$A$ capacitor of capacitance $(4.0 \pm 0.2) \mu F$ is charged to a potential of $(10.0 \pm 0.1) V$. The charge on the capacitor is

Two resistors of resistances $R_{1} = 100 \pm 3 \ \Omega$ and $R_{2} = 200 \pm 4 \ \Omega$ are connected $(a)$ in series,$(b)$ in parallel. Find the equivalent resistance of the $(a)$ series combination,$(b)$ parallel combination. Use for $(a)$ the relation $R = R_{1} + R_{2}$ and for $(b)$ $\frac{1}{R^{\prime}} = \frac{1}{R_{1}} + \frac{1}{R_{2}}$ and $\frac{\Delta R^{\prime}}{R^{\prime 2}} = \frac{\Delta R_{1}}{R_{1}^{2}} + \frac{\Delta R_{2}}{R_{2}^{2}}$.

In a simple pendulum experiment for determination of acceleration due to gravity $(g)$, time taken for $20$ oscillations is measured by using a watch of $1\,s$ least count. The mean value of time taken comes out to be $30\,s$. The length of the pendulum is measured by using a meter scale of least count $1\,mm$ and the value obtained is $55.0\,cm$. The percentage error in the determination of $g$ is close to ........... $\%$

Using the expression $2 d \sin \theta = \lambda$,one calculates the values of $d$ by measuring the corresponding angles $\theta$ in the range $0^{\circ}$ to $90^{\circ}$. The wavelength $\lambda$ is exactly known and the error in $\theta$ is constant for all values of $\theta$. As $\theta$ increases from $0^{\circ}$:

When two resistors of resistances $R_1=(200 \pm 2) \Omega$ and $R_2=(400 \pm 4) \Omega$ are connected in series,then the equivalent resistance of the combination is

The maximum percentage errors in the measurement of mass $(M)$,radius $(R)$,and angular velocity $(\omega)$ of a ring are $2 \%$,$1 \%$,and $1 \%$ respectively. Find the maximum percentage error in the measurement of its moment of inertia $(I = M R^2)$ about its geometric axis. (in $\%$)