In the circuit,if the forward voltage drop for the diode is $0.5 \, V$,the current will be........$mA$.

If $f(x) = \sin^6 x + \cos^6 x$ for $x \in R$,then $f(x)$ lies in the interval

If $z$ and $\omega$ are two non-zero complex numbers such that $|z\omega| = 1$ and $\text{arg}(z) - \text{arg}(\omega) = \frac{\pi}{2}$,then $\bar{z}\omega$ is equal to

Which of the following is not correctly matched?

The r.m.s. velocity of $CO_2$ at a temperature $T$ (in kelvin) is $x \ cm \ s^{-1}$. At what temperature (in kelvin),the r.m.s. velocity of nitrous oxide would be $4 x \ cm \ s^{-1}$ (in $T$)? (Atomic weights of $C, N$ and $O$ are respectively $12, 14$ and $16$)

$A$ 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: