, , 5., , 4 cm, Q 11 cm, , R, , In below figure, a circle with centre O is, inscribed in a quadrilateral ABCD such that, it, touches the sides BC, AB, AD and CD at point, P, Q, R and S respectively. If AB = 29 cm, AD, = 23 cm, B = 90° and DS = 5 cm, then the, radius of the circle (in cm) is, [2013] ...[1M], , 3 cm, D, , C, P, If figure, O is the centre of a circle, PQ is a chord, and PT is the tangent at P. If POQ = 70°, then, TPQ is equal to, [2011] ...[1M], B, , 2., , T, O, , 6., , (A) 55°, (B) 70°, (C) 45°, (D) 35°, In figure, AB and AC are tangents to the circle, with center O such that BAC = 40°. Then, BOC is equal to, [2011] ...[1M], , 40°, , (B) 18, , (C) 6, , (D) 15, , In below figure, PA and PB are two tangents, drawn from an external point P to a circle with, centre C and radius 4 cm. If PA  PB, then the, length of each tangent is, [2013] ...[1M], , A, , C, , (A) 40°, (B) 50°, (C) 140°, (D) 160°, In figure, a circle touches the side DF of EDF, at H and touches ED and EF produced at K, and M respectively. If EK = 9 cm, then the, perimeter of EDF (in cm) is, [2012] ...[1M], E, , D, K, , (A) 18, (C) 12, , P, B, , O, , C, , 4., , B, , P, , (A) 11, , B, , A, , H, , Q, , r, C, , Q, , r, , O, , S, , P, , 3., , A, , R, , 7., , (A) 3 cm, , (B) 4 cm, , (C) 5 cm, , (D) 6 cm, , In figure, QR is a common tangent to the given, circles, touching externally at the point T. The, tangent at T meets QR at P. If PT = 3.8 cm,, then the length of QR (in cm) is [2014] ...[1M], Q, , P, , R, , T, , F, M, , (B) 13.5, (D) 9, , (A) 3.8, , (B) 7.6, , (C) 5.7, , (D) 1.9, , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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46, 8., , Mathematics, , Chapter-wise Previous Years' Questions (Class-10), , In figure, PQ and PR two tangents to a circle, with centre O. If QPR = 46°, QOR equals:, [2014] ...[1M], Q, , 14. Tangents PA and PB are drawn from an external, point P to two concentric circle with centre O, and radii 8 cm and 5 cm respectively, as shown, in figure, if AP = 15 cm, then find the length of, BP., [2012] ...[2M], , A, 46º, , O, , P, , P, , O, R, , 9., , B, , (A) 67°, , (B) 134°, , (C) 44°, , (D) 46°, , In the following figure, PQ is a chord of a circle, with centre O and PT is a tangent. If QPT =, 60°, find PRQ, [2015] ...[1M], , 15. In figure, an isosceles triangle ABC, with, AB = AC, circumscribes a circle. Prove that the, point of contact P bisects the base BC., [2012] ...[2M], , A, , Q, O, , R, P, , T, , 10. In the figure, PQ is a tangent at a point C to a, circle with centre O. If AB is a diameter and, CAB = 30º, find PCA., [2016] ...[1M], C, , O, , B, , C, , P, , 16. In figure, the chord AB of the larger of the two, concentric circles, with centre O, touches the, smaller circle at C. Prove that AC = CB., , P, , A, , Q, , R, , [2012] ...[2M], , Q, , B, , O, , 11. If the angle between two tangents drawn from an, external point P to a circle of radius a and, centre of O, is 60°, then find the length of OP., [2017] ...[1M], 12. If all the sides of a parallelogram touch a circle,, show that the parallelogram is a rhombus., [2008, 2010, 2012] ...[3M], [2013, 2014] ...[2M], , A, , C, , C, , A, B, , B, , 17. In below figure, a circle is inscribed in triangle, ABC touches its sides AB, BC and AC at points, D, E and F respectively. If AB = 12 cm, BC =, 8 cm and AC = 10 cm, then find the length of, AD, BE and CF., [2013] ...[2M], , 13. In figure, a circle touches all the four sides of a, quadrilateral ABCD whose sides are AB = 6 cm,, BC = 9 cm and CD = 8cm, find the length of, side AD., [2011] ...[2M], , D, , C, , E, , F, , A, , D, , B, , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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Chapter-wise Previous Years' Questions (Class-10), , Mathematics, , 18. Prove that the line segment joining the point of, contact of two parallel tangents of a circle, passes through its centre., [2014] ...[2M], 19. If from an external point P of a circle with centre, O, two tangents PQ and PR are drawn such, that QPR = 120º, prove that 2PQ = PO., , 47, , 23. In figure, from an external point P, two tangents, PT and PS are drawn to a circle with centre O, and radius r. If OP = 2r, show that OTS =, OST = 30º, [2016] ...[2M], T, , [2014] ...[2M], , O, , 20. In the following figure, two tangents RQ and RP, are drawn from an external point R to the circle, with centre O, if PRQ = 120º, then prove that, OR = PR + RQ., [2015] ...[2M], , Q, , P, , S, , 24. Prove that the tangents drawn at the end points, of a chord of a circle make equal angles with, the chord., [2017] ...[2M], , P, O, , 25. A circle touches all the four sides of a quadrilateral, ABCD. Prove that AB + CD = BC + DA., , R, , [2017] ...[2M], Q, , 21. In figure, a ABC is drawn to circumscribe a, circle of radius 3 cm, such that the segments, BD and DC are respectively of lengths 6 cm and, 9 cm. If the area of ABC is 54 cm2, then find, the lengths of sides AB and AC. [2015] ...[2M], , 26. In given figure, a triangle PQR is drawn to, circumscribe a circle of radius 6 cm such that, the segments QT and TR into which QR is, divided by the point of contact T, are of lengths, 12 cm and 9 cm respectively. If the area of, PQR = 189 cm2, then find the lengths of sides, PQ and PR., [2011] ...[3M], P, , A, , O, , O, , 3 cm, , B, , 6 cm, , D, , 9 cm, , C, , Q, , 22. In figure, a quadrilateral ABCD is drawn to, circumscribe a circle, with centre O, in such a, way that the sides AB, BC, CD and DA touch, the circle at the points P, Q, R and S, respectively. Prove that AB + CD = BC + DA., [2012[4], 2016] ...[2M], D, , R, , S, , 27. Prove that opposite sides of a quadrilateral, circumscribing a circle subtend supplementary, angles at the centre of the circle. [2012] ...[3M], 28. In Figure, PQ is a chord of length 8 cm of a, circle of radius 5 cm and centre O. The tangents, at P and Q intersect at point T. Find the length, of TP., [2019] ...[3M], , C, , P, , Q, , 5, , O, , A, , P, , R, , T, , B, , T, , 8, , O, Q, , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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48, , Mathematics, , Chapter-wise Previous Years' Questions (Class-10), , 29. Prove that the tangent at any point of a circle is, perpendicular to the radius through the point of, contact., [2011, 2012, 2013] ...[4M], 30. In figure, I and m are two parallel tangents to a, circle with centre O, touching the circle at A and, B respectively. Another tangent at C intersects, the line I at D and m at E. Prove that, DOE = 90º, [2013] ...[4M], A, , D, , 34. In the given figure, XY and XY are two parallel, tangents to a circle with centre O and another, tangent AB with point of contact C, is, intersecting XY at A and XY at B. Prove that, AOB = 90°., [2017] ...[4M], X, , P, , A, , Y, , O, , l, , C, O, , C, B, , Q, , X, m, , E, , 31. Prove that the length of the tangents drawn from, an external point to a circle are equal., , ABC is an isosceles triangle in which AB = AC,, circumscribed about a circle, as shown in figure,, Prove that the base is bisected by the point of, contact., [2008] ...[6M], , 32. Prove that the tangent drawn at the midpoint of, an arc of a circle is parallel to the chord joining, the end points of the arc., [2015] ...[4M], , A, , 33. In figure, two equal circles, with centres O and, O, touch each other at X. OO produced meets, the circle with centre O at A. AC is tangent to, the circle with centre O, at the point C. OD is, , R, , DO , perpendicular to AC. Find the value of, ., CO, [2016] ...[4M], , B, , Q, , P, , C, , 36. Prove that the lengths of the tangents drawn, from an external point to a circle are equal., , C, D, O, , Y, , 35. Prove that the lengths of tangents drawn from an, external point to a circle are equal. Using the, above, prove the following :, , [2014, 2015, 2016, 2017] ...[4M], , A, , B, , Using the above theorem prove that:, X, , O, , If quadrilateral ABCD is circumscribing a circle,, then AB + CD = AD + BC., [2009] ...[6M], , Chapter - 11 : Constructions, 1., , Draw a line-segment AB of length 7 cm. Using, ruler and compasses, find a point P on AB such, that, , 2., , AP, 3,  ., AB, 5, , [2011] ...[2M], , Draw a right triangle in which the sides containing, the right angle are 5 cm and 4 cm. Construct a, similar triangle whose sides are, sides of the given triangle., , 3., , 5, times the, 3, , [2008] ...[3M], , 4., , Draw a right triangle in which sides (other than, hypotenuse) are of length 8 cm and 6 cm. The, 3, construct another triangle whose sides are, 4, times the corresponding sides of the first, triangle., [2009] ...[3M], Construct a triangle ABC in which BC = 8 cm,, B = 45° and C = 30°. Construct another, triangle similar to ABC such that its sides are, 3, of the corresponding sides of ABC., 4, [2010] ...[3M], , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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Chapter-wise Previous Years' Questions (Class-10), , Mathematics, , 49, , 5., , Draw a pair of tangents to a circle of radius 3, cm, which are inclined to each other at an angle, of 60°., [2011] ...[3M], , 10. Construct a ABC in which AB = 6 cm,, A = 30º and B = 60º, construct another, ABC similar to ABC with base AB = 8 cm., , 6., , Draw a right triangle in which the sides (other, than hypotenuse) are of lengths 4 cm and 3 cm., Then construct another triangle whose sides are, 3, times the corresponding sides of the given, 5, triangle., [2011] ...[3M], , [2015] ...[4M], , 7., , 8., , 9., , Draw a triangle ABC with side BC = 6 cm,, C = 30° and A = 105°. Then construct, 2, times the, another triangle whose sides are, 3, corresponding sides of ABC., [2012] ...[3M], Construct a tangent of a circle of radius 4 cm, from a point on the concentric circle of radius, 6 cm., [2013] ...[3M], Draw a right triangle ABC in which AB = 6 cm,, BC = 8 cm and B = 90º. Draw BD, perpendicular from B on AC and draw a circle, passing through the points B, C and D., Construct tangents from A to this circle., , 11. Draw a circle of radius 4 cm. Draw two tangents, to the circle inclined at an angle of 60° to each, other., [2016] ...[4M], 12. Construct a triangle ABC with side BC = 7 cm,, B = 45°, A = 105°. Then construct another, 3, times the, 4, corresponding sides of the ABC. [2017]...[4M], , triangle whose sides are, , 13. Draw a triangle ABC with BC = 6 cm, AB = 5, cm and ABC = 60°. Then construct a triangle, whose sides are, of the ABC., , 3, of the corresponding sides, 4, [2018] ...[4M], , 14. Construct a ABC in which CA = 6 cm,, AB = 5 cm and BAC = 45°. Then construct a, triangle whose sides are, sides of ABC., , [2014] ...[3M], , 3, of the corresponding, 5, [2019] ...[4M], , Chapter - 12 : Areas Related to Circles, 1., , If the diameter of a semicircular protractor is, 14 cm, then find its perimeter., [2009] ...[1M], , 2., , The perimeter (in cm) of a square circumscribing, a circle of radius a cm, is, [2011] ...[1M], , 3., , 4., , (A) 8a, , (B) 4a, , (C) 2a, , (D) 16a, , If the area of a circle is equal to sum of the, areas of two circles of diameters 10 cm and, 24 cm, then the diameter of the larger circle, (in cm) is, [2012] ...[1M], (A) 34, , (B) 26, , (C) 17, , (D) 14, , If the difference between the circumference and, the radius of a circle is 37 cm, then using, , 5., , Find the perimeter of the shaded region in figure,, if ABCD is a square of side 14 cm and APB and, 22 , CPD are semicircles.  Use  ,  [2011]...[2M], 7 , , , P, , A, , 6., ,  Use   22 , , , 7 , , C, , 22, , the circumference of the circle is, 7, (in cm), [2013] ...[1M], (B) 44, , (C) 14, , (D) 7, , B, , In figure, OABC is a square of side 7 cm. If, OAPC is a quadrant of a circle with centre O,, then find the area of the shaded region., , , , (A) 154, , C, , D, , [2012] ...[2M], B, P, , O, , A, , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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50, 7., , 8., , Mathematics, , Chapter-wise Previous Years' Questions (Class-10), , Two circular pieces of equal radii and maximum, area, touching each other are cut out from a, rectangular card board of dimensions 14 cm ×, 7 cm. Find the area of the remaining card board., , 12. A chord of a circle of radius 14 cm subtends an, angle of 120° at the centre. Find the area of the, corresponding minor segment of the circle., ,  Use   22 , [2013] ...[2M], , , 7 , , In figure, a square OABC is inscribed in a, quadrant OPBQ of a circle. If OA = 20 cm, find, the area of the shaded region (Use  = 3.14)., , [2011] ...[3M], , [2014] ...[2M], Q, B, , C, , Use   22 and, , 7, , 3  1.73 , , , 13. In figure, PQ and AB are respectively the arcs of, two concentric circles of radii 7 cm and 3.5 cm, and centre O. If POQ = 30°, then find the area, 22 , of the shaded region.  Use  ,  [2012]...[3M], 7 , , P, A, , 30°, , O, , B, O, , 9., , A, , P, , In figure, ABC is a quadrant of a circle of radius, 14 cm and a semicircle is drawn with BC as, diameter. Find the area of the shaded region., [2008] ...[3M], , 14. In a circle of radius 21 cm, an arc subtends an, angle of 60° at the centre. Find (i) the length of, the arc (ii) area of the sector formed by the arc., ,  Use   22 , , , 7 , , , [2013] ...[3M], , 15. In below figure, AB and CD are two diameters of, a circle with centre O, which are perpendicular, to each other. OB is the diameter of the smaller, circle. If OA = 7 cm, find the area of the shaded, , B, , A, , Q, , 22 , region.  Use  , , 7 , , , C, , [2013] ...[3M], , C, , 10. The area of an equilateral triangle is 49 3 cm2., Taking each angular point as centre, circles are, drawn with radius equal to half the length of the, side of the triangle. Find the area of triangle not, , O, , B, , included in the circle. Take 3  1.73 , , A, , [2009] ...[3M], 11. In below figure, the boundary of shaded region, consists of four semicircular arcs, two smallest, being equal. If diameter of the largest is 14 cm, and that of the smallest is 3.5 cm, calculate the, , 22 , area of the shaded region. Use  , 7 , , [2010] ...[3M], , D, 16. In figure, PSR, RTQ and PAQ are three, semicircles of diameters 10 cm, 3 cm and 7 cm, respectively. Find the perimeter of the shaded, region. [Use  = 3.14], [2014] ...[3M], S, A, , P, , Q, 7 cm, , R, , 3 cm, , T, , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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Chapter-wise Previous Years' Questions (Class-10), , Mathematics, , 51, , 17. If a circle is inscribed in an equilateral triangle, ABC of side 12 cm. Find the radius of inscribed, circle and the area of the shaded region., Use   3.14 and, , , 3  1.73 , , [2014]...[3M], 3 cm, , A, , 3 cm, , 3 cm, , 22. In the given figure, two concentric circles with, centre O have radii 21 cm and 42 cm. If, AOB = 60°, find the area of the shaded region., , O, , B, , C, , 22 , , Use   7 , , [2017] ...[3M], C1, , 18. Find the area of the minor segment of a circle, of radius 14 cm, when its central angle is 60º., Also find the area of the corresponding major, 22 , , [2015] ...[3M], segment. Use  , , 7 , 19. In figure, O is the centre of a circle such that, diameter AB = 13 cm and AC = 12 cm. BC is, joined. Find the area of the shaded region., (Take  = 3.14), [2016] ...[3M], A, , O, , C2, , C 60º D, A, , B, , 23. Find the area of the shaded region in figure,, where arcs drawn with centres A, B, C and D, intersect in pairs at midpoints P, Q, R and S of, the sides AB, BC, CD and DA respectively of a, square of side 12 cm. [Use  = 3.14], , O, , B, , [2018] ...[3M], A, , C, , 20. In figure, find the area of the shaded region,, enclosed between two concentric circles of radii, 7 cm and 14 cm where AOC = 40°., 22 , , Use   7 , , P, , B, , S, , Q, , [2016] ...[3M], R, , D, , C, , 24. Find the area of the shaded region in given, figure 4, if ABCD is a rectangle with sides 8 cm, and 6 cm and O is the centre of circle., (Take  = 3.14), , O, , [2019] ...[3M], B, A, , 40º, , D, , C, , D, 6, , 21. Three semicircles each of diameter 3 cm, a, circle of diameter 4.5 cm and a semicircle of, radius 4.5 cm are drawn in the given figure. Find, the area of the shaded region., [2017] ...[3M], , A, , C, , 8, O, , B, , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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52, , Mathematics, , Chapter-wise Previous Years' Questions (Class-10), , B, , 25. Find the area of the shaded region in figure, if, AC = 24 cm, BC = 10 cm and O is the centre, of the circle. [Use  = 3.14], [2010] ...[4M], , P, , A, , O, , , , r, , A, , O, , 28. In the given figure, ABCD is a rectangle of, dimensions 21 cm × 14 cm. A semicircle is, drawn with BC as diameter. Find the area and, the perimeter of the shaded region in the figure., , C, , B, , [2017] ...[4M], , 26. In the following figure, PQRS is square lawn with, side PQ = 42 metres. Two circular flower beds, are there on the sides PS and QR with centre, at O, the intersections of its diagonals. Find the, total area of the two flower beds (shaded parts)., , A, , B, , 21 cm, , 14 cm, , [2015] ...[4M], S, , R, O, , P, , Q, , Use   22 , , 7 , , 27. In figure, is shown a sector OAP of a circle with, centre O, containing . AB is perpendicular to, the radius OA and meets OP produced at B., Prove that the perimeter of shaded region is, , , , r  tan   sec  , 1 ., 180 , , , C, , D, , 29. In below figure, three circles each of radius 3.5, cm are drawn in such a way each of them, touches the other two. Find the area enclosed, between these three circles (shaded region)., [2011] ...[6M], , [2016] ...[4M], , Chapter - 13 : Surface Areas and Volumes, 1., , The surface area of a sphere is 616 cm2. Find, its radius., [2008] ...[1M], , 2., , The slant height of a frustum of a cone is 4 cm, and the perimeters (circumferences) of its, circular ends are 18 cm and 6 cm. Find the, curved surface area of the frustum., 22, (Use  , ), [2010]...[1M], 2017...[3M], 7, , 3., , The radius (in cm) of the largest right circular, cone that can be cut out from a cube of edge, 4.2 cm is, [2011] ...[1M], , 4., , (A) 4.2, , (B) 2.1, , (C) 8.4, , (D) 1.05, , If the radius of the base of a right circular, cylinder is halved, keeping the height same, then, the ratio of the volume of the cylinder thus, obtained to the volume of original cylinder is, [2012] ...[1M], (A) 1 : 2, , (B) 2 : 1, , (C) 1 : 4, , (D) 4 : 1, , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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Chapter-wise Previous Years' Questions (Class-10), , 5., , The number of solid spheres, each of diameter, 6 cm that can be made by melting a solid metal, cylinder of height 45 cm and diameter 4 cm is, [2014] ...[1M], (A) 3, , (B) 5, , (C) 4, , (D) 6, , Two cubes each of volume 27 cm3 are joined, end to end to form a solid. Find the surface area, of the resulting cuboid., [2011] ...[2M], , 7., , A cone of height 20 cm and radius of base 5 cm, is made up of modelling clay. A child reshapes, it in the form of a sphere. Find the diameter of, the sphere., [2011] ...[2M], , 1, cm3. Find, 2, 22 , , its curved surface area. Use  , 7 , , , The volume of a hemisphere is 2425, , [2012] ...[2M], 9., , An open metal bucket is in the shape of a, frustum of a cone of height 21 cm with radii of, its lower and upper ends as 10 cm and 20 cm, respectively. Find the cost of milk which can, completely fill the bucket at ` 30 per litre., , Use   22 , , 7 , , [2011] ...[3M], , 10. From a solid cylinder of height 7 cm and base, diameter 12 cm, a conical cavity of same height, and same base diameter is hollowed out. Find, the total surface area of the remaining solid., Use   22 , 7 , , , [2012] ...[3M], , 11. A cylindrical bucket, 32 cm high and with radius, of base 18 cm, is filled with sand. This bucket, is emptied on the ground and a conical heap of, sand is formed. If the height of the conical heap, is 24 cm, then find the radius and slant height, of the heap., [2012] ...[3M], 12. A vessel is in the form of hemispherical bowl, surmounted by a hollow cylinder of same, diameter. The diameter of the hemispherical bowl, is 14 cm and the total height of the vessel is, 13 cm. Find the total surface area of the vessel., Use   22 , , 7 , , 53, , 13. A wooden toy was made by scooping out a, hemisphere of same radius from each end of a, solid cylinder. If the height of the cylinder is, 10 cm, and its base is of radius 3.5 cm, find, 22 , , the volume of wood in the toy. Use  , 7 , , [2013] ...[3M], , 6., , 8., , Mathematics, , [2013] ...[3M], , 14. A farmer connects a pipe of internal diameter, 20 cm from a canal into cylindrical tank which, is 10 m in diameter and 2 m deep. If the water, flows through the pipe at the rate of 4 km per, hour, in how much time will the tank be filled, completely?, [2014] ...[3M], 15. A solid metallic right circular cone 20 cm high, and whose vertical angle is 60°, is cut into two, parts at the middle of its height by a plane, parallel to its base. If the frustum so obtained be, drawn into a wire of diameter, length of the wire., , 1, cm, find the, 12, [2014] ...[3M], , 16. Due to sudden floods, some welfare associations, jointly requested the government to get 100, tents fixed immediately and offered to contribute, 50% of the cost. If the lower part of each tent, is of the form of a cylinder of diameter 4.2 m, and height 4 m with the conical upper part of, same diameter but height 2.8 m, and the canvas, to be used costs ` 100 per sq. m, find the, amount, the association will have to pay. What, values are shown by these association?, 22 , , [2015] ...[3M], Use   7 , 17. A hemispherical bowl of internal diameter 36 cm, contains liquid. This liquid is filled into 72, cylindrical bottles of diameter 6 cm. Find the, height of each bottle, if 10% liquid is wasted in, this transfer., [2015] ...[3M], , 18. A cubical block of side 10 cm is surmounted by, a hemisphere. What is the largest diameter that, the hemisphere can have? Find the cost of, painting the total surface area of the solid so, formed, at the rate of ` 5 per sq. cm., [Use  = 3.14], [2015] ...[3M], 19. 504 cones, each of diameter 3.5 cm and height, 3 cm, are melted and recast into a metallic, sphere, find the diameter of the sphere and, 22 , , hence find its surface area. Use  , , 7 , [2015] ...[3M], , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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54, , Mathematics, , Chapter-wise Previous Years' Questions (Class-10), , 20. In figure, a tent is in the shape of a cylinder, surmounted by a conical top of same diameter., If the height and diameter of cylindrical part are, 2.1 m and 3 m respectively and the slant height, of conical part is 2.8 m, find the cost of canvas, needed to make the tent if the canvas is, available at the rate of ` 500/sq. metre., 22 , , Use   7 , , 25. A wooden article was made by scooping out a, hemisphere from each end of a solid cylinder, as, shown in figure. If the height of the cylinder is 10, cm and its base is of radius 3.5 cm. Find the, total surface area of the article. [2018] ...[3M], , [2016] ...[3M], , 2.8 m, , 26. A heap of rice is in the form of a cone of base, diameter 24 m and height 3.5 m. Find the, volume of the rice. How much canvas cloth is, required to just cover the heap? [2018] ...[3M], , 2.1 m, , 27. Water in a canal, 6 m wide and 1.5 m deep, is, flowing with a speed of 10 km/hour. How much, area will it irrigate in 30 minutes; if 8 cm, standing water is needed?, [2019] ...[3M], , 3m, , 21. A conical vessel, with base radius 5 cm and, height 24 cm, is full of water. This water is, emptied into a cylindrical vessel of base radius, 10 cm. Find the height to which the water will, 22 , , rise in the cylindrical vessel.  Use  , , , 7 , , [2016] ...[3M], , 28. Figure shows a decorative block which is made, of two solids – a cube and a hemisphere. The, base of the block is a cube with edge 5 cm, and the hemisphere, fixed on the top, has a, diameter of 4.2 cm. Find the total 2 surface area, 22 , of the block. Take  , 7 , , , [2009] ...[4M], , 22. A sphere of diameter 12 cm, is dropped in a right, circular cylindrical vessel, partly filled with water., If the sphere is completely submerged in water,, the water level in the cylindrical vessel rises by, 5, cm. Find the diameter of the cylindrical, 9, vessel., [2016] ...[3M], 3, , 23. In a canal, 5.4 m wide and 1.8 m deep, water, is flowing with a speed of 25 km/hr. How much, area can it irrigate in 40 minutes, if 10 cm of, standing water is required for irrigation?, [2017] ...[3M], 24. The dimensions of a solid iron cuboid are 4.4 m, × 2.6 m × 1.0 m. It is melted and recast into a, hollow cylindrical pipe of 30 cm inner radius and, thickness 5 cm. Find the length of the pipe., [2017] ...[3M], , 29. Water is flowing through a cylindrical pipe, of, internal diameter 2 cm, into a cylindrical tank of, base radius 40 cm, at the rate of 0.4 m/s., Determine the rise in level of water in the tank, in half an hour., [2013] ...[4M], 30. A bucket open at the top, and made up of a, metal sheet is in the form of a frustum of a, cone. The depth of the bucket is 24 cm and the, diameters of its upper and lower circular ends, are 30 cm and 10 cm respectively. Find the cost, , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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Chapter-wise Previous Years' Questions (Class-10), , of metal sheet used in it at the rate of ` 10 per, 100 cm2. [Use  = 3.14], [2013] ...[4M], 15 cm, , 24 cm, , Mathematics, , 55, , 35. In a rainwater harvesting system, the rainwater, from a roof of 22 m × 20 m drains into a, cylindrical tank having diameter of base 2 m and, height 3.5 m. If the tank is full, find the rainfall, in cm., [2017] ...[4M], 36. The diameters of the lower and upper ends of a, bucket in the form of a frustum of a cone are, 10 cm and 30 cm respectively. If its height is, 24 cm, find :, [2018] ...[4M], (i) The area of the metal sheet used to make, the bucket., , 5 cm, , 31. Sushant has a vessel, of the form of an inverted, cone, open at the top, of height 11 cm and, radius of top as 2.5 cm and is full of water., Metallic spherical balls each of diameter 0.5 cm, , 2, th of the, 5, water in the vessel flows out. Find how many, balls were put in the vessel. Sushant made the, arrangement so that the water that flows out, irrigates the flower beds. What value has been, shown by Sushant?, [2014] ...[4M], are put in the vessel due to which, , 32. From a solid cylinder of height 2.8 cm and, diameter 4.2 cm a conical cavity of the same, height and same diameter is hollowed out. Find, the total surface area of the remaining solid., [Take  = 22/7], [2014] ...[4M], 33. From each end of a solid metal cylinder, metal, was scooped out in hemispherical form of same, diameter. The height of the cylinder is 10 cm, and its base is of radius 4.2 cm. The rest of the, cylinder is melted and converted into a, cylindrical wire of 1.4 cm thickness. Find the, , (ii) Why we should avoid the bucket made by, ordinary plastic? [Use  = 3.14], 37. A bucket open at the top is in the form of a, frustum of a cone with a capacity of 12308.8, cm3. The radii of the top and bottom of circular, ends of the bucket are 20 cm and 12 cm, respectively. Find the height of the bucket and, also the area of the metal sheet used in making, it. (Use  = 3.14), [2019] ...[4M], 38. If the radii of the circular ends of a conical, bucket, which is 16 cm high, are 20 cm and 8, cm, find the capacity and total surface area of, 22 , the bucket. Use  , 7 , , , [2008] ...[6M], , 39. A juice seller serves his customers using a, glass as shown in figure. The inner diameter of, the cylindrical glass is 5 cm, but the bottom of, the glass has a hemispherical portion raised, which reduces the capacity of the glass. If the, height of the glass is 10 cm, find the apparent, capacity of the glass and its actual capacity., (Use  = 3.14), [2009] ...[6M], , 22 , , length of the wire. Use  , [2015] ...[4M], , 7 , , 34. Due to heavy floods in a state, thousands were, rendered homeless. 50 schools collectively, offered to the state government to provide place, and the canvas for 1500 tents to be fixed by, the governments and decided to share the whole, expenditure equally. The lower part of each tent, is cylindrical of base radius 2.8 cm and height, 3.5 m, with conical upper part of same base, radius but of height 2.1 m. If the canvas used to, make the tents costs ` 120 per sq. m, find the, amount shared by each school to set up the, tents. What value is generated by the above, 22 , , problem?  Use  , , , 7 , , 40. A cylindrical vessel with internal diameter 10 cm, and height 10.5 cm is full of water. A solid cone, of base diameter 7 cm and height 6 cm is, completely immersed in water. Find the volume of, (i) Water displaced out of the cylindrical vessel., (ii) Water left in the cylindrical vessel., , [2016] ...[4M], , [2009] ...[6M], , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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56, , Mathematics, , Chapter-wise Previous Years' Questions (Class-10), , 41. A milk container is made of metal sheet in the, shape of frustum of a cone whose volume is, 3, 10459 cm3. The radii of its lower and upper, 7, circular ends are 8 cm and 20 cm respectively., Find the cost of metal sheet used in making the, container at the rate of ` 1.40 per square, , 22 , , centimeter. Use  , [2010] ...[6M], 7 , , 42. A toy is in the form of a hemisphere surmounted, by a right circular cone of the same base radius, as that of the hemisphere. If the radius of base, 2, of the cone is 21 cm and its volume is, of the, 3, volume of the hemisphere, calculate the height, of the cone and the surface area of the toy., [2010] ...[6M], , 43. Water is flowing at the rate of 15 km/hour, through a pipe of diameter 14 cm into a, cuboidal pond which is 50 m long and 44 m, wide. In what time will the level of water in the, pond rise by 21 cm?, [2011] ...[6M], 44. A bucket is in the form of a frustum of a cone, and it can hold 28.49 litres of water. If the radii, of its circular ends are 28 cm and 21 cm, find, , 22 , the height of the bucket. Use  , 7 , , [2012] ...[6M], 45. A solid is in the shape of a cone standing on a, hemisphere with both their radii being equal to, 7 cm and the height of the cone is equal to its, diameter. Find the volume of the solid., Use   22 , [2012] ...[6M], , 7 , , Chapter - 14 : Statistics, 1., , Find the class marks of classes 10 – 25 and, 35 – 55., [2008] ...[1M], , 2., , The table below shown the salaries of 280, persons :, [2018] ...[3M], , Salary (In thousand), , 4., , The mean of the following distribution is 18. Find, the frequency f of the class 19 – 21.[2018]...[4M], , Class, , Frequency, , 11 – 13, , 3, , No. of Person, , 13 – 15, , 6, , 5 – 10, , 49, , 15 – 17, , 9, , 10 – 15, , 133, , 15 – 20, , 63, 15, , 17 – 19, 19 – 21, , 13, f, , 21 – 23, , 5, , 23 – 25, , 4, , 20 – 25, 25 – 30, 30 – 35, , 6, 7, , 35 – 40, , 4, , 40 – 45, , 2, , 45 – 50, , 1, , 5., , The following distribution gives the daily income, of 50 workers of a factory :, [2018] ...[4M], , Calculate the median salary of the data., 3., , Find the mode of the following frequency, distribution., [2019] ...[3M], , Class, , Frequency, , 0 - 10, , 8, , 10 - 20, , 10, , 20 - 30, , 10, , 30 - 40, , 16, , 40 - 50, , 12, , 50 - 60, , 6, , 60 - 70, , 7, , Daily, income (In), , Number, of workers, , 100 – 120, , 12, , 120 – 140, , 14, , 140 – 160, , 8, , 160 – 180, , 6, , 180 – 200, , 10, , Convert the distribution above to a less than type, cumulative frequency distribution and draw its, ogive., , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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Chapter-wise Previous Years' Questions (Class-10), , 6., , If the median of the following frequency, distribution is 32.5. Find the values of f1 and f2., Class, Frequency, , 7., , Mathematics, , 9., , During the medical check-up of 35 students of, a class their weights were recorded as follows:, , 0-10 10-20 20-30 30-40 40-50 50-60 60-70 Total, , f1, , 5, , 9, , 12, , f2, , 3, , 2, , 40, , [2019] ...[4M], The marks obtained by 100 students of a class, in an examination are given below., , Weight (in kg) Number of students, 38  40, 3, 40, 42, 44, 46, , Marks, , 8., , 57, , 0–5, , 2, , 5 – 10, , 5, , 10 – 15, , 6, , 15 – 20, , 8, , 20 – 25, , 10, , 25 – 30, , 25, , 30 – 35, , 20, , 35 – 40, , 18, , 40 – 45, , 4, , 45 – 50, , 2, , 42, 44, 46, 48, , 2, 4, 5, 14, , 48  50, 50  52, , 4, 3, , Draw a less than type and a more than type, ogive from the given data. Hence obtain the, median weight from the graph., [2009] ...[6M], , Draw ‘a less than’ type cumulative frequency, curves (ogive). Hence find median.[2019] ...[4M], Find mean, median and mode of the following, data:, [2008] ...[6M], , 10. Find the mean, mode and median of the, following frequency distribution: [2010] ...[6M], , Class, , Classes Frequency, 0  20, 6, 20  40, 8, 40  60, 10, 60  80, 80  100, 100  120, 120  140, , , , , , , 12, 6, 5, 3, , Frequency, , 0 – 10, , 4, , 10 – 20, , 4, , 20 – 30, , 7, , 30 – 40, 40 – 50, , 10, 12, , 50 – 60, , 8, , 60 – 70, , 5, , Chapter - 15 : Probability, , 1., , A die is thrown once. Find the probability of, getting a number less than 3., , 2., , [2008] ...[1M], , 4., , A card is drawn from a well-shuffled deck of 52, playing cards. The probability that the card will, not be an ace is, [2011] ...[1M], (A), , 1, 13, , [2009] ...[1M], , (B), , 1, 4, , A card is drawn at random from a well shuffled, , (C), , 12, 13, , (D), , 3, 4, , Two coins are tossed simultaneously. Find the, probability of getting exactly one head., , 3., , pack of 52 playing cards. Find the probability of, getting a red face card., , [2010] ...[1M], , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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58, 5., , Mathematics, , Chapter-wise Previous Years' Questions (Class-10), , Two dice are thrown together. The probability of, getting the same number on both dice is, [2012] ...[1M], (A), , 1, 2, , (B), , 1, 3, , (C), , 1, 6, , (D), , 1, 12, , 13. A ticket is drawn at random from a bag, containing tickets numbered from 1 to 40. Find, the probability that the selected ticket has a, number which is a multiple of 5. [2011] ...[2M], , OR, A pair of dice is thrown once. Find the, probability of getting the same number on each, dice., [2008] ...[2M], 6., , The probability of getting an even number, when, a die is thrown once, is, [2013] ...[1M], (A), , 7., , 1, 2, , (B), , 1, 3, , 1, 5, (C), (D), 6, 6, A box contains 90 discs, numbered from 1 to 90., If one disc is drawn at random from the box, the, probability that it bears a prime-number less, than 23, is, [2013] ...[1M], (A), , 7, 90, , (B), , 10, 90, , 4, 9, (D), 45, 89, If two different dice are rolled together, the, probability of getting an even number on both, dice, is :, [2014] ...[1M], , (A), , 1, 36, , (B), , 1, 2, , 1, 1, (D), 6, 4, A number is selected at random from the, numbers 1 to 30. The probability that it is a, prime number., [2014] ...[1M], , (C), 9., , (A), , 2, 3, , (B), , 14. A number is selected at random from first 50, natural numbers. Find the probability that it is a, multiple of 3 and 4., [2012] ...[2M], 15. A card is drawn at random from a well shuffled, pack of 52 playing cards. Find the probability, that the drawn card is neither a king nor a, queen., [2013] ...[2M], 16. Rahim tosses two different coins simultaneously., Find the probability of getting at least one tail., [2014] ...[2M], 17. Two different dice are tossed together. Find the, probability., (i) Of getting doublet, (ii) Of getting a sum 10, of the numbers on the, two dice., [2018] ...[2M], , (C), 8., , 12. The probability of selecting a rotten apple, randomly from a heap of 900 apples is 0·18., What is the number of rotten apples in the, heap?, [2017] ...[1M], , 18. An integer is chosen at random between 1 and, 100. Find the probability that it is, (i) Divisible by 8, (ii) Not divisible by 8, , [2018] ...[2M], , 19. A game consists of tossing a coin 3 times and, noting the outcome each time. If getting the, same result in all the tosses is a success, find, the probability of losing the game. [2019]...[2M], 20. A die is thrown once. Find the probability of, getting a number which (i) is a prime number (ii), lies between 2 and 6., [2019] ...[2M], 21. Two dice are thrown simultaneously. What is the, probability that, , 1, 6, , 1, 11, (D), 3, 30, 10. Two different dice are tossed together. Find the, probability that the product of the two numbers, on the top of the dice is 6., [2015] ...[1M], , (C), , 11. A card is drawn at random from a well shuffled, pack of 52 playing cards. Find the probability of, getting neither a red card nor a queen., [2016] ...[1M], , (i) 5 will not come up on either of them?, (ii) 5 will come up on at least one?, (iii) 5 will come up at both dice? [2009] ...[3M], 22. Cards bearing numbers 1, 3, 5, ..., 35 are kept, in a bag. A card is drawn at random from the, bag. Find the probability of getting a card bearing, (i) A prime number less than 15, (ii) A number divisible by 3 and 5. [2010]...[3M], , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456

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Chapter-wise Previous Years' Questions (Class-10), , Mathematics, , (i) Extremely patient, , 23. Two dice are rolled once. Find the probability of, getting such numbers on the two dice, whose, product is 12., [2011] ...[3M], 24. A box contains 80 discs which are numbered, from 1 to 80. If one disc is drawn at random, from the box, find the probability that it bears a, perfect square number., [2011] ...[3M], , (ii) Extremely kind or honest. Which of the, above values you prefer more? [2013]...[4M], 30. A bag contains cards numbers from 1 to 49., A card is drawn from the bag at random, after, mixing the cards thoroughly. Find the probability, that the number on the drawn card is, , 25. A card is drawn from a well shuffled deck of 52, cards. Find the probability of getting (i) a king of, red colour (ii) a face card (iii) the queen of, diamond., [2012] ...[3M], 26. The probability of selecting a red ball at random, from a jar that contains only red, blue and, 1, orange balls is . The probability of selecting, 4, 1, a blue ball at random from the same jar is ., 3, If the jar contains 10 orange balls, find the total, number of balls in the jar., [2015] ...[3M], , 59, , [2014] ...[4M], (A) An odd number, (B) A multiple of 5, (C) A perfect square, (D) An even prime number, 31. A card is drawn at random from a well-shuffled, deck of playing cards. Find the probability that, the card drawn is, [2015] ...[4M], (i) A card of spade or an ace., , 27. Three different coins are tossed together. Find, the probability of getting, [2016] ...[3M], , (ii) A black king., (iii) Neither a jack nor a king, , (i) Exactly two heads, , (iv) Either a king or a queen., , (ii) At least two heads, (iii) At least two tails., 28. A bag contains 15 white and some black balls., If the probability of drawing a black ball from the, bag is thrice that of drawing a white ball, find the, number of black balls in the bag. [2017] ...[3M], 29. A group consists of 12 persons, of which 3 are, extremely patient, other 6 are extremely honest, and rest are extremely kind. A person from the, group is selected at random. Assuming that, each person is equally likely to be selected, find, the probability of selecting a person who is, , 32. A number x is selected at random from the 1, 2,, 3 and 4. Another number y is selected at, random from the numbers 1, 4, 9 and 16. Find, the probability the product of x and y is less than, 16., [2016] ...[4M], 33. Two different dice are thrown together. Find the, probability that the numbers obtained have, [2017] ...[4M], (i) Even sum, and, (ii) Even product, , ‰ ‰ ‰, , Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456