PGT Mathematics. 1. The domain of f(x) = is:-

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1 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 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 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

2 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 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 = If Δ(x) = then, is:- a. 0 b. -1/2 c. 1/4 d. 1/2 Page 2

3 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 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 = Solution set for -2 6x - 1 < 2 is:- a. [-2, 2) b. [-1/6, 1/2) c. [-1, 3) Page 3

4 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 The remainder left out when 8 2n n + 1 is divided by 9 is:- a. 0 b. 7 c. 8 d 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 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

5 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/ 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 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

6 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 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

7 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 Ce -tanx b. y = tanx 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

8 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 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 b. 4 3 c. 8 3 Page 8

9 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 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 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 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

10 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/ 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 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 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

11 b. 3π + 4 c. 4π + 6 d. 6π If the perimeter of an isosceles right triangle is ( )m, then the area of triangle is:- a. 4.5m 2 b. 81 m 2 c. 5.4m 2 d. 9 m 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 If 2 a + 3 b = 17 and 2 a b + 1 = 5, then:- a. a = 2, b = -3 b. a = 2, b = 3 c. a = 3, b = 2 d. a = -2, b = 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 % b % c % 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

12 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

MockTime.com. NDA Mathematics Practice Set 1.

MockTime.com. NDA Mathematics Practice Set 1. 346 NDA Mathematics Practice Set 1. Let A = { 1, 2, 5, 8}, B = {0, 1, 3, 6, 7} and R be the relation is one less than from A to B, then how many elements will R contain? 2 3 5 9 7. 1 only 2 only 1 and