In the circuit shown in the figure, what is the value of $I_1$ just after pressing the key $K$?

$A$ circle of radius $4$,drawn on a chord of the parabola $y^2 = 8x$ as diameter,touches the axis of the parabola. Then,the slope of the chord is

If $f: R \rightarrow R$ and $g: R \rightarrow R$ are defined by $f(x)=2x+3$ and $g(x)=x^2+7$,then the values of $x$ such that $g(f(x))=8$ are

When a $J$-shaped conducting rod is rotating in its own plane with constant angular velocity $\omega$,about one of its ends $P$,in a uniform magnetic field $\vec B$ (directed normally into the plane of the paper),then the magnitude of the emf induced across it will be:

If two compounds have the same empirical formula but different molecular formula,they must have:

If $\frac{d}{d x}\left[(x+1)\left(x^2+1\right)\left(x^4+1\right)\left(x^8+1\right)\right] = \left(15 x^p-16 x^q+1\right)(x-1)^{-2}$,then $(p, q)$ is equal to