I
HOME-WORK
1.
1
Domainoff(x) == [sin- (2x)+1r/6 is
(B)
2.
The donmin of the funcHon f(x) = sin-•{ log, (
(A)
3.
½x' ) } is
[-2,-l)u[l,2]
c-
cos-'
The domain of the function f(x) ==
~x
1
(
6.
is
(D) ¢
(B) (-: +2n,r,: +2n,r)
(D) None of these
+2n7']
.J
The domain of the function f(x) == tan- 1 x(x + 1) + sin-
(A) [-1 , 0)
(D) (-2,-l)u(l, 2)
. ) is
4 + ; smx
(A)[-:+2m,, :+2n,r]
5.
I)
(C) (-oo, -3) u [3 , oo)
(B)[-3, 3)
The domain of the function f(x) = cos-
(C) ( - : +2n7', :
(C) [-2,-l]u[l, 2]
(B) (-2,-l]u[l,2]
(A)(-oo , -3) u (3, oo)
4.
[4-1 ' 21]
(B) {-1 , 0}
1
.Jx 2 + x + 1 is
(C) (- oo , - 1) u [O, oo)
(D)(-oo, oo)
(C) [ 0, ; ]
(D) None of these
The range oftl1e function y = sin-{i :~, ) is
(A) ( 0, ; )
(B) [
0,;)
-•(7-5 x+3)
2
7.
2 x2 + 2
The maximum value of sec
5;,r
(A)-
6
is
7;,r
5;,r
(B)
12
(C)
12
2TC
3
(D) -
8.
. -1(
The true set of values of 'k ' for which sm
1 ) k,,
.
= - may have a solution
1+sm 2 x
6
(B) [ I , 3]
9.
The function f(x) = 0 has eight distinct solutions and f also satisfy f( 4 + x) =f (4 - x) , the sum of al I eigl1t
solutions is
(A) 12
I0.
(D) [2 , 4]
If range of the function
(A) b2 = 3c
(D) 15
(C) 16
(B) 32
J(x) = tan -I(3x 2 +bx+ c) is [ 0, ; ) ; (domain is R) , then
(C) b2 = 12c
(B) b2 = 4c
(D) b2 = 8c
INTEGER TYPE QUESTIONS
1.
Number of integers which are not present in the domain off(x) =sin-IC : :2 ) is
2.
Least non negative integer in the domain of f(x) = sec- (x+..!..) is
3.
If S be the domain of f (x) = sin - t (x-1 x I) then least integral value in Sis
1.
1
X
Column-I
Column-U
2 •
(A)Rangeof F(x)=coC I(2x-x)
1s
2- .Ji
(B) Range of f(x)=4 x -2x +I is
2 + ✓2]
(Q) [ _ 2_' _2_
(C) Range of f(x) =3sinx+4cos(x+~)+s is
I
.
(D) Range of F(x) = 2 + sin x + cosx is
(S)
[s- ✓2s - 12✓3 , s+ ✓2s - 12✓3]