3 Infomaths/Mca/Maths/Old Questions

OLD QUESTIONS-CW1

3 INFOMATHS/MCA/MATHS/OLD QUESTIONS

FUNCTIONS

1. is a real-valued function in the domain :

PU CHD-2012

(A) (–¥, – 1] È [3, ¥) (B) (–¥, – 1] È (2, 3]

2. If X = {a, b, c, d} then no. of 1–1. Then number of functions from X ® X are

Pune-2012

(a) 64 (b) 13 (c) 24 (d) 16

3. If R+ is set of all real +ve nos. then F: R+ ® R+ be defined by f(x) = 3x. Then f(x) is

Pune-2012

(a) neither one-one nor onto (b) one-one and onto

4. If f :R ® R, where .

Then fof

Pune-2012

(a) 1 (b) - 1 (c) (d) 0

5. If the function f: [1, ∞) → [1, ∞) is defined by f(x) = 2x(x−1) , then f −1(x) is

KIIT-2010, NIMCET-2011

(a) (b)

6. Let the function f (x) = x2 from the set of integers to the set of integers. Then :

PU CHD-2011

(A) f is one-one and onto

(B) f is one-one but not onto

(D) f is neither one-one nor onto

7. The value of P and Q for which the identity f(x+1) - f (x) = 8x + 3 is satisfied, where f (x) = Px2 + Qx + R, are :

PU CHD-2011

(A) P = 2, Q = 1 (B) P = 4, Q = –1

8. Let , then f(x) =

PU CHD-2011

(A) x2 (B) x2 – 1 (C) x2 – 2 (D) x2 + 2

9. The range of the function f(x) = 1/(2 – cos3x) =

PU CHD-2011

(A) (B)

10. If f = {(1, 1), (2, 3), (0, - 1), (-1, -3)} be a function described by the formula f(x) = ax + b for some integers a, b, then the value of a, b is

BHU-2011

(a) a = - 1, b = 3 (b) a = 3, b = 1

11. Set A has 3 elements and set B has 4 elements. The

number or injection that can be defined from A to B is

NIMCET-2010

(a) 144 (b) 12 (c) 24 (d) 64

12. Let A and B be sets and the cardinality of B is 6. The number of one-to-one functions from A to B is 360. Then the cardinality of A is (Hyderabad Central University – 2009)

(a) 5 (b) 6 (c) 4 (d) Can’t be determined

13. Suppose that g(x) = and f{g(x)} = then f(x) is KIITEE-2010

(a) 1 + 2x2 (b) 2 + x2 (c) 1 + x (d) 2 + x

14. If for x Î R, then f(2010) is

KIITEE-2010

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

15. The function is

KIITEE-2010

(a) neither an even nor an odd function

(b) an even function

(d) a periodic function

16. The domain of is KIITEE-2010

(a) [1, 9] (b) [-, 9] (c) [-9, 1] (d) [-9, -1]

17. A function f from the set of natural numbers to integers defined by if is :

KIITEE-2010

(a) one-one but not onto (b) onto but not one-one

18. For real x, let f(x) = x3 + 5x + 1, then KIITEE-2010

(a) f is onto R but not one-one

(b) f is one-one and onto R

(d) f is one-one but not onto R

19. Let f(x) = [x2 - 3] where [ ] denotes the greatest integer function. Then, the number of points in the interval (1, 2) where the function is discontinuous is

(MCA : NIMCET – 2009)

(a) 4 (b) 2 (c) 6 (d) None of these

20. Let f(x) = - log2x + 3 and aÎ[1, 4] the f(a) is equal to

(MCA : KIITEE - 2009)

(a) [1, 3] (b) [2, 4] (c) [1, 2] (d) [1, 9]

21. The function is

(MCA : KIITEE - 2009)

(a) periodic (b) odd

22. Which of the function is periodic?

(MCA : KIITEE - 2009)

(a) f(x) = x cos x

(b) f(x) = sin (1/x)

(c)

(d) f(x) = {x}, the fractional part of x

23. The function f : R ® R given by f(x) = 3.2 sin x is

(MCA : KIITEE - 2009)

(a) one – one (b) onto

24. The domain of the function is

(MCA : KIITEE - 2009)

(a) [1/2, 3/2] (b) (1/2, 3/2) (c) [1/2, ¥) (d) (-¥, 3/2]

25. The period of the function f(x) = cosec23x + cot 4x is

(MCA : KIITEE - 2009)

(a) p (b) p/8 (c) p/4 (d) p/3

26. Let f : R ® R be a function defined by

then (MCA : KIITEE - 2009)

(a) f is both one – one and onto

(b) f is one – one but not onto

(d) f is neither one – one nor onto

27. The domain of is

(MCA : KIITEE - 2009)

(a) R ~ {1, 2} (b) (-¥, 2)

28. If f(x – 1) = 2 x2 – 3x + 1 then f(x + 1) is given by

(MCA : KIITEE - 2009)

(a) 2x2 + 5x + 1 (b) 2x2 + 5x + 3

29. If y = log3 x and F = {3, 27}. Then the set onto which the set F is mapped contains (MCA : KIITEE - 2009)

(a) {0, 3} (b) {1, 3} (c) {0, 1} (d) {0, 2}

30. If f : [1, ¥) ® [2, ¥) is given by then f – 1(x) equals to (MCA : KIITEE - 2009)

(a) (b)

31. If then f(x + y) is equal to (KIITEE – 2009)

(a) f(x) f(y) (b) f(x) + f(y)

32. Let for all real x and y. If f’(0) exists and equals – 1 and f(0) = 1, then, f(2) is

Hyderabad Central Univ. – 2009

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

33. If f(x) = sin (log x), then, the value of

f(xy) + f(x/y) – 2f(x) cos log (y) is

Hyderabad Central Univ. – 2009

(a) 0 (b) – 1 (c) 1 (d) – 2

34. Consider the function on R. Let x1 and x2 be two real values such that f(x1) = f(x2). Then x1 – x2 is always of the form

Hyderabad Central Univ. – 2009

(a) np : n Î Z (b) 2np : n Î Z

35. If f(x) + f(1 – x) = 2, then the value of

MCA : NIMCET - 2008

36. If f(x) is a polynomial satisfying

and f(3) = 28, then f(4) is given by NIMCET - 2008

(a) 63 (b) 65 (c) 67 (d) 68

37. The number of functions f from the set A = {0, 1, 2} in to the set B = {0, 1, 2, 3, 4, 5, 6, 7} such that f(i) £ f(j) for i < j and ij Î A is. NIMCET - 2008

(a) 8C3 (b) 8C3 + 2(8C2)

38. The range of the function f(x) = 7-xPx-3 is

MCA : KIITEE – 2008

(a) {1, 2, 3, 4} (b) {1, 2, 3}

39. Let A = {x|-1 < x < 1} = B. If f: A ® B be bijective then f(x) could be defined as

MCA : KIITEE – 2008

(a) |x| (b) sin Õx (c) x|x| (d) None

40. Let f : R ® R be a mapping such that then the property of the function f is.

MCA : KIITEE – 2008

(a) one – one (b) one – many

41. If f(x) = x2 + 4 and g(x) = x3 – 3 then the degree of the polynomial f[g(x)] ICET - 2007

(a) 6 (b) 5 (c) 3 (d) 3

42. If f(x) = 2x2 + 5x + 1 and g(x) = x – 4

then {a Î R : g (f(a)) = 0} =

ICET - 2007

(a) {-1/2, 3} (b) {-1/2, -3} (c) {1/2, - 3} (d) {1/2, 3}

43. If f : |R ®| R and g : |R ® R| are defined by f(x) = x - (x) and g(x) = (x) for each x in |R where (x) is the greatest integer not exceeding x, then, the range of gof is. ICET – 2005

(a) f (b) (0) (c) Z (d) |R

44. The number of injections of the set {1, 2, 3} into the set {1, 2, 3, 4, 5, 6} is ICET – 2005

(a) 10 (b) 30 (c) 60 (d) 120

45. The number of mappings from {a, b, c} to {x, y} is PUNE - 2007

(a) 3 (b) 6 (c) 8 (d) 9

46. If f = {(6, 2), (5, 1)}, g = {2, 6), (1, 5)} then f o g = PUNE - 2007

(a) {(6, 6) (5, 5)} (b) (2, 2) (1, 1)

47. If (x + 2y, x – 2y) = xy then f(x, y) is equal to (KIITEE - 2009)

(a) (b)

48. The function f and g are given by f(x) = (x), the fractional part of x and g(x) = 1/2 sin[x]p, where [x] denotes the integral part of x, then the rage of (g o f) is (MCA : KIITEE - 2009)

(a) [-1, 1] (b) {-1, 1} (c) {0} (d) {0, 1}

49. The least period of the function

f(x) = [x] + [x + 1/3] + [x + 2/3] – 3x + 10

where [x] denotes the greatest integer £ x is KIITEE – 2008

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

LIMITS & CONTINUITY

1. The value of is :

PU CHD-2012

(A) 1 (B) –1 (C) ¥ (D) Does not exist

2. If f (1) = 2 f '(1) = 1 then

Pune-2012

(a) – 1 (b) 0 (c) 1 (d) 2

3. F(x) = x + |x|. Then F(x) is continuous for ………….

Pune-2012

(a) x = 0 only (b) for all x Î R

4. What is the value of a for which is continuous?

NIMCET-2012

(a) π (b) π /2 (c) 2/ π (d) 0

5. is equal to :

BHU-2012

(a) 0 (b) 1 (c) e (d) 1/e

6. The function f(x) defined by , then:

BHU-2012

(a) f(x) is continuous at x = 0

(b) f(x) has discontinuity of first kind at x = 0

(d) f(x) has removable discontinuity at x = 0

7. Let f(x) be the function defined on the interval (0, 1) by

then f is continuous at

HCU-2011

(a) no point in (0, 1)

(b) at exactly 2 points in (0, 1)

(d) at more than 2 points in (0, 1)

8. Suppose f(x) = [x2] – [x]2 where [x] denotes the largest integer £ x. Then which of the following statements is true?

HCU-2011

(a) f(x) ≥ 0 " x Î R

(b) f(x) can be discontinuous at points other than the integral values of x

(d) f(x) ¹ 0 everywhere, except on the interval [0, 1]

9. equals to

NIMCET-2011

(a) 0 (b) 1 (c) –1 (d) none of these

10. Let f (2) = 4 and f´ (2) = 1. Then is given by :

PU CHD-2011

(A) 2 (B) –2 (C) –4 (D) 3

11. If

Then, f (x) is

BHU-2011

(a) continuous at (b) continuous at x = 1

12. The value of is equal to

BHU-2011

(a) p + 1 (b) p - 1 (c) p (d) 3

13. If f(1) = 1, f ' (1) = 2, then KIITEE-2010

(a) (b) 4 (c) 1 (d) 1/2 (e) None of these

14. The integer n for which is a finite non – zero number is

MCA : NIMCET - 2008

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

15. If when [.] denotes the greatest integer function then is equal to KIITEE - 2008

(a) 0 (b) 1 (c) – 1 (d) None

16. ICET - 2007

(a) – 1 (b) 0- (c) 1 (d) 2

17. ICET - 2007