|cos x|
17. Total number of solutions of 2 = 3|sin x|, belonging to the interval [–10, 10] are;
(A) 20 (B) 40 (C) 80 (D) none of these
17. B
18. Number of solutions of the equation cos x = |x|, x [-/2, /2] is
(A) 1 (B) 2 (C) 3 (D) 4
18. B
0, 3
19. The number solutions of equation tan x = x in interval
2
(A) 1 (B) 2 (C) 3 (D) 4
19. B
24. Total number of solutions of |||x| – 2| - 1| = 1/2 is
(A) 1 (B) 2 (C) 8 (D) 6
24. C
|x|2 b
4. If the equation e 2 has four solutions then b lies in
(A) (n2 2, n2) (B) (2, n2) (C) (0, n2) (D) none of these
4. A
13. Which of the following represents the graph of function f(x) = | 1 x | 1| 1
(A) y (B) y
x x
o o
(C) y (D) y
x x
o o
13. A
MATCH THE FOLLOWING
14. Column B represents the number of solutions of equations given in column A now match the
following. {.} is fractional part of x function
Column A Column B
(A) 15{x} 2x 3 (p) 7
(B) x (q) 5
{x} = n
3
(C) | x | | sin x | x ( , ) (r) 6
(D) {x} { x} x ( 3,3) (s) 11
14. A R B P C P DS
23. Find the value of the parameter ‘on’ for which the following functions are invertible
(i) f x x 3 mx 2 3x 11
(ii) f x m 2 x 3 3mx 2 9mx 1
(iii) f x x 3
a2 4a 3 x 2 a 1 x
23. (i) 3, 3 (ii) m , 3 0,
(iii) a 1, 0
3
1 2
9. Let f be function defined as f : 0, e 2 , , f x ln x 3ln x 2, then f 1 x
4
equals:
3 4x 1 3 4x 1
(A) log (B) log
2 2
3 4x 1 3 4x 1
(C) e 2
(D) e 2
9. D
10. Let f : X Y de defined as f x sin x cos x 2 2 . If f is invertible, then X Y , is:
3 3
(A) , 2, 3 2 (B) ,
2, 3 2
4 4 4 4
3 3 5
(C) , 2, 3 2 (D) , 2, 3 2
4 4 4 4
10. D
28. Let A 1,2,3,4 . Number of function f : A A are three satisfying fof x x x A, is:
(A) 10 (B) 11
(C) 12 (D) 13
28. D
35.
Let f x x 2 and g x f f f ......f x ..... . If the equation g x k, k 0, 2 has 8
n times
distinct solutions then the value n is equal to:
(A) 3 (B) 4
(C) 5 (D) 8
35. B
