Let $y=y(x)$ be the solution of the differential equation $(\tan x)^{1 / 2} \mathrm{~d} y=\left(\sec ^3 x-(\tan x)^{3 / 2} y\right) \mathrm{d} x, 0 < x <\frac{\pi}{2}, y\left(\frac{\pi}{4}\right)=\frac{6 \sqrt{2}}{5}$. If $y\left(\frac{\pi}{3}\right)=\frac{4}{5} \alpha$, then $\alpha^4$ equals

$\_\_\_\_$ .

$$ \text { Match List - I with List - II. } $$

where h (Planck's constant), G (gravitational constant) and c (speed of light in vacuum) as fundamental units.

Choose the correct answer from the options given below :

In an experiment to determine the resistance of a given wire using Ohm's law, the voltmeter and ammeter readings are noted as 10 V and 5 A , respectively. The least counts of voltmeter and ammeter are 500 mV and 200 mA , respectively. The estimated error in the resistance measurement is $\_\_\_\_$ $\Omega$

A mass of 1 kg is kept on a inclined plane with $30^{\circ}$ inclination with respect to horizontal plane and it is at rest initially. Then the whole assembly is moved up with constant velocity of $4 \mathrm{~m} / \mathrm{s}$. The work done by the frictional force in time 2 s is $\_\_\_\_$ J. (Take $g=10 \mathrm{~m} / \mathrm{s}^2$ )