If the points with position vectors $60 \hat{i}+3 \hat{j}$,$40 \hat{i}-8 \hat{j}$,and $a \hat{i}-52 \hat{j}$ are collinear,then $a$ is equal to

$A$ transistor is used as an amplifier in $CB$ mode with a load resistance of $5 \; k\Omega$. The current gain of the amplifier is $0.98$ and the input resistance is $70 \; \Omega$. The voltage gain and power gain respectively are:

The value of $c$ in the Lagrange's mean value theorem for $f(x)=\sqrt{x-2}$ in the interval $[2,6]$ is

How many atoms of calcium will be deposited from a solution of $CaCl_2$ by a current of $25 \ mA$ flowing for $60 \ s$?

At $550 \ K$,the $K_c$ for the following reaction is $10^4 \ L \ mol^{-1}$: $X_{(g)} + Y_{(g)} \rightleftharpoons Z_{(g)}$. At equilibrium,it was observed that $[X] = \frac{1}{2}[Y] = \frac{1}{2}[Z]$. What is the value of $[Z]$ (in $mol \ L^{-1}$) at equilibrium?

The work function of nickel is $5 \text{ eV}$. When light of wavelength $2000 \text{ \AA}$ falls on it, it emits photoelectrons. The potential difference necessary to stop the fastest electrons emitted is (given $h = 6.67 \times 10^{-34} \text{ J-s}$): (in $\text{ V}$)