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KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD–32, SAMPLE PAPER TEST 06 FOR TERM-I (2021), (ANSWER), SUBJECT: MATHEMATICS, CLASS : X, General Instructions:, 1. The Question Paper contains three sections., 2. Section A has 20 questions. Attempt any 16 questions., 3. Section B has 20 questions. Attempt any 16 questions., 4. Section C has 10 questions. Attempt any 08 questions., 5. All questions carry equal marks., 6. There is no negative marking., , MAX. MARKS: 40, DURATION: 1½ Hrs, , SECTION – A, Section – A consists of 20 questions. Attempt any 16 questions from this section., The first attempted 16 questions would be evaluated., 1. If the LCM of a and 18 is 36 and the HCF of a and 18 is 2, then a =, (a) 2, (b) 3, (c) 4, Ans. (c), , (d) 1, , 2. The HCF of 95 and 152, is, (a) 57, (b) 1, Ans. (c), , (d) 38, , (c) 19, , 3. If one of the zeros of the quadratic polynomial (k – 1)x2 + kx + 1 is -3, then the value of k is, (a) 4/3, (b) -4/3, (c) 2/3, (d) -2/3, Ans. (a), 4. The lines represented by the equations 9x + 3y + 12 = 0 and 18x + 6y + 24 will, (a) intersect at a point, (b) be parallel, (c) be coincident, (d) None of these, Ans. (c), 5. If one of the zeros of the cubic polynomial x3 + ax2 + bx + c is - 1, then the product of other two, zeros is, (a) b – a + 1, (b) b – a – 1, (c) a – b + 1, (d) a – b – 1, Ans. (a), 6. If am ≠ bl, then the system of equations ax + by = c and, lx + my = n, (a) has a unique solution, (b) has no solution, (c) has infinitely many solutions, (d) may or may not have a solution, Ans. (a), 7. The HCF and LCM of two numbers are 33 and 264 respectively. When the first number is, completely divided by 2 the quotient is 33. The other number is, (a) 132, (b) 133, (c) 134, (d) 135, Ans. (a), 8. ∆ABC ~ ∆PQR such that ar(∆ABC) = 4 ar(∆PQR). If BC = 12 cm, then QR =, (a) 9 cm, (b) 10 cm, (c) 6 cm, (d) 8 cm, Ans. (c), Prepared by: M. S. KumarSwamy, TGT(Maths), , Page - 1-

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9. The areas of two similar triangles are 121 cm2 and 64 cm2 respectively. If the median of the first, triangle is 12.1 cm, then the corresponding median of the other triangle is, (a) 11 cm, (b) 8.8 cm, (c) 11.1 cm, (d) 8.1 cm, Ans. (b), 10. If x = a cosθ and y = b sinθ, then b2x2 + a2y2 =, (a) a2b2, (b) ab, (c) a4b4, Ans. (a), , sin , is equal to, 1  cos, 1  cos, 1  cos , 1  cos , (a), (b), (c), sin , cos , sin , Ans. (c), 3, 12. If (1 + cos A)(1 – cos A) = , the value of sec A is, 4, (a) 2, (b) –2, (c) ±2, Ans. (c), , (d) a2 + b2, , 11., , (d), , 1  sin , cos , , (d) 0, , 13. If the area of a circle is equal to the sum of the areas of two circles of diameters 10 cm and 24 cm,, then diameter of the larger circle (in cm) is, (a) 34, (b) 26, (c) 17, (d) 14, Ans. (b), 14. If the area of a sector of a circle is 5/18 of the area of the circle, then the sector angle is equal to, (a) 60°, (b) 90°, (c) 100°, (d) 120°, Ans. (c), 15. One card is drawn from a well shuffled deck of 52 cards. The probability that it is black queen is, (a) 1/26, (b) 1/13, (c) 1/52, (d) 2/13, Ans. (a), 16. A bag contains cards numbered from 1 to 25. A card is drawn at random from the bag. The, probability that the number on this card is divisible by both 2 and 3 is, (a) 1/5, (b) 3/25, (c) 4/25, (d) 2/25, Ans. (c), 17. The area of the triangle formed by the lines x = 3, y = 4 and x = y is, (a) 1/2 sq. unit, (b) 1 sq. unit, (c) 2 sq. unit, Ans. (a), , (d) None of these, , 18. If P(2, 4), Q(0, 3), R(3, 6) and S(5, y) are the vertices of a parallelogram PQRS, then the value of y is, (a) 7, (b) 5, (c) -7, (d) - 8, Ans. (a), 19. The value(s) of x, if the distance between the points A(0, 0) and B(x, – 4) is 5 units, is, (a) ± 2, (b) ± 3, (c) ± 4, (d) ± 5, Ans. (b), 20. The perimeter of a triangle with vertices (0, 4) and (0, 0) and (3, 0) is, (a) 7 + √5, (b) 5, (c) 10, (d) 12, Ans. (d), Prepared by: M. S. KumarSwamy, TGT(Maths), , Page - 2-

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SECTION – B, Section – B consists of 20 questions. Attempt any 16 questions from this section., The first attempted 16 questions would be evaluated., 21. The decimal expansion of the rational number, decimals?, (a) 2 places, Ans. (c), , (b) 3 places, , 43, will terminate after how many places of, 2 453, , (c) 4 places, , (d) 5 places, , 22. 3 bells ring at an interval of 4, 7 and 14 minutes. All three bells rang at 6 am. When the three bells, will ring together next?, (a) 6:20 am, (b) 6:24 am, (c) 6:28 am, (d) 6:30 am, Ans. (c), 23. If 2x + 5y – 1 = 0, 2x + 3y – 3 = 0, then, (a) x = 1, y = – 3 (b) x = 3, y = –1, (c) x = 2, y = 5, Ans. (b), , (d) x = 5, y = – 3, , 24. The pair of equations kx + 3y = 7, 2x + 6y = 14 will have infinitely many solutions for k, (a) 0, (b) 1, (c) 2, (d) 3, Ans. (b), 25. The coordinates of the point which is equidistant from the vertices of the triangle formed by the, points O(0, 0), A(a, 0) and B(0, b) are, a b, a c, b c, d c, (a) ,, (b) ,, (c) ,, (d) ,, 2 2, 2 2, 2 2, 2 2, Ans. (a), 26. The point which lies on the perpendicular bisector of the line segment joining the points A(– 2, –, 5) and B(2, 5) is, (a) (0, 0), (b) (0, 2), (c) (2, 0), (d) (– 2, 0), Ans. (a), 27. If a = 23 x 3, b = 2 x 33 x 5, c = 3n x 5 and LCM (a, b, c) = 23 x 34 x 5, then n =, (a) 1, (b) 2, (c) 3, (d) 4, Ans. (d), 28. Given that two of the zeros of the cubic polynomial ax3 + bx2 + cx + d are 0, the third zero is, (a) -b/a, (b) b/a, (c) c/a, (d) -d/a, Ans. (a), 29. If one zero of the quadratic polynomial x2 + 3x + k is 2, then the value of k is, (a) 10, (b) - 10, (c) 5, (d) - 5, Ans. (b), 30. A man goes 12 m due west and then 9 m due north. How far is he from the starting point?, (a) 12 m, (b) 15 m, (c) 18 m, (d) 24 m, Ans. (b), 31. In an isosceles triangle PQR, PQ = QR and PR2 = 2PQ2. Then ∠Q is, (a) 30°, (b) 60°, (c) 90°, Ans. (c), Prepared by: M. S. KumarSwamy, TGT(Maths), , (d) None of these, Page - 3-

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3 5 , 1 3, 32. The ratio in which the point P  ,  divides the line segment joining the points A  ,  and,  4 12 , 2 2, B(2, -5) is, (a) 2 : 3, (b) 1 : 3, (c) 1 : 5, (d) 2 : 5, Ans. (c), 33. If the distance (in metres) covered by a wheel of diameter 35 cm, in one revolution is, (a) 2.2, (b) 1.1, (c) 9.625, (d) 96.25, Ans. (b), 34. ∆ABC and ∆BDE are two equilateral triangles such that D is the mid-point of BC. The ratio of the, areas of triangles ABC and BDC is, (a) 2 : 1, (b) 1 : 2, (c) 4 : 1, (d) 1 : 4, Ans. (c), 35. If sinθ – cosθ = 0 then the value of sin4θ + cos4θ is, (a) 1, (b) 3/4, (c) 1/2, Ans. (c), , (d) 1/4, , 36. Evaluate: 4 sin2 60° + 3 tan2 30° – 8 sin 45° cos 45°, (a) 0, (b) 1, (c) 2, Ans. (a), , (d) 5, , 37. A square ABCD is inscribed in a circle of radius 10 units. The area of the circle, not included in the, square is (Take = 3.14), (a) 84 cm2, (b) 108 cm2, (c) 114 cm2, (d) 122 cm2, Ans. (c), 38. Two dice are rolled simultaneously. The probability that they show different faces is, (a) 2/7, (b) 1/6, (c) 1/3, (d) 5/6, Ans. (d), 39. A game consists of tossing a coin 3 times and noting the outcomes each time. If getting the same, result in all the tosses is a success, the probability of losing the game is, (a) 3/4, (b) 1/4, (c) 3/8, (d) 1, Ans. (a), 40. A letter of English alphabet is chosen at random. The probability that the chosen letter is a consonant, is, (a) 7/26, (b) 5/26, (c) 11/26, (d) 21/26, Ans. (d), , SECTION – C, Section- C consists of two Cases followed by questions., There are a total of 10 questions in this section. Attempt any 08 questions from this section., The first attempted 08 questions would be evaluated., Case Study – 1, Travelling by a Bike on a highway gives lots of fun and thrills. People drive and enjoy the moment of, thrills., , Prepared by: M. S. KumarSwamy, TGT(Maths), , Page - 4-

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On morning two friends who are living at a distance of 150 km apart decided to meet at another place., So, they drive their Bikes from point A and point B at the same time and meet after 15 hours on a, highway., , In an another incident they decide to meet in a hurry. So, they drive their Bike in opposite, directions and meet in one hour., , 41. Using the speed of Bike at A, x km/h and the speed of Bike at B, y km/h, the pair of linear, equations representing the situation is, (a) 15x + 15y = 150, x + y = 150 (b) 15x - 15y = 150, x + y = 150 (c) 15x - 15y = 150, x - y = 150, (d) 15x + 15y = 150, x - y = 150, Ans. (b), 42. On comparing the coefficients of the pair of linear equations formed by the above situations,, following conditions can arise, a, b, a, b, c, a, b c, (a) 1  1 (b) 1  1  1 (c) 1  1  1 (d) None of these, a2 b2, a2 b2 c2, a2 b2 c2, Ans. (a), 43. The lines drawn on the graph paper for the pair of linear equations formed due to above situations, can have one of following possibilities., (a) The two lines intersect at one point, (b) The two lines do not intersect, (c) The two lines coincide, (d) Cannot be said anything, Ans. (a), 44. The solutions of the pair of linear equations formed by above situation is, (a) a unique solution (b) no solution (c) infinitely many solution (d) not to be determined, Ans. (a), 45. The speeds of Bike at A and Bike at B are, (a) 70 km/h, 80 km/h (b) 90 km/h, 60 km/h (c) 80 km/h, 70 km/h (c/) 60 km/h, 90 km/h, Ans. (c), Case Study – 2, One day Kumar Sir, while explaining different types of parabolas for different quadratic polynomial to, the students of Class X-B. After explanation, he draws different parabola and asking questions to the, students. Out of all the different parabola, one parabola is shown in below figure. Based on this figure,, Answer the following questions:, Prepared by: M. S. KumarSwamy, TGT(Maths), , Page - 5-

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46. What is the name of the shape of the figure?, (a) Upward Parabola, (b) Downward Parabola, Ans. (b), , (c) Right Parabola, , (d) Left Parabola, , 47. How many zeroes are there for the polynomial?, (a) 1, (b) 2, Ans. (b), , (c) 3, , (d) 4, , 48. The zeroes of the polynomial are, (a) (-2, 0), (b) (0, 2), Ans. (d), , (c) (-1, 2), , (d) (-2, 2), , 49. The expression of the polynomial is, (a) x2 + 4x + 4, (b) x2 – 4x + 4, Ans. (d), , (c) x2 – 4, , (d) - x2 + 4, , 50. The value of the polynomial if x = -2 is, (a) 16, (b) 12, Ans. (d), , (c) 8, , (d) 0, , Prepared by: M. S. KumarSwamy, TGT(Maths), , Page - 6-