PGT Mathematics 1. The domain of f(x) = is:- a. (-2, + ) b. R-{-1, -2, -3} c. (-3, + )-{-1, -2} d. R-{-1, -2} 2. If f is a function such that f(0) = 2, f(1) = 3 & f(x+2) = 2f(x)-f(x + 1) for every real x then f(5) is:- a. 1 b. 7 c. 5 d. 13 3. If cos -1 x =tan -1 x, then sin(cos -1 x) is:- a. 1/x 2 b. x c. 1/x d. x 2 4. If cos -1 (3/5) - sin -1 (4/5) = cos -1 x, then x is:- a. -1 b. 1 c. 0 5. In a city, three daily newspapers A, B, C are published. 42% of the people in that city read A, 51% read B and 68% read C. 30% read A & B, 28% read B & C, 36% read A & C, 8% do not read any of the three newspapers. The percentage of persons who read all the three papers is:- a. 18% b. 25% c. 20% 6. The least positive root of the function sinx - π/2 + 1 = 0 lies in the interval:- a. [0, π/2] b. [π/2, π] c. [π/2, 3π/2] Page 1
7. If sin 4 x + cos 4 y + 2 = 4 sinx cosy, 0 x, y π/2, then sin x + cos y is:- a. 2 b. 0 c. -2 8. If A & B are two matrices such that AB = B and BA = A, then A 2 - B 2 is equal to:- a. 2AB b. A + B c. 2BA 9. The system of linear equations x + y + z = 2, 2x + y - z = 3, 3x + 2y + kz = 4 has a unique solution if:- a. -1 < k < 1 b. k 0 c. -2 < k < 2 d. k = 0 10. If Δ(x) = then, is:- a. 0 b. -1/2 c. 1/4 d. 1/2 Page 2
11. If the system of linear equations x + 2ay + az = 0 x + 3by + bz = 0 x + 4cy + cz = 0 has a non zero solution, then a, b, c:- a. Are in AP b. Satisfy a + 2b + 3c = 0 c. Are in GP d. Are in HP 12. For each n N, 2 3n - 1 is divisible by:- a. 16 b. 8 c. 32 13. The solution of the equation z - z = 1 + 2i is:- a. (3/2) + 2i b. (3/2) - 2i c. 2 - (3/2)i 14. The equation of represents a:- a. Parabola b. Hyperbola c. Straight line d. Circle 15. If α and β are the roots of the equation x 2 + x α + β = 0, then the values of α and β are:- a. α = 2, β = 1 b. α = 2, β = -2 c. α = 1, β = -2 d. α = 1, β = -1 16. Solution set for -2 6x - 1 < 2 is:- a. [-2, 2) b. [-1/6, 1/2) c. [-1, 3) Page 3
17. The Chief Ministers of 11 states of India meet to discuss the language problem. The number of ways they can seat themselves at a round table so that the Punjab and Delhi Chief Ministers sit together is:- a. 9! X 2! b. 10! c. 11! X 2! 18. In an examination a candidate has to pass in each paper to be successful. If the total number of ways to fail is 63, how many papers are there in the examination? a. 8 b. 14 c. 6 19. The remainder left out when 8 2n - 62 2n + 1 is divided by 9 is:- a. 0 b. 7 c. 8 d. 2 20. If A and B are coefficients of x n in the expansion of (1 + x) 2n and (1 + x) 2n - 1 respectively then:- a. A = B b. A = 2B c. 2A = B 21. The product of 9 1/3. 9 1/9. 9 1/27...to infinity is:- a. 81 b. 3 c. 9 22. If a x = b y = c z = k and x, y, z are in GP, then:- a. log c a = log a c Page 4
b. log b a = log b c c. log b a = log c b 23. equals:- a. 1/8 b. 1/4 c. π/2 d. 1/16 24. Let f(x) =. Then f(x) is continuous on:- a. [-6, 6] b. [6, 10] c. [1, 7] d. [-2, 2] 25. is equal to:- a. 0 b. c. 1 26. The set of all points where the function f(x) = 2x x is differentiable is:- a. (0, ) b. (-, 0) c. (-, ) 27. If y = (x 2 + 1) sinx then y'(0) is:- a. 0 b. e 2 c. 1/2 Page 5
28. The coordinates of the point on the parabola y 2 = 8x, which is at minimum distance from the circle x 2 + (y + 6) 2 = 1 are:- a. (18, -12) b. (2, -4) c. (2, 4) 29. If the curves y 2 = 6x, 9x 2 + by 2 = 16, cut each other at right angles then the value of b is:- a. 9/2 b. 2 c. 4 30. If then:- a. k = (-1/5) b. k = (-1/2) c. k = (-1/8) 31. is equal to:- a. b. + C c. log(x 4 + 1) + C 32. If then g(x + π) equals to:- a. g(x) / g(π) b. g(x) + g(π) c. g(x). g(π) Page 6
d. g(x) - g(π) 33., equals to:- a. π b. π/4 c. π/3 d. π/2 34. Area of the region is equal to:- a. 1/7 sq unit b. 1/3 sq unit c. 1/6 sq unit 35. The solution of differential equation 2x(dy/dx) - y = 3 represents a family of:- a. Ellipses b. Circles c. Straight lines d. Parabolas 36. Solution of the differential equation cos 2 x (dy/dx) + y = tanx is equals to:- a. y = tanx - 1 + Ce -tanx b. y = tanx - 1 + C c. y = cotx + Ce -tanx 37. The value of 'a', so that the volume of the parallelepiped formed by i + aj + k, j + ak and ai + k becomes minimum is:- a. 3 b. -3 c. 3 d. 1/ 3 Page 7
38. Let a = i + 2j + k, b = i - j + k and c = i + j - k. A vector in the plane of a & b whose projection on c is (1/ 3) is:- a. 4i - j + 4k b. 3i + j + 3k c. 4i + j - 4k d. 2i + j + 2k 39. Let a, b, c be distinct non-negative numbers. If the vectors ai + aj + ck, i + k and ci + cj + bk lie in a plane, then c is:- a. Equal to zero b. AM of a & b c. HM of a & b d. GM of a & b 40. A line makes the same angle θ, with each of the x and z-axis. If the angle β, which it makes with y- axis, is such that sin 2 β = 3 sin 2 θ, then cos 2 θ equals to:- a. 3/5 b. 2/5 c. 3/2 d. 1/5 41. The radius of the circular section of the sphere r = 5 by the plane r.(i + j + k) = 3 3 is:- a. 8 b. 16 c. 4 42. The line of the intersection of the planes r.(3i - j + k) = 1 and r.(i + 4j - 2k) = 2 is parallel to the vector:- a. 2 i + 7j -13k b. -2 i -7j + 13k c. 2 i +7j + 13k d. -2 i + 7j + 13k 43. The length of the side of an equilateral triangle, inscribed in the parabola y 2 = 8x so that one angular point is at the vertex is:- a. 16 3 b. 4 3 c. 8 3 Page 8
44. The eccentricity of the curve represented by the equation x 2 + 2y 2-2x + 3y + 2 = 0 is:- a. 1/2 b. 1/ 2 c. 0 45. If Then x is:- a. e y + 1 b. e y c. e y - 1 d. log(1 + y) 46. The mean of 10 numbers is 12.5, the mean of the first six is 15 and the last five is 10. The sixth number is:- a. 18 b. 15 c. 12 47. If the Standard Deviation of numbers 2, 4, 5 & 6 is a constant α, then the standard deviation of the numbers 4, 6, 7 & 8 is:- a. α b. 2α c. α+2 48. If the mean of a binomial distribution is 25, then its standard deviation lies in the interval given below:- a. [0,25) b. [0,5) c. (0,5] Page 9
49. A student is given a true-false exam with 10 questions. If he gets 8 or more correct answers, he passes the exam. Given that he guesses at the answer to each question, the probability that he passes the exam is:- a. 7/128 b. 6/128 c. 9/128 50. If A and B are two independent events such that, P(A') = 7/10, P(B') = α and P(AUB) = 8/10, then α is:- a. 2/7 b. 1 c. 5/7 51. In a right angled triangle, the hypotenuse is four times as long as the perpendicular drawn to it from the opposite vertex. One of the acute angle is:- a. 15 b. 45 c. 30 52. If pairs of lines 3x 2-2pxy - 3y 2 = 0 and 5x 2-2qxy - 5y 2 = 0 are such that each pair bisects the angle between the other pair, then pq is equal to:- a. -15 b. -1 c. -3 d. -5 53. A circle touches the x-axis and also touches the circle with centre at (0, 3) and radius 2. The locus of the centre of the circle is:- a. Hyperbola b. Circle c. Ellipse d. Parabola 54. Each circle of radius 1 cm, touches each other. Then the perimeter of rope incomparing the three circles is:- a. 2π + 6 Page 10
b. 3π + 4 c. 4π + 6 d. 6π + 6 55. If the perimeter of an isosceles right triangle is (6 + 3 2)m, then the area of triangle is:- a. 4.5m 2 b. 81 m 2 c. 5.4m 2 d. 9 m 2 56. A conical cavity is drilled in a circular cylinder of height 15 cm and base radius 8 cm. The height and the base radius of the cone are also same. Then, the whole surface area of remaining solid is:- a. 440π cm 2 b. 960π cm 2 c. 640π cm 2 d. 240π cm 2 57. If 2 a + 3 b = 17 and 2 a + 2-3 b + 1 = 5, then:- a. a = 2, b = -3 b. a = 2, b = 3 c. a = 3, b = 2 d. a = -2, b = 3 58. At what point the origin be shifted if the coordinates of a point (4,5) become (-3,9)? a. (1, 4) b. (7,14) c. (7, -4) 59. What percent profit would be if 34% of cost price is 26% of the selling price? a. 25.16% b. 30.77% c. 88.40% d. 74% 60. If the height of a triangle is decreased by 40% and its base is increased by 40%, what will be the effect on its area? a. 16% Increase Page 11
b. 8% Decrease c. No change d. 16% Decrease 02 Feedback 61. How was the overall experience while giving the test? a. Excellent b. Very Good c. Good d. Average Page 12