Function ${\sin ^{ - 1}}\sqrt x $ is defined in the interval
$(-1, 1)$
$[0, 1]$
$[-1, 0]$
$(-1, 2)$
If $\theta$ is small $\&$ positive number then which of the following is/are correct ?
The graph of function $f$ contains the point $P (1, 2)$ and $Q(s, r)$. The equation of the secant line through $P$ and $Q$ is $y = \left( {\frac{{{s^2} + 2s - 3}}{{s - 1}}} \right)$ $x - 1 - s$. The value of $f ‘ (1)$, is
Let $A=\{(x, y): 2 x+3 y=23, x, y \in N\}$ and $B=\{x:(x, y) \in A\}$. Then the number of one-one functions from $\mathrm{A}$ to $\mathrm{B}$ is equal to ................
If $f(x)$ satisfies the relation $f\left( {\frac{{5x - 3y}}{2}} \right)\, = \,\frac{{5f(x) - 3f(y)}}{2}\,\forall x,y\in R$ $f(0) = 1, f '(0) = 2$ then period of $sin \ (f(x))$ is
If $f(x) = \frac{{\alpha x}}{{x + 1}},x \ne - 1$, for what value of $\alpha $ is $f(f(x)) = x$