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Sample Question Paper
Class – X Session -2021-
TERM 1
Subject- Mathematics (Standard) 041
Time Allowed: 90 minutes Maximum Marks: 40 General Instructions:
**1. The question paper contains three parts A, B and C
- Section A consists of 20 questions of 1 mark each. Any 16 questions are to be attempted
- Section B consists of 20 questions of 1 mark each. Any 16 questions are to be attempted 4 Section C consists of 10 questions based on two Case Studies. Attempt any 8 questions.
- There is no negative marking.** SECTION A Section A consists of 20 questions of 1 mark each. Any 16 questions are to be attempted Q No Marks 1 The ratio of LCM and HCF of the least composite and the least prime numbers is (a) 1:2 (b) 2:1 (c) 1:1 (d) 1: 1 2 The value of k for which the lines 5 x +7 y =3 and 15 x + 21 y = k coincide is (a) 9 (b) 5 (c) 7 (d) 18 1 (^3) A girl walks 200m towards East and then 150m towards North. The distance of the girl from the starting point is (a)350m (b) 250m (c) 300m (d) 225 1 4 The lengths of the diagonals of a rhombus are 24cm and 32cm, then the length of the altitude of the rhombus is (a) 12cm (b) 12.8cm (c) 19 cm` (d) 19.2cm 1 (^5) Two fair coins are tossed. What is the probability of getting at the most one head? (a) ¾ (b) ¼ (c) ½ (d) 3/8^1 (^6) ∆ABC~∆PQR. If AM and PN are altitudes of ∆ABC and ∆PQR respectively and AB^2 : PQ^2 = 4 : 9, then AM:PN = (a) 16:81 (b) 4:9 (c) 3:2 (d) 2: 1 7 If 2 sin^2 β – cos^2 β = 2, then β is (a) 0ᵒ (b) 90ᵒ (c) 45ᵒ (d) 30ᵒ 1 8 Prime factors of the denominator of a rational number with the decimal expansion 44.123 are (a) 2,3 (b) 2,3,5 (c) 2,5 (d) 3, 1 (^9) The lines x = a and y = b, are (a) intersecting (b) parallel (c) overlapping (d) (None of these) 1 (^10) The distance of point A(-5, 6) from the origin is (a) 11 units (b) 61 units (c) √11 units (d) √61 units 1 11 If a² = 23/25, then a is (a) rational (b) irrational (c) whole number (d) integer^1
12 If LCM( x , 18) =36 and HCF( x , 18) =2, then x is (a) 2 (b) 3 (c) 4 (d) 5 1 (^13) In ∆ABC right angled at B, if tan A= (^) √ 3 , then cos A cos C- sin A sin C = (a) - 1 (b) 0 (c) (^1) (d) √ 3 / 2 1 14 If the angles of ∆ABC are in ratio 1:1:2, respectively (the largest angle being angle C), then the value of sec A cosec B
tan A cot B is (a) 0 (b) 1/2 (c) 1 (^) (d) (^) √ 3 / 1 (^15) The number of revolutions made by a circular wheel of radius 0.7m in rolling a distance of 176m is (a) 22 (b) 24 (c) 75 (d) 40 1 16 ∆ABC is such that AB=3 cm, BC= 2cm, CA= 2.5 cm. If ∆ABC ~ ∆DEF and EF = 4cm, then perimeter of ∆DEF is (a) 7.5 cm (b) 15 cm (c) 22.5 cm (d) 30 cm 1 (^17) In the figure, if DE∥ BC, AD = 3cm, BD = 4cm and BC= 14 cm, then DE equals (a) 7 cm (b) 6 cm (c) 4 cm (d) 3 cm 1 (^18) If 4 tanβ = 3, then 4 𝑠𝑖𝑛𝛽−^3 cos^ 𝛽 4 sin 𝛽+ 3 cos 𝛽
(a) 0 (b) 1/3 (c) 2/3 (d) ¾ 1 (^19) One equation of a pair of dependent linear equations is – 5 x + 7 y = 2. The second equation can be a) 10 x +14 y +4 = 0 b) – 10 x – 14 y + 4 = 0 c) – 10 x +14 y + 4 = 0 (d) 10 x – 14 y = – 4 1 (^20) A letter of English alphabets is chosen at random. What is the probability that it is a letter of the word ‘ MATHEMATICS ’? (a) 4/13 (b) 9/26 (c) 5/13 (d) 11/ 1 SECTION B Section B consists of 20 questions of 1 mark each. Any 16 questions are to be attempted QN MARKS (^21) If sum of two numbers is 1215 and their HCF is 81, then the possible number of pairs of such numbers are (a) 2 (b) 3 (c) 4 (d) 5 1 22 Given below is the graph representing two linear equations by lines AB and CD respectively. What is the area of the triangle formed by these two lines and the line x =0? 1
32 In the given figure, D is the mid-point of BC, then the value of cot 𝑦° cot 𝑥°^ is (a) 2 (b) 1/2 (c) 1/ 3 (d) 1/ 1 33 The smallest number by which 1/13 should be multiplied so that its decimal expansion terminates after two decimal places is (a) 13/10 0 (b) 13/10 (c) 10 /13 (d) 100/ 1 (^34) Sides AB and BE of a right triangle, right angled at B are of lengths 16 cm and 8 cm respectively. The length of the side of largest square FDGB that can be inscribed in the triangle ABE is (a) 32/3cm (b) 16 /3cm (c)8/3cm (d) 4 /3cm 1 35 Point P divides the line segment joining R(-1, 3) and S(9,8) in ratio k:1. If P lies on the line x – y +2=0, then value of k is (a) 2/3 (b) 1/ 2 (c) 1/3 (d) 1/ 1 36 In the figure given below, ABCD is a square of side 14 cm with E, F, G and H as the mid points of sides AB, BC, CD and DA respectively. The area of the shaded portion is (a) 44cm² (b) 49 cm² (c) 98 cm² (d) 49π/2 cm² 1 (^37) Given below is the picture of the Olympic rings made by taking five congruent circles of radius 1cm each, intersecting in such a way that the chord formed by joining the point of intersection of two circles is also of length 1cm. Total area of all the dotted regions assuming the thickness of the rings to be negligible is 1
(a) 4(π/12-√3/4) cm² (b) (π/6 - √3/4) cm² (c) 4(π/6 - √3/4) cm² (d) 8(π/6 - √3/4) cm² (^38) If 2 and ½ are the zeros of p x^2 +5 x + r , then (a) p = r = 2 (b) p = r = - 2 (c) p = 2, r= - 2 (d) p = - 2, r= 2 1 (^39) The circumference of a circle is 100 cm. The side of a square inscribed in the circle is (a) 50√2 cm (b) 100/π cm (c) 50√2/π cm (d) 100√2/π cm 1 (^40) The number of solutions of 3 x+y^ = 243 and 243 x-y^ = 3 is (a) 0 (b) 1 (c) 2 (d) infinite 1 SECTION C Case study based questions: Section C consists of 10 questions of 1 mark each. Any 8 questions are to be attempted. Q41-Q45 are based on Case Study - 1 Case Study - 1 41 What is the value of k? (a) 0 (b) - 48 (c) 48 (d) 48/- 16 1 42 At what time will she touch the water in the pool? (a) 30 seconds (b) 2 seconds (c) 1 .5 seconds (d) 0 .5 seconds 1 The figure given alongside shows the path of a diver, when she takes a jump from the diving board. Clearly it is a parabola. Annie was standing on a diving board, 48 feet above the water level. She took a dive into the pool. Her height (in feet) above the water level at any time‘t’ in seconds is given by the polynomial h(t) such that h(t) = - 16t² + 8t + k.
46 The coordinates of the centroid of ΔEHJ are (a) (-2/3, 1) (b) (1,-2/3) (c) (2/3,1) (d) ( - 2/3,-1) 1 (^47) If a player P needs to be at equal distances from A and G, such that A, P and G are in straight line, then position of P will be given by (a) (-3/2, 2) (b) (2,-3/2) (c) (2, 3/2) (d) ( - 2,-3) 1 48 The point on x axis equidistant from I and E is (a) (1/2, 0) (b) (0,-1/2) (c) (-1/2,0) (d) ( 0,1/2) 1 (^49) What are the coordinates of the position of a player Q such that his distance from K is twice his distance from E and K, Q and E are collinear? (a) (1, 0) (b) (0,1) (c) (-2,1) (d) ( - 1,0) 1 (^50) The point on y axis equidistant from B and C is (a) (-1, 0) (b) (0,-1) (c) (1,0) (d) ( 0,1) 1
