The input resistance of a common emitter transistor amplifier,if the output resistance is $500 \, k\Omega$,the current gain $\alpha = 0.98$ and power gain is $6.0625 \times 10^6$,is ......... $\Omega$.

$A$ bomb moving with velocity $(40 \hat{i} + 50 \hat{j} - 25 \hat{k}) \text{ m/s}$ explodes into two pieces of mass ratio $1:4$. After the explosion,the smaller piece moves away with velocity $(200 \hat{i} + 70 \hat{j} + 15 \hat{k}) \text{ m/s}$. The velocity of the larger piece after the explosion is:

The relaxation time in conductors

$\int \sqrt{4 \cos ^2 x - 5 \sin ^2 x} \cos x \, dx =$

The value of $\sqrt{12\sqrt{5} + 2\sqrt{55}}$ is

Which of the following oxides reacts with both $HCl$ and $NaOH$?