If $\int \sqrt{\sec 2 x-1} d x=\alpha \log _e\left|\cos 2 x+\beta+\sqrt{\cos 2 x\left(1+\cos \frac{1}{\beta} x\right)}\right|+$ constant, then $\beta-\alpha$ is equal to ____________.

$50^{\text {th }}$ root of a number $x$ is 12 and $50^{\text {th }}$ root of another number $y$ is 18 . Then the remainder obtained on dividing $(x+y)$ by 25 is ____________.

A vehicle travels $4 \mathrm{~km}$ with speed of $3 \mathrm{~km} / \mathrm{h}$ and another $4 \mathrm{~km}$ with speed of $5 \mathrm{~km} / \mathrm{h}$, then its average speed is

Match List I with List II:

List I		List II
A.	Torque	I.	$\mathrm{kg} \mathrm{m}^{-1} \mathrm{~s}^{-2}$
B.	Energy density	II.	$\mathrm{kg} \,\mathrm{ms}^{-1}$
C.	Pressure gradient	III.	$\mathrm{kg}\, \mathrm{m}^{-2} \mathrm{~s}^{-2}$
D.	Impulse	IV.	$\mathrm{kg} \,\mathrm{m}^{2} \mathrm{~s}^{-2}$

Choose the correct answer from the options given below: