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If f(x) = [pic]

0 ; x=1 , Then [pic] equals

a. 2

b. 3

c. 1

d. None of these

2.. If [x] is the greatest integer function [pic] is

A 1 B 0 C 1/2 D . None of these

3.[pic]

a. 23

b. 12

c.14

d. none of these

4. [pic] is

A 1 B 0 C 3 D infinity E 1/2

5. [pic]

a. 0

b. 4

c . – 4

d.None of these

6. [pic]

a. [pic]

b. [pic]

c. [pic]

d. None of these

7. [pic]

a. Infinity

b. 1/4

c. 3

d. None of these.

8. Which of the following statements are true?

a. Every continuous function is differentiable.

b. Every differentiable function is continuous.

c. The limit of a function at x = a exist implies that it must have the indeterminate value at a.

d. None of these

9. [pic]

A -4

B 4

C -2

D 2

E 2a2 + 1

10.[pic] Then dy/dx is

A.-6sin6x B. 0 C.12 sin3x cos3x D 6 (sin 3x + cos 3x)

11.The range of f(x)=-3x-3 for domain {-2,1,2,5}

A {3,-6,-18} B {-6,-9,-18} C {3,-6,-9) D {3,-6,-9,-18}

12. The range of the function with graph as shown is:

[pic]

A R

B (−1, 12)

C (0, 3)

D [−4, 12)

E [0, 12)

13.The following function is

[pic]

a. one one onto

b. one one into

c. Many one onto

d. None of these

14.The function f(x)[pic] is said to be onto if

a. Range = Y

b. Co domain = Range

c. Either a or b is true.

d. Both a and b is true.

15. The function f: (−3, 4] ( R, f(x) = x2 − 3 has range:

A (6, 13)

B [ −3, 13]

C (0, 6)

D [0, 13]

E (−3, 6]

16. For f: [ (1, 5)( R, f(x) = x2, the range is:

A R

B [0, ()

C [0, 25)

D [4, 25]

E [0, 5]

17. [pic]

Answer :B

18. Evaluate: lim x²cos(1/x) as x→∞ *

a. 1

b. 1/2

c. does not exist

d. -1/2

19.The points of discontinuity of the following function are

[pic]

a. 1,2

b. 1,-2

c. 1 only

d. None of these

20. The points of discontinuity of the following function are

[pic]

a. 1,2

b. 1,-2

c. 1 only

d. None of these

21.The greatest integer function is discontinuous at

a. 1,2

b. at every rational point

c. at every integer point

d. None of these

22.If f and g are differentiable functions

a. f+g is always differentiable

b. fg is always differentiable

c. f/g is always differentiable

d. one of the above is not true.

23.which of The following functions are continuous

a. 1/x

b. sin x + cos x

c. sin(1/x)

d. None of these

24.The value of k for which f(x) is continous are

[pic]

a. 1

b. 1,-2

c. 6

d. None of these

25. The values of a and b for which f(x) is continous are

[pic]

a. a=1, b=2

b. b=1,a= - 2

c. a=2, b=1

d. None of these

26.The points of discontinuity of the following function are

[pic]

a. 1

b. 1,-2

c. 0

d. None of these

27.

If y=[pic] , Then dy/dx i

a. (x+1)/y

b. x/2ay

c. 4y(x+1)

d. None of these

28. [pic]

a. 1/t

b. t

c. Sqrt t

d. None of these

29. Find dy/dx , if

[pic]

a. [pic]

b. [pic]

c. [pic]

d. None of these

30. [pic]

a. –cot [pic]

b. cos[pic]

c. - sin [pic]

d. None of these

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