24
MCQ (Single Correct Answer)
Let $n(A)=m$ and $n(B)=n$. Then, the total number of non-empty relations that can be defined from $A$ to $B$ is
A
$m^n$
B
$n^m-1$
C
$m n-1$
D
$2^{m n}-1$
25
MCQ (Single Correct Answer)
If $[x]^2-5[x]+6=0$, where $[\cdot]$ denote the greatest integer function, then
A
$x \in[3,4]$
B
$x \in(2,3]$
C
$x \in[2,3]$
D
$x \in[2,4)$
26
MCQ (Single Correct Answer)
Range of $f(x)=\frac{1}{1-2 \cos x}$ is
A
$\left[\frac{1}{3}, 1\right]$
B
$\left[-1, \frac{1}{3}\right]$
C
$(-\infty,-1] \cup\left[\frac{1}{3}, \infty\right)$
D
$\left[-\frac{1}{3}, 1\right]$
27
MCQ (Single Correct Answer)
Let $f(x)=\sqrt{1+x^2}$, then
A
$f(x y)=f(x) \cdot f(y)$
B
$f(x y) \geq f(x) \cdot f(y)$
C
$f(x y) \leq f(x) \cdot f(y)$
D
None of these
28
MCQ (Single Correct Answer)
Domain of $\sqrt{a^2-x^2}(a>0)$ is
A
$(-a, a)$
B
$[-a, a]$
C
$[0, a]$
D
$(-a, 0]$