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Sample Question Paper - 3, Class – X Session -2021-22, TERM 1, Subject- Mathematics (Standard) 041, , Time Allowed: 1 hour and 30 minutes, , Maximum Marks: 40, , General Instructions:, 1. The question paper contains three parts A, B and C., 2. Section A consists of 20 questions of 1 mark each. Attempt any 16 questions., 3. Section B consists of 20 questions of 1 mark each. Attempt any 16 questions., 4. Section C consists of 10 questions based on two Case Studies. Attempt any 8 questions., 5. There is no negative marking., Section A, Attempt any 16 questions, 1., , If the sum of LCM and HCF of two numbers is 1260 and their LCM is 900 more than their HCF,, , [1], , then the product of two numbers is, , 2., , a) 205400, , b) 203400, , c) 194400, , d) 198400, , Ritu can row downstream 20 km in 2 hours and upstream 4 km in 2 hours. The speed of the, , [1], , current is, , 3., , a) 12 km/hr, , b) 6 km/hr, , c) 4 km/hr, , d) 8 km/hr, , Consider the following statements:, , [1], , i. Every equilateral triangle is necessarily an isosceles triangle., ii. Every right-angled triangle is necessarily an isosceles triangle., iii. A triangle in which one of the median is perpendicular to the side it meets, is necessarily, an isosceles triangle., The correct statements are:, a) III only, , b) I and III, , c) II and III, 4., , 5., , If, , 2x, 3, , −, , y, 2, , +, , 1, 6, , d) I and II, = 0, , and, , x, 2, , +, , 2y, 3, , = 3, , [1], , then, , a) x = - 2, y = -3, , b) x = 2, y = -3, , c) x = -2, y = 3, , d) x = 2, y = 3, , Choose the correct option and justify your choice:, a) cos60o, , 2 tan 30, 2, , 1−tan, , b) sin30o, , 0, , 30, , 0, , [1]

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c) sin60o, 6., , 7., , 8., , 9., , 10., , 11., , 12., , 13., , 14., , If, , 241, , =, , 4000, , d) tan60o, 241, , 2, , m, , ×5, , n, , , then, , [1], , a) m = 3 and n = 2, , b) m = 5 and n = 3, , c) m = 2 and n = 5, , d) m = 4 and n = 5, , The number polynomials having zeroes as – 2 and 5 is, , [1], , a) 1, , b) 2, , c) 3, , d) more than 3, , If the radius of a circle is diminished by 10%, then its area is diminished by, a) 20%, , b) 10%, , c) 19%, , d) 36%, , If α and β are the zeroes of the polynomial ax2 + bx + c, then the value of, 2, , a), , b −2ac, , c), , a, , b), , ac, 2, , d), , bc, , In the adjoining figure∠P QR, , =, , ∠P RS ., , α, β, , [1], , +, , β, α, , is, , [1], , 2, , b, , ac, 2, , c, , ab, , If PR = 8cm, PS = 4 cm, then PQ is equal to, , a) 16 cm., , b) 12 cm., , c) 24 cm., , d) 32 cm., , If the probability of an event is ‘p’, the probability of its complementary event will be, a) p, , b) p – 1, , c) 1 – p, , d), , 1−, , b) 4, , c) 3, , d) 2, , [1], , 1, p, , Every prime number has exactly ________ factors., a) more than 4, , [1], , –, , The height of an equilateral triangle is 3√3 cm. Its area is, 2, a) 6√–, 3 cm, , b) 27 cm2, , 2, c) 9√–, 3 cm, , 2, d) 27√–, 3 cm, , A chord of a circle of radius 10 cm subtends a right angle at the centre. The area of the minor, segments (given, π = 3.14) is, a) 32.5 cm2, , b) 34.5 cm2, , c) 30.5 cm2, , d) 28.5 cm2, , [1], , [1], , [1]

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15., , 16., , 17., , If △ABC ∼, a), , 36, , c), , 6, , PQR such that AB = 1.2 cm, PQ = 1.4 cm, then, , △, , b), , 49, , d), , 7, , ar(ΔABC ), ar(ΔP QR), , is, , [1], , 3, 7, 9, 49, , (1 + tan θ + sec θ) (1 + cotθ – cosecθ) =, , [1], , a) 0, , b) 2, , c) 1, , d) –1, , The system of linear equations a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 has infinitely many, , [1], , solutions if, a), , a1, , =, , a2, , b1, , ≠, , b2, , c1, c2, , c) None of these, 18., , b), , a1, , d), , a1, , a2, , a2, , =, , ≠, , b1, b2, , =, , c1, c2, , b1, b2, , A bag contains cards numbered from 1 to 25. A card is drawn at random from the bag. The, , [1], , probability that the number on this card is divisible by both 2 and 3 is, a), c), 19., , b), , 2, 25, , d), , 3, 25, , 1, 5, 4, 25, , Every point on the number line corresponds to a ________ number which may be either, , [1], , rational or irrational., , 20., , a) non-terminating, , b) decimal, , c) real, , d) terminating, , The area of a square that can be inscribed in a circle of radius 10 cm is, a) 100 sq. cm, , b) 300 sq. cm, , c) 200 sq. cm, , d) 150 sq. cm, , [1], , Section B, Attempt any 16 questions, 21., , If, , 1, x, , +, , a), , 2, y, , x =, , = 4, −1, 2, , and, , ,y =, , 3, y, , −, , 1, x, , = 11, , then, , [1], b) x =, , 1, 3, , c) x = -2, y = 3, 22., , 23., , In the given figure, if, , −1, 2, , ,y=3, , d) x = 2, y = 3, ar(ΔALM ), ar(trapezium LM C B), , =, , 9, 16, , ,, , and LM||BC, Then AL:LB is equal to, , a) 3 : 5, , b) 4 : 1, , c) 3 : 4, , d) 2 : 3, , The HCF and the LCM of 12, 21, 15 respectively are:, a) 3, 140, , b) 420, 3, , c) 12, 420, , d) 3, 420, , [1], , [1]

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24., , a) 23, , b) 25, , c) 24, 25., , [1], , If (tan θ + cot θ) = 5 then (tan2 θ + cot2 θ) = ?, , d) 27, , A fraction becomes, , 9, 11, , , if 2 is added to both the numerator and denominator. If 3 is added to, , both the numerator and denominator it becomes, , 26., , a), , 9, , c), , 7, , 7, , 9, , 5, 6, , [1], , , then the fraction is, , b), , −9, , d), , −7, , 7, , 9, , ABC is an isosceles triangle right-angled at B. Two equilateral triangles are constructed with, , [1], , side BC and AC as shown in the figure. If ar(ΔACE) = 20 cm2 then ar(ΔBCD) is, , 27., , a) 10 cm2, , b) 16 cm2, , c) 12 cm2, , d) 15 cm2, , In a rhombus of side 10 cm, one of the diagonals is 12 cm long. The length of the second, , [1], , diagonal is, , 28., , a) 22 cm, , b) 20 cm, , c) 16 cm, , d) 18 cm, , A circle drawn with origin as the centre passes through (, , 13, 2, , , 0). The point which does not lie in [1], , the interior of the circle is, a), c), 29., , 30., , 31., , 32., , −3, 4, , 5,, , ,1, , −1, 2, , 7, , b), , 2,, , d), , (−6,, , 3, 5, 2, , ), , [1], , cos4A - sin4A is equal to, a) 2 sin2 A - 1, , b) 2 sin2 A + 1, , c) 2 cos2 A + 1, , d) 2 cos2 A - 1, , If 2x – 3y = 11 and (a + b)x – (a + b – 3)y = 4a + b has infinite number of solutions, then, a) a = – 9 and b = 3, , b) a = – 9 and b = – 3, , c) a = 9 and b = 3, , d) a = 9 and b = – 3, , 0.515115111511115... is, , [1], , a) a rational number, , b) a prime number, , c) an integer, , d) an irrational number, , If p and q are co-prime numbers, then p2 and q2 are, a) even, , [1], , b) coprime, , [1]

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c) not coprime, 33., , 34., , 35., , −, −−−−−−−−−−−, −, √(1 − cos2 θ) sec2 θ, , d) odd, =, , [1], , a) tanθ, , b) cotθ, , c) sinθ, , d) cosθ, , In making 1000 revolutions, a wheel covers 88 km. The diameter of the wheel is, a) 40 m, , b) 28 m, , c) 24 m, , d) 14 m, , [1], , A school has five houses A, B, C, D and E. A class has 23 students, 4 from house A, 8 from house [1], B, 5 from house C, 2 from house D and rest from house E. A single student is selected at, random to be the class monitor. The probability that the selected student is not from A, B and, C is, a), c), , 36., , 37., , 38., , 39., , 8, , b), , 23, 4, , d), , 23, , 6, 23, 17, 23, , The lines represented by 3x + y – 12 = 0 and x – 3y + 6 = 0 intersects the y – axis at, a) (0, – 2) and (0, 12), , b) (0, 2) and (0, – 12), , c) (0, – 2) and (0, – 12), , d) (0, 2) and (0, 12), , The LCM and HCF of two rational numbers are equal, then the numbers must be, a) equal, , b) prime, , c) co-prime, , d) composite, , −−−−, −, √, , 1−sin A, 1+sin A, , [1], , [1], , [1], , =?, , a) sec A - tan A, , b) sec A + tan A, , c) none of these, , d) sec A tan A, , A card is drawn at random from a pack of 52 cards. The probability that the card is drawn is a, , [1], , jack, a queen or a king is, a), c), 40., , 11, 13, 3, 13, , b), d), , 1, 26, 1, 13, , The line segment joining points (-3, -4) and (1, -2) is divided by y-axis in the ratio, a) 1:3, , b) 2:3, , c) 3:2, , d) 3:1, Section C, Attempt any 8 questions, , Question No. 41 to 45 are based on the given text. Read the text carefully and answer the, questions:, , [1]

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In a soccer match, the path of the soccer ball in a kick is recorded as shown in the following graph., , 41., , 42., , 43., , 44., , 45., , The zeroes of the polynomial, represented in the given graph, are, a) 5, -2, , b) -2, 7, , c) -3, 8, , d) -1, 7, , Which of the following polynomial has -2 and -3 as its zeroes?, a) x2 - 5x - 5, , b) x2 + 5x + 6, , c) x2 + 5x - 6, , d) x2 + 6x - 5, , For what value of x, the value of the polynomial f(x) = (x - 3)2 + 9 is 9?, a) 3, , b) 1, , c) 4, , d) 2, , The shape of path of the soccer ball is a, , [1], , [1], , [1], , [1], , a) Parabola, , b) Circle, , c) None of these, , d) Line, , The axis of symmetry of the given parabola is, , [1], , a) line parallel to x-axis, , b) x-axis, , c) y-axis, , d) line parallel to y-axis, , Question No. 46 to 50 are based on the given text. Read the text carefully and answer the, questions:, Mary and John are very excited because they are going to go on a dive to see a sunken ship. The dive is, quite shallow which is unusual because most sunken ship dives are found at depths that are too deep, for two junior divers. However, this one is at 40 feet, so the two divers can go to see it., , They have the following map to chart their course. John wants to figure out exactly how far the boat, will be from the sunken ship. Use the information in this lesson to help John figure out the following.

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46., , 47., , The coordinates of the boat and the sunken ship respectively, a) (-3, 7) and (4, 8), , b) (4, 8) and (-3, 7), , c) (3, -7) and (4, 8), , d) (8, 4) and (7, -3), , How much distance will Mary and John swim through the water from the boat to the sunken, , [1], , [1], , ship?, , 48., , a) 7 units, , b) 8 units, , c) 6 units, , d) 9 units, , If each square represents 160 cubic feet of water, how many cubic feet of water will Mary and, , [1], , John swim through from the boat to the sunken ship., , 49., , 50., , a) 1120 cubic feet, , b) 1280 cubic feet, , c) 2280 cubic feet, , d) 2210 cubic feet, , The shortest distance (in the map) between the boat and the sunken ship is, a), , −, −, √48, , b), , −, −, √49, , c), , −, −, √47, , d), , −, −, √50, , If the distance between the points (x, -1) and (3, 2) is 5, then the value of x is, a) -7 or -1, , b) -7 or 1, , c) 7 or 1, , d) 7 or -1, , [1], , [1]