Which one of the following is the ratio of the lowering of vapour pressure of $0.1 \ M$ aqueous solutions of $BaCl_2, NaCl$ and $Al_2(SO_4)_3$ respectively?

If the equation $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$ represents a pair of straight lines,then the square of the distance of their point of intersection from the origin is

$\int_0^1 \sin \left(2 \tan ^{-1} \sqrt{\frac{1+x}{1-x}}\right) d x$ is equal to :

$X + H_2SO_4 \to Y$ (a colorless gas with a pungent smell).
$Y + K_2Cr_2O_7 + H_2SO_4 \to$ green colored solution.
What are $X$ and $Y$?

The time in seconds required to produce a potential difference of $20 \ V$ across a capacitor of $1000 \ \mu F$ when it is charged at a steady rate of $200 \ \mu C/s$ is:

$A$ particle of mass $m$ is constrained to move on the $x$-axis. $A$ force $F$ acts on the particle. $F$ always points toward the position labeled $E$. For example,when the particle is to the left of $E$,$F$ points to the right. The magnitude of $F$ is constant except at point $E$ where it is zero. The system is horizontal. $F$ is the net force acting on the particle. The particle is displaced a distance $A$ towards the left from the equilibrium position $E$ and released from rest at $t=0$. What is the period of the motion?