$\mathop {\lim }\limits_{x \to 0} \frac{{\sin^2 x}}{{\sqrt{2} - \sqrt{1 + \cos x}}}$ equals

$A$ plane passing through the points $(0, -1, 0)$ and $(0, 0, 1)$ and making an angle $\frac{\pi}{4}$ with the plane $y - z + 5 = 0$,also passes through the point:

Two tuning forks $A$ and $B$ produce $8 \, Hz$ beats when sounded together. $A$ gas column $37.5 \, cm$ long in a pipe closed at one end resonates in its fundamental mode with fork $A$,whereas a column of length $38.5 \, cm$ of the same gas in a similar pipe is required for resonance with fork $B$. The frequencies of these two tuning forks are:

An $e.m.f.$ of $15 \ V$ is applied in a circuit containing $5 \ H$ inductance and $10 \ \Omega$ resistance. The ratio of the currents at time $t \to \infty$ and at $t = 1 \ s$ is:

Both corpus luteum and macula lutea are

$A$ spring balance is attached to the ceiling of a lift. $A$ man hangs his bag on the spring and the spring reads $49 \, N$,when the lift is stationary. If the lift moves downward with an acceleration of $5 \, m/s^2$,the reading of the spring balance will be .......... $N$.