In the measurement of a physical quantity $X = \frac{A^2 B}{C^{1/3} D^3}$,the percentage errors in the measurements of $A, B, C$,and $D$ are $2\%, 2\%, 4\%$,and $5\%$,respectively. The minimum percentage error in the measurement of $X$ is contributed by:

In an atom,the order of increasing energy of electrons with quantum numbers $(i)$ $n=4, l=1$,$(ii)$ $n=4, l=0$,$(iii)$ $n=3, l=2$,and $(iv)$ $n=3, l=1$ is:

Consider two statements $S_1$ and $S_2$.
$S_1$: If $f(x)$ is a differentiable function with $f'(x) = 0$ in $(a, b)$ and $f(x)$ is increasing in $(a, b)$,then $\frac{f(x)}{f'(x)}$ is also increasing in $(a, b)$.
$S_2$: Both $\sin x$ and $\tan x$ are increasing functions in $(0, \frac{\pi}{2})$.
Which of the following is true?

Principal,azimuthal and magnetic quantum numbers are respectively related to:

Equation of one of the tangents passing through $(2,8)$ to the hyperbola $5 x^2-y^2=5$ is

$A$ wheel which is initially at rest is subjected to a constant angular acceleration about its axis. It rotates through an angle of $15^{\circ}$ in time $t \ s$. The increase in angle through which it rotates in the next $2t \ s$ is (in $^{\circ}$)