Exponential and Logarithmic Series

BITS MOCK TEST-2

8 INFOMATHS/MCA/MATHEMATICS

SECTION – 1 MATHS

1 The value of C0 + 2C1 + 3C2 + .. + (n + 1) Cn is

(a) (n + 2) 2n – 1 (b) n.2n – 1

2. The three consecutive coefficients in the expansion of (1 + x)n are 28, 56 and 70, then n is

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

3. The greatest term in expansion of (5 – 4x)-7, when x = ½, is

(a) t2 (b) b2 = t3 (c) t4 = t5 (d) t3 = t4

4. The sum of coefficient in expansion of (1 + x – 3x)216, is

(a) 2216 (b) 2216 – 1 (c) –1 (d) 1

5. The value of , is

(a) 2 e (b) 3 e (c) 3e – 1 (d) e

6. Value of

(a) (b) (c) (d)

7. Sum of series , is

(a) log (3/4) (b) log (4/3)

8. Value of determinant is

(a) a b c (b) 2 abc (c) 3 abc (d) 4abc

9. If w is a cube root of unity, then value of

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

10. One root of

(a) 3 (b) 4 (c) 2 (d) 1

11. If D = and D’ = then D’ is equal to

(a) D (b) 3 D (c) 9 D (d) 27 D

12. The matrix A = is

(a) Singular (b) Invertibla

13. If A is square matrix of order n ´ n, then adj (adj A) is

(a) |A|n – 1 A (b) |A|n – 2 A

14. Last row of inverse of is

(a) (b) 2, 4, -2

15. If A is (n ´ 1) non zero matrix and B is (1 ´ n) non-zero matrix the R (AB) is

(a) 2 (b) n (c) n2 (d) 1

16. The correct set of eigen value of is

(a) 4, -2, -3 (b) –5, 2, 2

17. The number of solution of x + y – z = 0 3x – y –z = 0 and x – 3y + z = 0, is

(a) 1 (b) 2 (c) 0 (d) ¥

18. The value of p for which the system of equations x + y + z = 1, x + 2y + z = 2 and x + 4y + 10z = p has a solution, is

(a) 3 (b) 4 (c) 15 (d) -6

19. Equation of circle passing through point of intersection of circles x2 + y2 = 6 and x2 + y2 – 6x + 8 = 0 and the point (1, 1) is

(a) x2 + y2 – 6x + 4 = 0 (b) x2 + y2 – 3x + 1 = 0

20. Circles x2 + y2 – 2x – 4y = 0 and x2 + y2 – 8y – 4 = 0 will touch

(a) Internally

(b) Externally

(d) None

21. If two circle x2 + y2 + 3x – 6y + 4 = 0 and x2 + y2 + 8x + py + 6 = 0 cut orthogonaly, then p is

(a) 2/5 (b) –2/5 (c) 2/3 (d) –2/3

22. Pole of line 2x + 3y + 4 = 0 with respect to circle x2 + y2 – 4x + 6y – 1 = 0, is

(a) (10, 29) (b) (-10, 39)

23. The coordinates of focus of parabola 2x2 + 5y – 3x + 4 = 0, are

(a) (b)

24. If and are end points of a focal chord of y2 = 4ax, then which is correct

(a) t t2 = 0 (b) t1 t2 = 2

25. The length of latus rectum of ellipse 4x2 + 9y2 – 8x – 36y + 4 = 0, is

(a) 4/3 (b)

26. The equation of diameter conjugate to diameter y = 3x for ellipse 4x2 + 9y2 = 36, is

(a) 4x + 27y = 0 (b) x + 3y = 0

27. The hyperbola whose focus is (2, 0), directrix is x – y = 0 and e = 2, is given by

(a) x2 – 4xy + y2 – 4 = 0

(b) x2 + y2 + xy + x + 4 = 0

(d) none

28. The point of contact of line y = x – 1 with 3x2 – 4y2 = 12, is

(a) (4, 3) (b) (3, 4)

29. The equation of tangents to hyperbola 3x2 – 4y2 = 12 which cut equal intercepts on coordinate axes, are

(a) x + y = ± 1 (b) y – x = ± 1

30. If y = tan-1 , then is

(a) 0 (b)

31. If y = tan-1 , then is

(a) 1 (b) 0 (c) 2 (d) –1

32. Differential coefficient of with respect to x2, is

(a) (b)

33. If y = Ö [log x + Ö{log x + Ö (log x + …..)}], then is

(a) (b)

34. The fourth differential of x3 logx, is

(a) x (b) 6x –1 (c) 6 x-2 (d) 3 x

35. If z = x-2 + x-1 y-1 + , then is equal to

(a) –2z (b) 2 z (c) z-2 (d) z-1

36. If z = log (x3 + y3 – x2 y – xy2), then is

(a) 2 (x + y) (b) 2 (x + y)-1

37. If sum of two numbers is 3, then maximum value of product of first and square of second, is

(a) 4 (b) 3 (c) 2 (d) 1

38. If x = 4 cos q, y = r sin q, then is

(a) r (b) r-1

39. The maximum value of x (1 – x)2 in the interval 0£ x £ 2, is

(a) 2 (b) 4/27 (c) 5 (d) 0

40. If y = loge (x + Ö(x2 – a2)), then

(a) (b)

41. Value of dx is equal to

(a) sin – 1 x + Ö(1 – x2) + c

(b) sin – 1 x – Ö(1 – x2) + c

(d) none

42. If , then A is

(a) (b) (c) (d)

43. is equal to

(a) (b) (c) (d) none

44. The value of is

(a) 0 (b) 1 (c) 0 (d) none

45.

(a) (b)

46. is equal to

(a) a- b (b) (c) b - a (d)

47. Area of figure bounded by y = sin x, y = cos x and in the first quadrant, is

(a) 2 (Ö2 – 1) (b) Ö3 + 1

48. Area bounded by the curve y = x3, the x axis and the ordinates x = -2 and x = 1, is

(a) -9 (b) –15/4 (c) 15/4 (d) 17/4

49. The ellipse 4x2 + 9x2 + 16x – 54y + 61= 0 is revolued about major axis, the volume of solid thus generated, is

(a) 24p (b) 32p (c) 16p (d) 12p

50. The value of is

(a) (b)

51. Study the sequence of alphabets and then given correct missing alphabet

M P K R I T ?

(a) U (b) V (c) G (d) H

52. the cost price of 10 articles is equal to setting price of 9 articles. The profit percent is

(a) 102. (b) 11.5 (c) 12.2 (d) 11.1

53. The missing term of series is

67, 57, 52, 42, 37, 27, 22 ?

(a) 12 (b) 10 (c) 18 (d) none

54. The radius of a sphere is increased by 5%. The increased percent in volume of sphere is

(a) 12.50 (b) 15.76 (c) 10.23 (d) 16.28

55. The coordinates of the middle point of the chord cut off by 2x – 5y + 18 = 0 by the circle x2 + y2 – 6x + 2y – 54 = 0 are

(a) (1, 4) (b) (2, 4) (c) (4, 1) (d) None

56. The centre of hyperbola

9x2 – 36x – 16y2 + 96y – 252 = 0 is

(a) (2, 3) (b) (-2, -3) (c) (-2, 3) (d) (2, -3)

57. If G1 and G2 are the geometric means of two series of sizes n1 and n2 respectively, then geometric mean G of combined series is

(a) log G = n1 log G1 + n2 log G2

(b)

(c)

(d) none

58. If X and Y are independent variables, then two lines of regression are

(a) x = 0, y = 0 (b) x = 0, y = conts,

59. Value of integral

(a) log (x (x + cos x)) + c

(b)

(c)

(d) None

60. The is equal to

(a) (b) (c) log a (d) log b

SECTION – 2 COMPUTER

1. A CPU generally contains

(a) registers and ALU

(b) control and timing section

(d) All of these

2. Which of the following coded entries are used to control access to computers ?

(a) Code words (b) Pass memory

3. Hard copy of document can be obtained from

(a) card reader (b) CRT

4. With a clock frequency of 3 MHz, the execution time for the instruction, “STA addr” of 8085 will be

(a) 4333 ns (b) 3975 ns

5. The Trap interrupt mechanism of the 8085 microposser executes

(a) an RST by hardware

(b) the instruction supplied by external device through the INTA signal

(d) a NOP

6. Pseudo-instructions are

(a) assembler directives

(b) instructions in any program that have no corresponding machine code instruction

(d) none of the above

(e) odd number of error detection

7. Which of the following binary numbers are not divisible by 4 ?

(a) 10101010101010 (b) 1110001110001

8. Programming in a language that actually controls the path of signals or data within

(a) micro programming

(b) systems programming

(d) machine language programming

A
1 / 1
1 / B / C
A

9. The output of a 3-input logic circuit f (x, y, z) is 1 if ax + by + cz < d and 0, otherwise (a, b, c, d are constant). For what values of a, b, c, d and does this represent an implementation of the AND gate.

(a) a = b = c = 1; d = 5/2

(b) a = b = c = - 1; d = - 5/2

(d) a = b = c = - 1; d = -3/2

10. The range of numbers that can be stored in 8 bits, if negative numbers are stored in 2’s complement form is

(a) – 128 to + 128 (b) – 128 to + 127

11. The Karnaugh map for the Boolean function F of 4 boolean variables is given below where A, B, C are don’t care conditions. What values of A, B, C, will result in the minimal expression?

(a) A = B = C = 1

(b) B = C = 1; A = 0

(d) A = B = 1’ C = C

12. The clock of a micro-processor can be divided by 5 using a

(a) 3 bit counter (b) 5 bit counter

13. A decimal number has 25 digits. The number of bits needed for its equivalent binary representation is, approximately,

(a) 50 (b) 60

14. The Boolean expression (A + C) (AB΄ + AC) (A ΄C΄ + B΄) can be simplified to

(a) AB (b) AB + A΄C

15. The first operating system used in micro-processors is

(a) Zenix (b) DOS

16. The advantage of MOS devices over bipolar devices is that

(a) it allows higher bit densities and also cost effective

(b) it is easy to facricate

(d) all of these

17. The main advantage of hexadecimal number is the case of conversion from hexadecimal to………… nd vice versa.

(a) decimal (b) binary

18. An OR gate has 6 inputs, how many input words are in its truth table?

(a) 64 (b) 32

19. Consider a set of n tasks with known runtimes rp r2 ……….. rn to be run on a uniprocessor machine. Which of the following processor scheduling algorithms with result in the maximum throughput?

(a) Round-Robin

(b) Shortest-Job-First

(d) First-Come-First-Served

20. Comparing the time T1 taken for a single instruction on a pipelined CPU with time T2 taken on a non-pipelined but identical CPU, we can say that.

(a) T1 £ T2

(b) T1 ³ T2

(d) T1 is T2 plus the time taken for one instruction fetch cycle