In a triangle,if $b=20, c=21$ and $\sin A=\frac{3}{5}$,then $a$ is equal to :

If the direction cosines of two lines are given by $l+m+n=0$ and $l^2-5m^2+n^2=0$,then the angle between them is

In a transformer,the number of turns in the primary coil is $140$ and that in the secondary coil is $280$. If the current in the primary coil is $4 \, A$,then the current in the secondary coil is......$A$.

The figure shows three resistor configurations $R_1, R_2$,and $R_3$ connected to a $3 \, V$ battery. If the power dissipated by the configurations $R_1, R_2$,and $R_3$ is $P_1, P_2$,and $P_3$ respectively,then:

$A$ vertical pole subtends an angle $\tan ^{-1}\left(\frac{1}{2}\right)$ at a point $P$ on the ground. If the angles subtended by the upper half and the lower half of the pole at $P$ are respectively $\alpha$ and $\beta$,then $(\tan \alpha, \tan \beta)$ is equal to

If $X$ is a Poisson variate such that $P(X=1)=2 P(X=2)$, then $P(X=3)$ is equal to