PGT Mathematics 1. 2. 3. 4. - 5. 6.aps-csb.in/OldQuestionPapers/PartB/PGT/Mathematic/4year.pdf ·...

6830371244894110 AWES PGT Mathematics Part B

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/x2

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 d. None of the above

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% d. None of the above

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]


d. None of the above

7. If sin4x + cos

4y + 2 = 4 sinx cosy, 0 ≤ x, y ≤ π/2, then sin x + cos y is:-

a. 2 b. 0 c. -2 d. None of the above

8. If A & B are two matrices such that AB = B and BA = A, then A2 - B

2 is equal to:-

a. 2AB b. A + B c. 2BA d. None of the above

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


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, 23n

- 1 is divisible by:-

a. 16 b. 8 c. 32 d. None of the above

13. The solution of the equation |z| - z = 1 + 2i is:-

a. (3/2) + 2i b. (3/2) - 2i c. 2 - (3/2)i d. None of the above

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 x2 + 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)



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! d. None of the above

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?


19. The remainder left out when 82n

- 622n + 1

is divided by 9 is:-

a. 0 b. 7 c. 8 d. 2

20. If A and B are coefficients of xn in the expansion of (1 + x)

2n and (1 + x)

2n - 1 respectively then:-

a. A = B b. A = 2B c. 2A = B d. None of the above

21. The product of 91/3

. 91/9

. 91/27

...........to infinity is:-


22. If ax = b

y = c

z = k and x, y, z are in GP, then:-

a. logca = logac


b. logba = logbc c. logba = logcb d. None of the above

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 d. None of the above

26. The set of all points where the function f(x) = 2x|x| is differentiable is:-

a. (0, ∞) b. (- ∞, 0) c. (-∞, ∞) d. None of the above

27. If y = (x2 + 1)

sinx then y'(0) is:-

a. 0 b. e

2

c. 1/2 d. None of the above


28. The coordinates of the point on the parabola y2 = 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) d. None of the above

29. If the curves y2 = 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 d. None of the above

30. If then:-

a. k = (-1/5) b. k = (-1/2) c. k = (-1/8) d. None of the above

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)


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 d. None of the above

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


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

2β = 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:-


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 y2 = 8x so that one angular

point is at the vertex is:-

a. 16√3 b. 4√3 c. 8√3



44. The eccentricity of the curve represented by the equation x2 + 2y

2 - 2x + 3y + 2 = 0 is:-

a. 1/2 b. 1/√2 c. 0 d. None of the above

45. If Then x is:-

a. ey + 1

b. ey

c. ey - 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:-


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 d. None of the above

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] d. None of the above


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 d. None of the above

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 d. None of the above

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° d. None of the above

52. If pairs of lines 3x2 - 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


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. 4.5m2

b. 81 m2

c. 5.4m2

d. 9 m2

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 cm2

b. 960π cm2

c. 640π cm2

d. 240π cm2

57. If 2a + 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) d. None of the above

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


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

PGT Mathematics 1. 2. 3. 4. - 5. 6.aps-csb.in/OldQuestionPapers/PartB/PGT/Mathematic/4year.pdf ·...

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