An oxide of an element is a gas and dissolves in water to give an acidic solution. The element belongs to

If $\int(1-\cos x) \operatorname{cosec}^2 x \, dx = f(x) + c$, then $f(x)$ is equal to

Two cells $E_1$ and $E_2$ having equal e.m.f '$E$' and internal resistances $r_1$ and $r_2$ $(r_1 > r_2)$ respectively are connected in series. This combination is connected to an external resistance '$R$'. It is observed that the potential difference across the cell $E_1$ becomes zero. The value of $R$ will be

$A$ rod is fixed between two points at $20^{\circ}C$. The coefficient of linear expansion of the material of the rod is $1.1 \times 10^{-5} /^{\circ}C$ and Young's modulus is $1.2 \times 10^{11} \, N/m^2$. Find the stress developed in the rod if the temperature of the rod becomes $10^{\circ}C$.

The angle between the asymptotes of the hyperbola $x^2-3y^2=3$ is

One die and a coin (both unbiased) are tossed simultaneously. The probability of getting $5$ on the top of the die and tail on the coin is