If $f(x) = x^5 - 5x^4 + 5x^3 - 10$ has local maximum and minimum at $x = p$ and $x = q$,respectively,then $(p, q)$ equals

If the image of $\left(\frac{-7}{5}, \frac{-6}{5}\right)$ in a line is $(1, 2)$,then the equation of the line is

If $f(x) = \frac{x}{1+x}$ and $g(x) = f(f(x))$, then $g^{\prime}(x)$ is equal to

The line $\frac{x}{a} + \frac{y}{b} = 1$ moves in such a way that $\frac{1}{a^2} + \frac{1}{b^2} = \frac{1}{2c^2}$,where $a, b, c \in R_0$ and $c$ is a constant. Then,the locus of the foot of the perpendicular from the origin on the given line is -

If $A$ is an invertible matrix of order $n$,then the determinant of $\operatorname{adj} A$ is equal to :

The correct order of increasing $s$-character (in percentage) in the hybrid orbitals of the following molecules/ions is :-
$I.$ $CO_3^{2-}$
$II.$ $XeF_4$
$III.$ $I_3^-$
$IV.$ $NCl_3$
$V.$ $BeCl_2$