On electrolysis of aqueous solution of $KI$ in presence of platinum electrodes,which of the following statements are correct?
$(a)$ Hydrogen gas is released at cathode
$(b)$ Oxygen gas is released at anode
$(c)$ $pOH$ of solution decreases
$(d)$ There is deposition of potassium at cathode

The solution of the differential equation $\frac{dy}{dx} = \sin(x+y) \tan(x+y) - 1$ is

$A$ resistor of $2 \Omega$,an inductor of $100 \mu H$,and a capacitor of $400 pF$ are connected in series across a source of $e_{rms} = 0.1 \text{ V}$. At resonance,the voltage drop across the inductor is: (in $\text{ V}$)

If $g$ is the acceleration due to gravity on the earth's surface,the gain in the potential energy of an object of mass $m$ raised from the surface of the earth to a height equal to the radius $R$ of the earth,is

The equation of the plane passing through $(1, 1, 1)$ and $(1, -1, -1)$ and perpendicular to $2x - y + z + 5 = 0$ is:

The two surfaces of a biconvex lens have the same radii of curvature. This lens is made of glass with a refractive index of $1.5$ and has a focal length of $10 ~cm$ in air. The lens is cut into two equal halves along a plane perpendicular to its principal axis to yield two plano-convex lenses. The two pieces are glued such that the convex surfaces touch each other. If this combination lens is immersed in water (refractive index $=$ $4/3$),its focal length (in $cm$) is: