Page 1 : https://play.google.com/store/apps/details?id=com.nodiaapp, Refer Indias’s Best Study App NODIA To Your classmates and Get FREE Unlimited Access, , Page 10, , Sample Paper 1 Solutions, , CBSE Maths Standard X, , Sample Paper 1 Solutions, Class – X Exam 2021-22 (TERM – II), Mathematics Standard (041), , Time Allowed: 120 minutes, Maximum Marks: 40, General Instructions:, 1. The question paper consists of 14 questions divided into 3 sections A, B, C., 2. All questions are compulsory., 3. Section A comprises of 6 questions of 2 marks each. Internal choice has been provided in two questions., 4. Section B comprises of 4 questions of 3 marks each. Internal choice has been provided in one question., 5. Section C comprises of 4 questions of 4 marks each. An internal choice has been provided in one question. It, contains two case study based questions., , SECTION A, , Here a = 7, a13 = 35, , an = a + ^n − 1h d, , a13 = a + 12d, 1., , 35 = 7 + 12d & d = 7, 3, , Solve for x (in terms of a and b ) :, a + b = 2, x ! a, b, x−b x−a, , Now, ,
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Ans :, We have, , ax − a2 + bx − b2 = 2x2 − 2 ^a + b h x + 2ab, 2x2 − 3 ^a + b h x + ^a + b h2 = 0, , 2x2 − 2 ^a + b h x − ^a − b h x + ^a + b h2 = 0, Thus, , S13 = 13 ;2 # 7 + 12 # b 7 lE, 3, 2, , a ^x − a h + b ^x − b h, =2, ^x − b h^x − a h, , a ^x − a h + b ^x − b h = 2 8x2 − ^a + b h x + abB, , 82x − ^a + b hB8x − ^a + b hB = 0, x = a + b, a + b, 2, ,
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O, Value of the roots of the quadratic equation,, x2 − x − 6 = 0 are ......... ., , Sn = n 82a + ^n − 1h dB, 2, , , = 13 614 + 28@ = 13 # 42 = 273, 2, 2, 3., , A circle is inscribed in a TABC touching AB , BC, and AC at P , Q and R respectively. If AB = 10 cm, AR = 7 cm and CR = 5 cm , then find the length of, BC,
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Ans :, As per given information we have drawn the figure, below., Here a circle is inscribed in a TABC touching AB ,, BC and AC at P , Q and R respectively., ,
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Ans :, x2 - x - 6 = 0, x 2 − 3 x + 2x − 6 = 0, x (x − 3) + 2 (x − 3) = 0, (x − 3) (x + 2) = 0 & x = 3 and x, =− 2, 2., , If the 1st term of a series is 7 and 13th term is 35., Find the sum of 13 terms of the sequence.,
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Ans :, Let the first term be a , common difference be d , n, th term be an and sum of n term be Sn ., , Since, tangents drawn to a circle from an external, point are equal,, AP = AR = 7 cm, CQ = CR = 5 cm, , No NEED To Take Printout of These Sample Papers., Purchase Hard Books of 20 Papers (All Solved) at Price Less Than Prinouts

Page 2 : CLICK HERE To Purchase Hard Books of CBSE Online Sample Papers., 20 Sample Paper in Each Subject and Rs 500/- For 4 Subjects, , CBSE Maths Standard X, Now,, , Sample Paper 1 Solutions, , ^40 − 24h, , = 20 +, 10, 80 − 24 − 36 #, , BP = (AB − AP) = 10 − 7 = 3 cm, BP = BQ = 3 cm, , , = 20 + 16 # 10 = 28, 20, , BC = BQ + QC = 3 + 5 = 8 cm, 4., ,
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O, , A solid metallic of dimensions 9m # 8 m # 2 m is, melted and recast into solid cubes of edge 2 m. Find, the number of cubes so formed., , Calculate the median from the following data :, Marks, ,
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Ans :, , n23 = 9 # 8 # 2, n#2#2#2 = 9#8#2, n = 9 # 8 # 2 = 18, 2#2#2, Hence, number of cubes recast is 18., Write the relationship connecting three measures of, central tendencies. Hence find the median of the, give data if mode is 24.5 and mean is 29.75., , and mean,, M = 29.75, The relationship connecting measures of central, tendencies is,, , 30, , 8, , 2, , No. of students, , c.f., , 0-10, , 5, , 5, , 10-20, , 15, , 20, , 20-30, , 30, , 50, , 30-40, , 8, , 58, , 40-50, , 2, , 60, , l = 20 , f = 30 , F = 20 , h = 10, , Median, Md, = l +e, , Thus 3Md = 24.5 + 2 # 59.50, , = 24.5 + 59.50 = 84.0, Median Md = 84 = 28, 3, , N, 2, , −F, h, f o#, , , = 20 + b 30 − 20 l # 10, 30, , = 20 + 100 = 20 + 3.33, 30, Thus Md = 23.33, , The following distribution shows the marks scored, by 140 students in an examination. Calculate the, mode of the distribution :, 10-20, , 20-30, , 30-40, , 40-50, , 24, , 40, , 36, , 20, , Section B, 7., ,
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Ans :, Class 20-30 has the maximum frequency 40,, therefore this is model class., l = 20 , f1 = 40 , f0 = 24 , f2 = 36 ,h = 10, f1 − f0, Mode, Mo = l + d 2f − f − f n h, 1, 0, 2, Here,, , 15, , Marks, , Now, , 3Md = Mo + 2M, , Number of 20, students, , 40-50, , We have, N = 60 ; N2 = 30, Cumulative frequency just greater than N2 is 50 and, the corresponding class is 20-30. Thus median class, is 20-20., , Mo = 24.5, , 0-10, , 30-40, , N = 60, ,
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Ans :, , Marks, , 20-30, , We prepare following cumulative frequency table to, find median class., , Volume of n cubes =Volume of cuboid, , 6., , 10-20, ,
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Ans :, , Let number of recast cubes be n ., , Mode,, , 0-10, , Number of 5, Students, , Volume of cuboid = 9 # 8 # 2 cm3, Volume of cube = 23 cm3, , 5., , Page 11, , Solve the following equation: 1 - 1 = 3 , x ! 0, x x-2, ,2,
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Ans :, We have 1 - 1 = 3, x x-2, x-2-x = 3, x (x - 2), , Get FREE Solution of This Paper and 20 Other Sample Papers (All Solved), , From Indias’s Best Study App NODIA, , NCERT Solutions, Previous 15 Years Solved Chapterwise Questions, 20 Solved Sample Papers, , (x ! 0, 2)

Page 3 : https://play.google.com/store/apps/details?id=com.nodiaapp, Refer Indias’s Best Study App NODIA To Your classmates and Get FREE Unlimited Access, , Page 12, , Sample Paper 1 Solutions, , CBSE Maths Standard X, , -2, =3, x (x - 2), 3x (x - 2) =− 2, 2, , 3x − 6x + 2 = 0, Comparing it by ax2 + bx + c , we get a = 3 , b = − 6, and c = 2 ., 2, x = − b ! b − 4ac, 2a, , Now,, , − (− 6) ! (− 6) 2 − 4 (3) (2), , =, 2 (3), , In ∆ABQ , tan 60c = AB, BQ, , , = 6 ! 36 − 24 = 6 ! 12, 6, 6, , 3 =h, y, , , = 6!2 3, 6, , = 3+ 3 , 3- 3, 3, 3, In ABP ,, 8., , The 17 th term of an AP is 5 more than twice its 8 th, term. If 11 th term of AP is 43, then find its nth term., , 1 = h, x+y, 3, ,
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Ans :, , x+y =, , Let a be the first term and d be the common, difference., nth term of an AP,, , x =, , = 2 3 h = 3 h m/min, 3 # 18, 27, Time for remaining distance,, Thus, speed of car s, , a + 16d = 5 + 2 (a + 7d), a + 16d = 5 + 2a + 14d, Since 11, , th, , t =, , ...(1), , h 3, 3, h 3, 27, , = 9 min, , Hence, time taken by car is 9 min., , a + (11 − 1) d = 43, a + 10d = 43, Solving equation (1) and (2), we have, , 3h−y, , , = 2 3h, 3, , a + (17 − 1) d = 5 + 2 [a + (8 − 1) d], , 2d - a = 5, term of AP is 43,, , 3h, , , = 3h− 3h, 3, , an = a + (n − 1) d, Since 17 th term of an AP is 5 more than twice of its, 8 th term, thus, , ...(2), , 10., , Construct a tangent to a circle of radius 4 cm from, a point on the concentric circle of radius 6 cm and, measure its length. Also to verify the measurement, by actual calculation., , a = 3 and d = 4, Hence, nth term would be, ,
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Ans :, , an = 3 + (n − 1) 4 = 4n − 1, 9., , y = h =h 3, 3, 3, tan 30c = AB, BP, , A man on the top of a vertical tower observes a car, moving at a uniform speed coming directly towards, it. If it takes 18 minutes for the angle of depression, to change from 30° to 60°, how soon after this will, the car reach the tower?,
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Ans :, Let h be the height of tower AB . Now as per given, in question, we have drawn figure below., , Steps of Construction :, Draw two concentric circles with centre O and, radii 4 cm and 6 cm., 2. Now take any point P on outer circle., 3. Join PO and bisect it and let the midpoint of PO, is represented by M ., 4. Taking M as centre and OM or MP as radius,, draw a circle such that this circle intersects the, circle (of radius 4 cm) at A and B ., 5. Join AP . PA is the required tangent., By measurement, PA = 4.5 cm, 1., , No NEED To Take Printout of These Sample Papers., Purchase Hard Books of 20 Papers (All Solved) at Price Less Than Prinouts

Page 4 : CLICK HERE To Purchase Hard Books of CBSE Online Sample Papers., 20 Sample Paper in Each Subject and Rs 500/- For 4 Subjects, , CBSE Maths Standard X, , Sample Paper 1 Solutions, , Page 13, , Section C, , Justification :, Join OA. As PO is diameter, +PAO = 90c, , 11., , (Angle in a semi-circle), PA = OA, OA is a radius of the inner circle., Verification of length of PA. In right TPAO ,, PO = 6 cm , OA = 4 cm, , The angle of depression of two ships from an, aeroplane flying at the height of 7500 m are 30c, and 45c. If both the ships are in the same that one, ship is exactly behind the other, find the distance, between the ships.,
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Ans :, Let A, C and D be the position of aeroplane and, two ship respectively. Aeroplane is flying at 7500 m, height from point B . As per given in question we, have drawn figure below., , PA =, , 62 − 42 =, , 36 − 16, , , = 20 = 4.47 cm, Hence, both lengths are approximately equal.,
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O, raw a circle of radius 2 cm with centre O and take, a point P outside the circle such that OP = 6.5 cm ., From P , draw two tangents to the circle.,
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Ans :, 1., 2., 3., 4., , Draw a line segment OP of length 6.5 cm., Draw a circle taking O as centre and radius 2, cm., Taking OP as diameter draw another circle, which intersects the first circle at Q and R ., Join P to Q and P to R ., Hence PQ, and PR are two tangents., , In right TABC we have, AB = tan 45c, BC, 7500 = 1, y, y = 7500, , ...(1), , In right TABD we have, AB = tan 30c, BD, 7500 = 1, x+y, 3, x + y = 7500 3, , ...(2), , Substituting the value of y from (1) in (2) we have, x + 7500 = 7500 3, x = 7500 3 − 7500, , , = 7500 ^ 3 − 1h, , Get FREE Solution of This Paper and 20 Other Sample Papers (All Solved), , From Indias’s Best Study App NODIA, , NCERT Solutions, Previous 15 Years Solved Chapterwise Questions, 20 Solved Sample Papers

Page 5 : https://play.google.com/store/apps/details?id=com.nodiaapp, Refer Indias’s Best Study App NODIA To Your classmates and Get FREE Unlimited Access, , Page 14, , Sample Paper 1 Solutions, , , = 7500 ^1.73 − 1h, , = 7500 # 0.73 = 5475 m, , Same will be the case with all other points on circle., Hence OP is the smallest line that connect AB and, smallest line is perpendicular., , Hence, the distance between two ships is 5475 m., 12., , Prove that tangent drawn at any point of a circle, perpendicular to the radius through the point, contact.,
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Ans :, Consider a circle with centre O with tangent AB at, point of contact P as shown in figure below, , CBSE Maths Standard X, , 13., , Thus, , OP = AB, , or,, , OP = PQ, , Hence Proved, , Underground water tank is popular in India. It, is usually used for large water tank storage and, can be built cheaply using cement-like materials., Underground water tanks are typically chosen by, people who want to save space. The water in the, underground tank is not affected by extreme weather, conditions. The underground tanks maintain cool, temperatures in both winter and summer. Electric, pump is used to move water from the underground, tank to overhead tank., , Let Q be point on AB and we join OQ . Suppose it, touch the circle at R ., We, , OP = OR, , Clearly, , OQ 2 OR, , (Radius), , OQ 2 OP, Same will be the case with all other points on circle., Hence OP is the smallest line that connect AB and, smallest line is perpendicular., Thus, , OP = AB, , or,, , OP = PQ, , Hence Proved, ,
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O, Prove that tangent drawn at any point of a circle, perpendicular to the radius through the point, contact.,
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Ans :, Consider a circle with centre O with tangent AB at, point of contact P as shown in figure below, , Ramesh has build recently his house and installed, a underground tank and overhead tank. Dimensions, of tanks are as follows :, Underground Tank : Base 2 m # 2 m and Height 1.1, m., Overhead tank : Radius 50 cm and Height 175 cm, (i) What is the capacity of the underground tank ?, (ii) What is the ratio of the capacity of the, underground tank to the capacity of the overhead, tank?,
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Ans :, (i), , Volume of underground tank,, lbh = 2 # 2 # 1.1 = 4.4, , , m3, 3, Since 1 m is equal to 1000 litres,, , Let Q be point on AB and we join OQ . Suppose it, touch the circle at R ., We, , OP = OR, , Clearly, , OQ 2 OR, OQ 2 OP, , (Radius), , 4.4 m 3 = 4.4 # 1000 = 4400 litres, (ii) Radius of overhead is 50 cm i.e. 12 meter and, height is 175 cm i.e 1.75 = 74 metre., Thus volume of overhead tank,, 22 1 1 7, 11, πr2 hcy = 7 # 2 # 2 # 4 = 8 m 3, Capacity of sump, = 411.4 = 3.2, = lbh, Capacity of Overhead tank, 8, πr2 hcy, , No NEED To Take Printout of These Sample Papers., Purchase Hard Books of 20 Papers (All Solved) at Price Less Than Prinouts

Page 6 : CLICK HERE To Purchase Hard Books of CBSE Online Sample Papers., 20 Sample Paper in Each Subject and Rs 500/- For 4 Subjects, , CBSE Maths Standard X, 14., , Sample Paper 1 Solutions, , An inspector in an enforcement squad of electricity, department visit to a locality of 100 families and, record their monthly consumption of electricity, on, the basis of family members, electronic items in the, house and wastage of electricity, which is summarise, in the following table., , Page 15, , 300-400, , 12, , 19 + x, , 400-500, , 17, , 36 + x, , 500-600, , 20, , 56 + x, , 600-700, , y, , 56 + x + y, , 700-800, , 9, , 65 + x + y, , 800-900, , 7, , 72 + x + y, , 900-1000, , 4, , 76 + x + y, , Total, , 76 + x + y, , Monthly, Consumption (in kwh), , Number of families, , 0-100, , 2, , 100-200, , 5, , 200-300, , x, , 300-400, , 12, , 400-500, , 17, , 500-600, , 20, , x + y = 100 − 76 = 24, Here median is 525, thus median class is 500-600., 100, N, Also 2 = 2 = 50 ., , 600-700, , y, , Now, l = 500 ,, , 700-800, , 9, , h = 100 ., , 800-900, , 7, , Median, Md, , 900-1000, , 4, , Since total frequency is 100 ,, 76 + x + y = 100, , Inspector calculated that median of the above data, is 525 and after that he lost two data which is given, as x and y in table., Based on the above information, answer the, following questions., (i), What is the value of lost data x ?, (ii) What is the value of lost data y ?, , N, 2, , = 50 , F = 36 + x , f = 20 and, = l +d, , 525 = 500 + b, , 50 − 36 − x, l # 100, 20, , 25 = (14 − x) # 5, 25 = 70 − 5x, 70 − 25 =, x =, 9, 5, =, =, −, Now, y, 24 9 15, (i), Thus x = 9, (ii) y = 15, ,
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Ans :, We prepare following cumulative frequency table, Monthly, Number of, Consumption (in kwh) families, , Cumulative, Frequency, , 0-100, , 2, , 2, , 100-200, , 5, , 7, , 200-300, , x, , 7+x, , Get FREE Solution of This Paper and 20 Other Sample Papers (All Solved), , From Indias’s Best Study App NODIA, , NCERT Solutions, Previous 15 Years Solved Chapterwise Questions, 20 Solved Sample Papers, , N, 2, , −F, h, f n