The volume-temperature graphs of a given mass of an ideal gas at constant pressures are shown below. What is the correct order of pressures?

If $\int \sin ^{-1}\left(\frac{2 x}{1+x^2}\right) d x=f(x)-\log \left(1+x^2\right)$ then $f(x)$ is equal to

If the angle $2 \theta$ is acute,then the acute angle between the pair of straight lines $x^2(\cos \theta - \sin \theta) + 2xy \cos \theta + y^2(\cos \theta + \sin \theta) = 0$ is:

The currents $i_1$ and $i_2$ through the resistors $R_1(=10\,\Omega)$ and $R_2(=30\,\Omega)$ in the circuit diagram with $E_1 = 3\,V$,$E_2 = 3\,V$,and $E_3 = 2\,V$ are respectively:

The simplest formula of a compound containing $50\%$ of element $X$ (atomic mass $10$) and $50\%$ of element $Y$ (atomic mass $20$) is

$A$ line $L$ has intercepts $a$ and $b$ on the coordinate axes. When the coordinate axes are rotated through an angle $\alpha$ keeping the origin fixed,the same line $L$ has intercepts $p$ and $q$ on the new axes. Then