Will you provide me the sample question paper of Birla Institute of Technology and Science Aptitude Test (BITSAT) Exam for preparation?

[prince karak]

I am providing you the sample question paper of Birla Institute of Technology and Science Aptitude Test (BITSAT) Exam

BITSAT Exam question paper

Mathematics

1. If α, β are the roots of ax2 + bx + c = 0 then (-1/α), (-1/β) are the roots of

(a) ax2 – bx + c = 0
(b) cx2 – bx + a = 0
(c) cx2 + bx + a = 0
(d) ax2 – bx – c = 0

2. The number of real roots of the equation

(x – 1)2 + (x – 2)2 + (x – 3)2 = 0 is

(a) 1
(b) 2
(c) 3
(d) None of these

3. If S is the set containing values of x satisfying [x]2 – 5[x] + 6 ≤ 0 , where [x] denotes GIF then S contains

(a) (2, 4)
(b) (2, 4]
(c) [2, 3]
(d) [2, 4)

4. Seven people are seated in a circle. How many relative arrangements are possible?

(a) 7!
(b) 6!
(c) 7P6
(d) 7C6

5. In how many ways can 4 people be seated on a square table, one on each side?

(a) 4!
(b) 3!
(c) 1
(d) None of these

6. Four different items have to be placed in three different boxes. In how many ways can it be done such that any box can have any number of items?

(a) 34
(b) 43
(c) 4P3
(d) 4C3

7. What is the probability that, if a number is randomly chosen from any 31 consecutive natural numbers, it is divisible by 5?

(a) (6/31)
(b) (7/31)
(c) (6/31) or (7/31)
(d) None of these

8. The mean of a binomial distribution is 5, then its variance has to be

(a) > 5
(b) = 5
(c) < 5
(d) = 25

9. If a is the single A.M. between two numbers a and b and S is the sum of n A.M ‘s between them, then S/A depends upon

(a) n, a, b
(b) n, a
(c) n, b
(d) n

10. 21/4 41/8 81/16 161/32 .. upto ∞ equal to

(a) 1
(b) 2
(c) 3/2
(d) 5/2

11. The odds in favour of India winning any cricket match is 2 : 3. What is the probability that if India plays 5 matches, it wins exactly 3 of them?

12. For an A.P., S2n = 3 Sn. The value of (S3n/Sn) is equal to

(a) 4
(b) 6
(c) 8
(d) 10

13. 1 + sin x + sin2 x + sin 3 x + … = 4 + 2√3, 0 < x < π, x ≠ π/2 then x =

(a) (π/6, π/3)
(b) (π/6, 5π/6)
(c) (π/3, 2π/3)
(d) (π/3, 5π/6)

14.

(a) x2
(b) x
(c) loge(1 + x)
(d) loge x2

15. The ends of a line segment are P(1, 3) and Q(1, 1). R is a point on the line segment PO such that PR : QR = 1 : λ. If R is an interior point of the parabola y2 = 4x, then

(a) λ ∈ (0, 1)
(b) λ ∈ (-3/5, 1)
(c) λ ∈ (-1/2, -3/5)
(d) None of these

16. Set of values for which

is true is

(a) φ
(b) nπ + (π/4), n ∈ Z
(c) (π/4)
(d) 2nπ + π/4, n ∈ Z

17. The distance between the lines 3x + 4y = 9 and 6x + 8y + 15 = 0 is

(a) 3/10
(b) 33/10
(c) 33/5
(d) None of these

18. Let A = (3, -4), B(1, 2) and P = (2k – 1, 2k + 1) is a variable point such that PA + PB is the minimum. Then k is

(a) 7/9
(b) 0
(c) 7/8
(d) None of these

19. The length of the y-intercept made by the circle x2 + y2 – 4x 6y – 5 = 0 is

(a) 6
(b) √14
(c) 2√14
(0 3

20. If x + y = k is normal to y2 =12x, then k =

(a) 3
(b) 6
(c) 9
(d) None of these

21. The number of values of c such that the straight line y = 4x + c touches the curve (x2/4 + y2 = 1)

(a) 1
(b) 1
(c) 2
(d) infinite

22.

(a) 0
(b) √2
(c) 1/2
(d) 1/√2

23. Locus of the point z satisfying Re (i/z) = k is a non-zero real number, is

(a) a straight line
(b) a circle
(c) an ellipse
(d) a hyperbola

24. The points of z satisfying arg

lies on

(a) an arc of a circle
(b) a parabola
(c) an ellipse
(d) a straight line

25. The coefficients of the (3r)th term and the (r + 2)th term in the expansion (1 + x)2n are equal, then

(a) n = 2r
(b) n = 3r
(c) n = 2r + 1
(d) None of these

26.

(a) 2e
(b) e
(c) e – 1
(d) 3e

27. If a = 13, b = 12, c = 5 in ∠ABC, then sin(A/2) =

(a) (1/√5)
(b) (2/3)
(c) √(32/35)
(d) (1/√2)

28. 2tan-1 (3/4)

(a) sin-1(24/25)
(b) sin-1(12/13)
(c) cos-1(24/25)
(d) cos-1(12/13)

29. Two pairs of straight lines have the equations y2 + xy – 12x2 = 0 and ax2 + 2hxy + by2 = 0. One line will be common among them if

(a) a = -3(2h + 3b)
(b) a = 8(h – 2b)
(c) a = 2 (b + h)
(d) Both (a) and (b)

30. If a circle passes through the point (3, 4) and cuts x2 + y2 = 9 orthogonally, then the locus of its centre is 3x + 4y = λ X. Then λ =

(a) 11
(b) 13
(c) 17
(d) 23

31. For what value of x, the matrix A is singular

(a) x = 0, 2
(b) x = 1, 2
(c) x = 2, 3
(d) x = 0, 3

32. 1f 7 and 2 are two roots of the following equation

then its third root will be

(a) -9
(b) 14
(c) 1/2
(d) None of these

33. Period of f(x) = sin4 x cos4 x

(a) π
(b) π/2
(c) 2π
(d) None of these

34. The range Of loge (sin x)

(a) (- ∞, ∞)
(b) (- ∞, 1)
(c) (- ∞, 0]
(d) (- ∞, 0)

35.

(a) (1/8)
(b) (-1/8)
(c) (2/3)
(d) (3/2)

36. Let y = log sin(x2), 0 < x ≤ π/2;. The value of (dy/dx) at x = (√π/2) is

(a) 0
(b) 1
(c) (π/-4)
(d)√π

37. For the curve x = t2 – 1, y = t2 – t tangent is parallel to x-axis where

(a) t = 0
(b) t = (1/√3)
(c) t = 1/2
(d) t = (-1/√3)

38. f(x) = x3 – 6x2 + 12x – 16 is strictly decreasing for

(a) x ∈ R
(b) X ∈ R – {1}
(c) x ∈ R+
(d) x ∈ (φ)

39. The value of b for which the function f(x) = sinx – bx + c is a strictly decreasing function ∀ x ∈ R is

(a) b ∈ (-1, 1)
(b) b ∈ (-α, 1)
(c) b ∈ (1, α)
(d) b ∈ [1, α)

40. Maximum value of the expression 2 sinx + 4 cosx + 3 is

(a) 2√5 + 3
(b) √5 – 3
(C) √5 + 3
(d) None of these

41. If sin θ = 3 sin(θ + 2 α) , then the value of tan(θ + α)+ 2 tanα is

(a) 3
(b) 2
(c) 1
(d) 0

42.

(a) 10
(b) (1/10)
(c) 1
(d) -1

43. If √1 + x2 + √1 + y2 = a then find (dy/dx) =

44. Length of the subtangent to the curve y = ex/a is

(a) ex/a
(b) a
(c) 2/a
(d) None of these

45. The value of c of mean value theorem when f(x) = x3 – 3x – 2 in [-2, 3] is

(a) (√7/3)
(b) (√3/7)
(c) (√7/3)
(d) (√3/7)
Physics

46. A gold coin has a charge of + 10-4 C. The number of electrons removed from it is

(a) 106
(b) 625 x 1010
(c) 1.6 x 10-25
(d) 1.6 x 10-13

47. A small sphere of mass m and electric charge q1 is suspended by a light thread. A second sphere carrying a charge q2 is placed directly below the first sphere at a distance ‘d’ away. Then

(a) tension in thread may reduce to zero if the spheres are positively charged
(b) tension in thread may reduce to zero if the spheres are oppositely charged
(c) tension in thread can never be zero
(d) tension in thread is independent of the nature of the charges

48. A pitch ball covered with a tin foil having a mass m kg hangs by a fine silk thread of length l metres in an electric field E. When the ball is given an electric charge of q coulomb, it stands out d metre apart from the vertical line. The magnitude of an electric field will be

49. The current I and voltage V graphs for a given metallic wire of two different temperatures T1 and T2 are shown in the following figure. It is concluded that

(a) T1 > T2
(b) T1 < T2
(c) T1 = T2
(d) T1, = 2T2

50. The resistance of a 20 cm long wire is 5 Ω.

The wire is stretched to form a uniform wire of 40 cm length. The resistance now will be

(a) 5 Ω
(b) 10 Ω
(c) 20 Ω
(d) 200 Ω