$A$ uniform rod of mass $M$ and length $L$ is placed on a smooth horizontal surface. $A$ horizontal force $F$ is applied at one end of the rod perpendicular to its length. The acceleration of the centre of mass of the rod is:

$20 \text{ mL}$ of $0.1 \text{ M}$ acetic acid is mixed with $50 \text{ mL}$ of potassium acetate. $K_a$ of acetic acid $= 1.8 \times 10^{-5}$ at $27^\circ \text{C}$. Calculate the concentration of potassium acetate if the $pH$ of the mixture is $4.8$. (in $\text{ M}$)

If the function $f$ defined on $\left( \frac{\pi }{6}, \frac{\pi }{3} \right)$ by $f(x) = \begin{cases} \frac{\sqrt{2} \cos x - 1}{\cot x - 1}, & x \neq \frac{\pi}{4} \\ k, & x = \frac{\pi}{4} \end{cases}$ is continuous,then $k$ is equal to

$A$ transistor is connected in common emitter $(CE)$ configuration. The collector supply is $8 \ V$ and the voltage drop across a resistor of $800 \ \Omega$ in the collector circuit is $0.5 \ V$. If the current gain factor $\alpha$ is $0.96$,find the base current in $\mu A$.

The potential difference between the plates of a parallel plate capacitor is changing at the rate of $10^6\, V/s$. If the capacitance is $2\,\mu F$,the displacement current in the dielectric of the capacitor will be.....$A$

The coils of a step-down transformer have $500$ and $5000$ turns. In the primary coil,an $AC$ of $4 \, A$ at $2200 \, V$ is sent. The value of the current and potential difference in the secondary coil will be: