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CBSE Class 10 Pre Board 2022 : Mathematics (Air Force Bal Bharati School (AFBBS), New Delhi)

8 pages, 50 questions, 3 questions with responses, 3 total responses,

Rosanne Chugh
Air Force Bal Bharati School (AFBBS), New Delhi
KG- 12TH

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AIR FORCE SCHOOLS COMMON PRE-BOARD EXAMINATION 2021-22 Term I CLASS X Please check that this question paper contains 08 printed pages. Please check that this question paper contains 50 questions Subject Mathematics Time: 90 minutes Max. 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. Any 16 questions are to attempted. 3. Section B consists of 20 questions of 1 mark each. Any 16 questions are to attempted. 4. Section C consists of 10 questions based on two case Studies. Attempt any 8 questions. 5. There is no negative marking. SECTION A (Q. 1 to Q. 20 Attempt any 16) 1. A fair die is thrown once. The probability of getting either a composite number or a prime number, is (a) 1 6 (b) 5 6 (c) 1 (d) 0 2. The area of the largest triangle, that can be inscribed in a semicircle of radius of radius r units, is (a) 2 1 (b) 2 1 (c) 2 2 (d) 2 2 (c) 1 (d) 0 3. Value of 9 2 9 2 is (a) 9 (b) -9 Page 1 of 8 4. ~ such that AB = 9.1 cm. and DE = 6.5 cm. If the perimeter of = 25 . Then the perimeter of is (a) 28 cm. (b) 35 cm. (c) 42 cm. (d) 49 cm. 5. If the centroid of the triangle XYZ, whose vertices are X(p, q), Y(q, r) and Z(r, p), is at origin then p3 + q3 + r3 = (a) 0 (b) p + q + r (c) pqr (d) 3pqr 6. If the system of linear equations 2x + ky = 7, 4x 8y 12 = 0 is consistent and independent, then the value of k is (a) -4 (b) 4 (c) all real numbers except 4 (d) all real numbers except -4 7. The graph of x2 1 (a) touches x axis at a point (b) intersects x axis at two distinct points (c) neither touches nor intersects x -axis (d) can t say 6 8. The decimal expansion of 1250 will terminate after (a) one decimal place (b) two decimal places (c) three decimal places (d) Four decimal places 9. Which of the following pairs of numbers can never be H.C.F. and L.C.M. respectively of two numbers? (a) (12, 24) (b) (15, 90) (c) (18, 54) (d) (17, 50) 10. The zeroes of the quadratic polynomial 2 + 99 + 127 are (a) Both positive (b) One positive and one negative (c) Both negative (d) Both equal Page 2 of 8 11. The area of the triangle formed by the lines x + y = 4, x-axis and y-axis, is (a) 4 sq. units (b) 8 sq. units (c) 16 sq. units (d) 32 sq. units 12. The point which divides the line segment joining the points (2, -2) and (-14, 6) in the ratio 3 : 5 internally, lies in quadrant (a) I (b) II (c) III (d) IV 13. The ratio of length of a side of an equilateral triangle and its altitude is (a) 2 : 1 (b) 1 : 2 (c) 2: 3 (d) 3: 2 14. If cot = , then the value of + cot is (a) k + 1 (b) k 1 1 (c) (d) k 5 15. If the area of a sector of a circle is 18 of the area of the circle, then the central angle of the sector is (a) 1000 (b) 900 (c) 750 (d) 600 16. The ace, king and queen of diamonds are removed from a pack of 52 playing cards. The cards are reshuffled and a card is drawn. The probability of getting a face card is (a) 9 49 (b) 10 49 (c) 11 49 (d) 12 49 17. Ratio of the areas of two similar triangles is 4 : 9. The ratio of their corresponding medians is (a) 16 : 81 (b) 4 : 9 (c) 2 : 3 (d) 81 : 16 5 sin 3 18. If 5 tan = 4, then 5 +3 is 1 (a) 7 2 (b) 7 (c) 0 (d) 3 7 19. If the zeroes of the quadratic polynomial 2 + + , ( 0) , are equal, then (a) c and a have opposite signs. (b) c and b have opposite signs. (c) c and a have same signs. (d) c and b have same signs. 20. If a = 23 x 3, b = 2 x 3 x 5, c = 3n x 5 and L.C.M.(a, b, c) = 23 x 33 x 5, then n = (a) 1 (b) 2 (c) 3 (d) 4 Page 3 of 8 SECTION B (Q. 21 to Q. 40 Attempt any 16) 21. The quadratic polynomial whose sum and difference of zeroes are 4 and 6 respectively, is (a) x2 + 4x + 6 (b) x2 4x + 6 (c) x2 4x 5 (d) x2 4x + 5 22. Ratio of L.C.M. and H.C.F. of smallest odd composite number and largest 2-digit composite number is (a) 1 : 3 (b) 3 : 1 (c) 1 : 11 (d) 11 : 1 23. The number, whose prime factorization is equal to the product of smallest three odd primes, is (a) 165 (b) 135 (c) 105 (d) 115 24. The sum of numerator and denominator of a fraction is 4 times the numerator. If the 2 numerator and denominator are increased by 3 , the fraction becomes . The pair of 3 equations representing the situation is (a) 3x y = 0 ; 3x - 2y + 3 = 0 (b) 3 + y = 0 ; 3x - 2y - 3 = 0 (c) y = 3x ; 3x + 2y + 3 = 0 (d) x y + 4 = 0 ; 3x + 2y - 3 = 0 25. One of the equations of a pair of linear equations having unique solution, is 2x y =1. The other possible equation is : (a) 2x y 3 = 0 (b) 4x 2y = 2 (c) 4x 2y = 1 (d) 3x y 5 =0 26. The point (3, 7a) lies on a circle whose centre is at origin and radius is 5 units. One of the values of a, is Page 4 of 8 1 (a) 7 3 3 (b) 7 (c) 7 4 (d) - 7 27. The coordinates of the circumcentre of the right triangle ABC having vertices A(0, -4) B(0, 0) and C(6, 0), are (a) (6, 4) (b) (6, -4) (c) (2, -4) (d) (3, -2) 28. In , DE BC, If AD = x + 3, AB = 2x, AE = x + 5 and AC = 2x + 3, then value of x is (a) 5 (b) 6 (c) 9 (d) 8 29. If in triangles ABC and DEF, = , then they will be similar when (a) = (b) = (c) = (d) = 30. Find the perimeter of a rhombus whose diagonals are 16 cm. and 12 cm. (a) 40 cm. (b) 100 cm. (c) 50 cm. (d) 150 cm. 31. If ABC is an equilateral triangle then value of cos(A + 2B 3C) is (a) 0 (b) 1 (c) 2 2 32. If 2 = , then (a) 4 (d) 3 = (b) 4 (c) 4 (d) 4 33. If = 2 , = 2 then x y = (a) xy (b) x + y (c) x2 + y2 (d) 2x y 34. A pair of dice is rolled. The probability of not getting a doublet is 1 (a) 6 5 1 (b) 6 (c) 2 1 (d) 3 35. A number is selected at random from -5 , -4, -3, -2, -1, 0, 1, 2, 3, 4, 5. The probability that its square is less than 5. 2 (a) 11 3 (b) 11 4 (c) 11 5 (d) 11 36. A letter of English alphabet is chosen at random. What is the probability that the chosen letter is a consonant. 19 (a) 26 (b) 5 26 (c) 21 26 1 (d) 26 37. Two poles of heights 5 m. and 8 m. stand vertically on a plane ground. If distance between their feet is 4 m., then the distance between their tops is (a) 10 m. (b) 17m. (c) 5 m. (d) 6 m. 38. The system of linear equations 2x + 3y = 2 and x ky= 1 has unique solution for Page 5 of 8 (a) Unique value of k (b) Exactly 2 values of k (c) No value of k (d) Infinite values of k 39. The lines representing the equations y = 3x, x = 5 and y = 0 make a (a) right triangle (b) acute triangle (c) obtuse triangle (d) isosceles triangle 40. The least number that is divisible by all the numbers from 1 to 10, is (a) 2100 (b) 2520 (c) 90 (d) none of these SECTION C (Q. 41 to Q. 50 Attempt any 8) Case Study 1 : A right triangular field ABC, right angled at B, with sides 7 m., 24 m. and 25m. is constructed. Three animals a cow, a buffalo and a horse are tied to three vertices A, B and C respectively by a rope of length 3.5 m. each as shown in the figure. Based on the above information, answer the following questions ; 41. Which animal will get the least area to graze? (a) Cow (b) buffalo (c) horse (d) can t say Page 6 of 8 42. The area available to buffalo will be .the total area available to the cow and horse. (a) less than (b) more than (c) equal to (d) can t say 43. Total area ( in sq. m.) grazed by the animals is (a) 77 4 (b) 77 2 (c) 77 (d) 154 44. Area ( in sq. m.) left ungrazed is (a) 91 2 (b) 259 4 (c) 351 4 (d) 167 2 45. Total length (in m.) of the arcs of three sectors, is (a) 3.5 (b) 3.5 (c) 3.52 (d) Case study 2 : Many modern cities like Chicago have been built on the basis of the Cartesian plane. In Chicago, even the names of streets follow the Cartesian coordinate system logic of East West and South North. Based on the above information, answer the following questions ; 46. What are the coordinates of the point of intersection of the diagonals of square ABCD? (a) (2a, 2a) (b) (a, a) (c) (2 , 2 ) (d) ( 0, 2a) (c) 4 (d) 4 2 47. Length of diagonal AC is (a) 2 (b) 2 2 Page 7 of 8 48. What are the coordinates of the reflection of point C in the y-axis? (a) (a, a) (b) (2a, 2a) (c) (-2a, -2a) (d) (-2a, 2a) 49. The ratio in which diagonal BD is divided by diagonal AC, is (a) (1 : 2) (b) (2 : 1) (c) 1 : 3) (d) (1:1) 50. If each side of the square be increased by 50%, what would be the coordinates of the vertex B? (a) (0, 3a) (b)( 3a, 0) (c) (3a, a) (d) (a, 3a) Page 8 of 8

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