LPU GUIDE
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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