In the given circuit, find the energy stored in the coil at steady state.

Four capacitors with capacitances $C_1=1 \mathrm{\mu F},C_2=1.5 \mathrm{\mu F}$, $C_3=2.5 \mathrm{\mu F}$ and $C_4=0.5 \mathrm{\mu F}$ are connected as shown and are connected to a $30$ volt source. The potential difference between points $a$ and $b$ is:

In a transistor amplifier, the voltage gain is

A long thin hollow metallic cylinder of radius $R$ has a current $i$ ampere. The magnetic induction $B$ away from the axis at a distance $\text{'}r\text{'}$ from the axis varies as shown in

Assertion (A) The colour of radiation does not change on passing through different media.
Reason (R) The media do not absorb or emit colours.

Match the following?

	Column$-\mathrm{I}$		Column$-\mathrm{II}$
(a)	Ratio of change in time period of a simple pendulum with temperature to its original time period	(i)	$\alpha \mathrm{\Delta }T$
(b)	Ratio of the value of a length to its scale reading	(ii)	$T$
(c)	Reciprocal of coefficient of volume expansion for an ideal gas of constant pressure	(iii)	$(1+\alpha \mathrm{\Delta }T)$
(d)	$\frac{F}{YA}=$	(iv)	$\frac{1}{2}\alpha \mathrm{\Delta }T$

In the common-base configuration, a transistor has current amplification factor 0.95 . If the transistor is used in common-emitter configuration and base current changes by \(2 \mu \mathrm{A}\), then the change in the collector current is

An electron having charge $1.6\times {10}^{-19} \mathrm{C}$ and mass $9\times {10}^{-31} \mathrm{kg}$ is moving with $4\times {10}^6 \mathrm{m} {\mathrm{s}}^{-1}$ speed in a magnetic field $2\times {10}^{-1} \mathrm{T}$ in a circular orbit. The force acting on electron and the radius of the circular orbit is _____

The weight of a body at earth's surface is \(w\). At a depth half way to the centre of the earth, it will be (assuming of uniform density for earth)

In which of the following pairs, both molecules possess dipole moment?

The ten's digit in \(1 !+4 !+7 !+10 !+12 !+13 !+15 !+16 !+17 !\) is divisible by

The energy of a parallel plate capacitor when connected to a battery is \(E\). With the battery still in connection, if the plates of the capacitor are separated, so that the distance between them is twice the original distance, then the electrostatic energy becomes

From the following data at \(25^{\circ} \mathrm{C}\), calculate the \(\Delta_{\mathrm{r}} \mathrm{H}^0\) for \(\mathrm{H}_2 \mathrm{O}(\mathrm{g}) \rightarrow 2 \mathrm{H}(\mathrm{g})+\mathrm{O}(\mathrm{g})\)
reaction: \(\Delta_{\mathrm{r}} \mathrm{H}^0\left(\mathrm{~kJ} \mathrm{~mol}^{-1}\right)\)
\[
\begin{array}{ll}
\frac{1}{2} \mathrm{H}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{OH}(\mathrm{g}) & 42.09 \\
\mathrm{H}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{H}_2 \mathrm{O}(\mathrm{g}) & -242 \\
\mathrm{H}_2(\mathrm{~g}) \rightarrow 2 \mathrm{H}(\mathrm{g}) & 436 \\
\mathrm{O}_2(\mathrm{~g}) \rightarrow 2 \mathrm{O}(\mathrm{g}) & 496
\end{array}
\]