If $\frac{\tan 3A}{\tan A} = a$,then $\frac{\sin 3A}{\sin A}$ is equal to

Assertion $(A)$: $A$ catalyst increases the rate of a reaction.
Reason $(R)$: In the presence of a catalyst,the activation energy of the reaction increases.
The correct answer is

$A$ sample of a radioactive element has a mass of $10 \, g$ at an instant $t = 0$. The approximate mass of this element in the sample after two mean lives is ........ $g$.

Based on the compounds of group $15$ elements, the correct statement($s$) is (are)

$(A)$ $Bi _2 O _5$ is more basic than $N _2 O _5$

$(B)$ $NF _3$ is more covalent than $BiF _3$

$(C)$ $PH _3$ boils at lower temperature than $NH _3$

$(D)$ The $N - N$ single bond is stronger than the $P - P$ single bond

$A$ particle starting from the origin $(0, 0)$ moves in a straight line in the $(x, y)$ plane. Its coordinates at a later time are $(\sqrt{3}, 3)$. The path of the particle makes an angle of $.......^{\circ}$ with the $x$-axis.

An iron load of $2 \ kg$ is suspended in air from the free end of a sonometer wire of length $1 \ m$. $A$ tuning fork of frequency $256 \ Hz$ is in resonance with $\frac{1}{\sqrt{7}}$ times the length of the sonometer wire. If the load is immersed in water,the length of the wire in metres that will be in resonance with the same tuning fork is (Specific gravity of iron $= 8$)