Page 2 : लोक शिक्षण संचालनालय, म.प्र. भोपाल द्वारा जारी, प्रश्न बैंक उत्तर सहित, @am@beah450, Question Bank, МАТНЕMАТICS - 10th, [Marks : 80, Time : 3 Hre), S., No., BLUE PRINT OF QUESTION PAPER, Marks wise, No. of Questlons, Total, Que-, stlons, Unit nnd content, Marks, nllotted, to ench, unlt, Objec-, tlve, Que-, stlons, 4, 3, Mark Marks Marks Marks, 1., Real Numbers, 1, 2., Polynomials, 5, 1, Pnir of Lincar, Equation in two variables, 4., 3., 2, 1, Quadratic Equations, Arithmatic progressions, 2., 1, 1, 2, S., Triangles, Co-ordinate Geometry, Introduction to Trigonomo, 6., 7, 2, 2, 7., 6, 2, 2, 2, 8., 8, 6, 1, 1, Circle, Constructions, 9., 5, 4, 10., Areas Related to, 11., 4, 2°, 1, 12. Surface Areas and Volumes, 1, 1, 13. Statistics, 6, • 2, 1', 14. Probability, 6, 2, 2, "Total, 80, 32, 20, 12, 16, 18+5=23, O Special Inistruction for making question paper:, (1) Question numbers 1 to 5 will have 32 objective type question. Correct option will have 06 marks, Fill, in the blanks 07 marks, correct pair 06 marks, answer in one word 7 marks, true-false 06 marks. Related, question. Each question carries 01 inark excepi for., (2) Objective type question, theru 'will be provision of internal choice in all question. These options will be, from-the same uniusub unit and having the sume difficulty level the answer limit for these questions will be, as follows., O Very short answer lype questions, O Short answer type questions, O Analytical type questiuns, 2 marks about 30 words, 3 marks about 75 words, 4 marks abou: 120 words, (3) 40 percent objective type questions, 40 percent text based questions, 20 percent analytical questions., Question should not be given in the question paper from thc reduced syllabus for the session 2021-22. 20, marks ure allotted for the prject work hascd oni the syllabus., ---- -

Page 3 : Reduced Curriculum Content, S.No., Chapter, Chapter-1, Name of Reduced Chapters/Subject matter, 1., 1.4- Rotation of irrational numbers, 1.5- Recursion of rational numbers and their decimal expansions., 2.4 Division Algorithm for polynomials., 3.3 - Graphical solution of a pair of linear equations., 3.5 - Equation that can be converted to a pair of lincar equations in two variables, can be converted into a pair of possible equations., 4.4 Complete the quadratic equations and solve., 5.4 - A.P. sum of first 4 terms., 2., Chapter-2, 3., Chapter-3, 4., Chapter-4, 5., Chapter-5, Chapter-6, 6., 6.4 - Criteria for similarity of Triangles., 6.5 - Areas of similar Triangles., 7., Chapter-9, Chapter-11, Chapter-13, Chapter-14, Some Applications of Trigonomcry, 11.3 - Construction of Tangents on any circle., 8., 9., 13.5 - Conc Frustrum., 10., 14.5 Graphical Representation of Cumula, Frequency Distribution. ., 1., Real Numbers Q.2 Fill, the blanks:, (1) Dividend = divisor x quotient +, The value of HCF of the numbers 8,9 and 25 will, ......., Objective Type Question Answers, Q.1. Write the correct answer from the given fou, options:, (1) The HCF of 96 and 404 will be-, (a) 120, (c) 10, (2) The HCF of 12 and 15 will, (a) 3, (c) 10, (3) Product of two numbers =32 and their LCM= 0.4.Answer in one word/sentence:, 8, then their HCF will be:, (a) 4, (c) 32, (4) The HCF of 4 and 7 will be:, (a) 1, (c) 3, (5) For some integer m, every sum integer is of the, form:, Ans. 1. Remainder, 2. 1, Q.3. Write True/False :, (1) Two positivc integers a and b, there exist whole, numbers q and r satisfying a= bq +r,0gr<b., (2) A prime factorization of a natural number is, (b) 4, (d) 3, unique apart from the order of its factos:, Ans. 1. True, 2. True., (1) Write the HCF of 94 and 404., (2) For an integer P, 2p + I will be even or odd., Ans. (1) 2, (2) Odd., Q.5. Use Euclid's division algorithm to find the, (b) 8, (d) 256, (b) 2, (d) 4, HCF of 135 and 225., Sol. Given ; Divisor = 135 and dividend 225, 135 ) 225 (1, (a) 2m +3., (c) 2m, (6) The ratio of LCM and HCF for the number 5,, 15, 20 will be:, (a) 9:1, (c) 11:1, Ans. 1.(b), 2.(a). 3.(a). 4.(), 5.(с), 6.(0), (b) 2m +1, (d) 2m +5, 135, 90) 135 (1, 90, 45 ) 90 ( 2, (b) 4:3, * (d) 12:1, 90, Hence, HCF (135, 225) = 45., Ans., 4, @amarwah45ở, damaryen50

Page 4 : Q.6. Use Euclid's division algorithm to find the Q.9. Show that every positive even integer is of the, HCF of numbers 867 and 255., Sol. Given, Divisor = 255 and Dividend = 867, fornı 2q, and that every positive odd integer is of, the form 2q + 1, where q is some integer., Sol. Let a be any positive integer and b = 2. Then,', by Euclid's algorithm, a = 2q+r, for some integer q, 20, and r=0 orr=1, because 0gr<2. So, a=2q or, 2q + 1., If a is of the form 2q, then a is an even integer. Also,, a positíve integer can be cither even or odd., Therefore, any positive odd integer is of the form 2q, 255 ) 867 (3, 765, 102 ) 255 (2, 204, 51) 102 (2, 102, +1., Q.10. Show that any positive odd integer is of the, form 4g +1 or 4q +3, where q is some integer., Sol. Let us start with taking a, where a is a positive, odd integer. We, Hence, HCF (255,867) = 51., Ans., Q.7. A sweetscller has 420 kaju barfis and 130, badam barfis. She wants to stack them in such a, way that each stack has the same number, and they and b=4., take up the least area of the tray. What is the Since 0 <r, number of that can be plaed in each stack for this, purposė?, Sol. This can be done by trial and error. But to do it, systematically, we find HCF (420, 130). Then this, number will given the maxiumum number of barfis, in each stack and the number of stacks will then, the least. The area of the tray that is used up, the least., Now, let us use Euclid's algorithm to find, We have :, the division algorithm with a, the possible remainders are 0, 1, 2, and 3., That is, where, nnot be 4q or 4q+2 (since they are both divisible, y 2). Therefore, any odd integcr is of the form 4q+, or 4q +3., Q.11. Express the number 140 as a product of its, be 4q, or 49 + 1, or 4q + 2, or 4q + 3,, the quotient. However, since a is odd, a, HCF. prime factors., Sol. 140 = 2x2x5x7=2? x 5 x7, Q.12. Express the number 156 as a product of its, prime factors., Sol. 156 = 2x2x3x 13=22 x3 x 13, Q.13.Find the LCM and HCF of 6 and 20 by the, prime factorisation method., Sol. We have:6=2' x 3' and 20=2×2×53D22× 5'., You can find HCF (6, 20) = 2 and LCM (6, 20) = 2 x, 2x3x5=60, as done in your earlier classes., 420 = 130 x 3 +30, 130 = 30 x 4 + 10, 30 = 10x 3+0, So, the HCF of 420 and 130, Therefore, the sweetsell, both kinds of barfis., Q.8. An Army contingent of 616 members is to, march behind an army band of 32 members, in parade. The two groups are to march in the, same numbers of columns. What is the Notc that HCF (6, 20) = 2' = Product of the smallesi, maximum number of columns in which they power of each common prime factor in the numbers., can march?, can make stacks of 10 for, %3D, LCM (6, 20)= 22 x 3' x 5' Product of the greatest, power of each prime factor, involyed in the numbers., Q.14. Find the H.C.F. of 6, 72 and 120 using the, %3D, Sol. To find the HCF of 616 and 32., 32 ) 616 ( 19, 8 )32 (4, prime factorisation method., 6 = 2 x 3, 72 = 2' x32, 120 = 2' x 3 x 5, 32, 32, Sól., 296, 288, i.e., 32 = 8 x 4 +0, i.e., 616 32 x 19 + 8, :: The HCF of 616 and 32 is 8., Hence, maxi number of columns is 8., :. HCF (6,72 and 120) = 2 x 3 = 6, and LCM (6,72 and 120) =23 x 32 x5 = 8 x 9 x, Ans., 5 = 360 – Ans.

Page 5 : (2) If a andB are the zeroes of the quadratic, polynomial ax² + bx +c then the value of a.ß is:, (1) If a andb are the zeroes of the quadratic, @amarwah450, Q.15. Find the LTM and HCF of the following 2., Polynomials, integers by applying the prime factorisation, method:, Objective Type Question Answers, 12, 15 and 21, Q.1. Choose the correct answer:, Sol. First of all we have the prime factorisation., 12 = 2 x 2 x 3 = 22 x 3, 15 = 3 x 5, and 21 = 3 x 7, (a) ;, LCM = 22 x 3 x 5 x 7= 420, HCF = 3, (b) :, and, Q.16. Given that HCF (306, 657)=9, find LCM (c), (306, 657)., Sol. HCF of given number x LCM of given polynomial ax + bx +c, then the value of a+B Ls:, number, =Product of given number (a), .. HCF (306, 657) x LCM (306, 657), = 306 x 657, So,9 x LCM(306, 657)3 306х 657, a, -b, (P), linear polynomial ax +b is:, (c), a, (3) The ze, 306x657, LCM (306, 657) =, (b), a, or, (a), = 22338, Ans., (d) ab, Q.17. Consider the numbers 4", where n is a natural, number, Check whether there is any value of n for, which 4" ends with the digit zero., Sol. If the number4", for any n, were to end with the, digit zero, then it would be divisible by, the prime factorisation of 4n would contain the (5) The zeroes of the polynomial x + 7x+ 10 will, prime 5. This is not possible because, the only prime in the factorisation of 4 is 2. So, the (a) 2,5, uniqueness of the Fundamental Theorem of (c)-2,5, Arithmetic guaruantees that, in the factorisation of, number n for which 4" ends with-the digit zero., You have already learnt how to find the HCF and, LCM of two positive initegers using the Fundamental, Theorem of Arithmetic in earlier classes, without, realising it! This method is also called the prime polynomial, the quadratic polynomial will be :, factorisation method. Let us recall this method, The zeroes of the polynomial x² -3 will be:, (b) +3, (d) 9., (a)± 3, That is, (c)3, (2)2a*, so, be:, (b) -2, -5, (d) 2, -5, e are no other primes (6) The degree for the polynomial (x+1) (x-x-, So, there is no natural +1) will be :, (a) 2, (c)4, (7) If -3 and 4 are the zeroes of the quadratic·, (b) 3, (d) 5, (а) х?—х- 12, (b) x2 +x+12, through an example., Q.18. Explain, why 7 x 11 x 13 + 13 and 7 x 6, (c), 2 2, -6, (d), +., -6, 2 2, x 5 x 4 x 3 x 2 x1+5 are composite numbers? (8) The total zeroes of a polynomial are thenumber, Sol. We have, 7x 11 x 13 + 13 = 13 x (7 x 11 x of points is equal to the total of the intersection of, the diagram of that polynomial on the following:, 1 + 1) = 13 x 78, Hence, it is a composite number. Again, 7x6x 5 (a) On x-axis, x 4 x 3 x 1 x 1 +5., %3D, (b) On y-axis, (c) On both x axis and y-axis (d) None of them, Ans. 1.(a), 2.(c), 3.(c), 4.(a), 5.(b), 6.(d), 7.(a), 8.(a)., Q.2. Fill in the blanks :, = 5 x (7x 6 x 4 x 3x2x1 + 1), = 5x (1008 + 1) = 5 x (1009) (1) The zeroes of the linear polynomial ax + b are, So, it is a composite number., wan450