If the circle $x^2+y^2+4x-6y+c=0$ bisects the circumference of the circle $x^2+y^2-6x+4y-12=0$,then $c$ is equal to

$A$ point charge $q$ is placed at a distance $a/2$ directly above the centre of a square of side $a$. The electric flux through the square is

Let $\overline{a}, \overline{b}$ and $\overline{c}$ be three non-zero vectors such that no two of them are collinear and $(\overline{a} \times \overline{b}) \times \overline{c}=\frac{1}{3}|\overline{b}||\overline{c}| \overline{a}$. If $\theta$ is the angle between the vectors $\overline{b}$ and $\overline{c}$,then the value of $\sin \theta$ is

$A$ coil of self-inductance $L$ is connected in series with a bulb $B$ and an $A.C.$ source. Brightness of the bulb decreases when

In how many ways can $8$ identical balls be distributed into $3$ distinct boxes such that no box remains empty?

If the roots of $x^3-42 x^2+336 x-512=0$ are in increasing geometric progression,then its common ratio is (in $: 1$)