$A$ polaroid is placed at $45^{\circ}$ to an incoming light of intensity $I_0$. Now,the intensity of light passing through the polaroid after polarization would be:

If $u=\sin ^{-1}\left(\frac{x}{y}\right)+\tan ^{-1}\left(\frac{y}{x}\right)$,then the value of $x \frac{\partial u}{\partial x}+y \frac{\partial u}{\partial y}$ is

If a unit vector is represented by $0.5\hat{i} - 0.8\hat{j} + c\hat{k}$,then the value of $c$ is:

If $\alpha, \beta$ and $\gamma$ are the roots of the equation $x^3+p x^2+q x+r=0$,then the coefficient of $x$ in the cubic equation whose roots are $\alpha(\beta+\gamma), \beta(\gamma+\alpha)$ and $\gamma(\alpha+\beta)$ is

Two wires are made of the same material and have the same volume. However,wire $1$ has cross-sectional area $A$ and wire $2$ has cross-sectional area $3A$. If the length of wire $1$ increases by $\Delta x$ on applying force $F$,how much force is needed to stretch wire $2$ by the same amount?

Assertion $(A)$: $K, Rb$ and $Cs$ form superoxides.
Reason $(R)$: The stability of the superoxides increases from $K$ to $Cs$ due to decrease in lattice energy.
The correct answer is