A capacitor of capacitance $C_1=1 \mu \mathrm{F}$ is charged using a $9 \mathrm{V}$ battery. $C_1$ is then removed from the battery & connected to capacitors $C_2$ and $C_3$ of $2 \mu \mathrm{F}$ and $3 \mu \mathrm{F}$ respectively as shown in the figure. Find the charge on $C_3$ after equilibrium has reached is

A coil of area $10 {\mathrm{m}}^2$ is placed in a uniform magnetic field of $0.3\mathrm{k}$ lb. ${\mathrm{m}}^{-2}$, with its plane perpendicular to the field. The coil rotates at a uniform rate to complete the revolution in $8 \mathrm{s}$. find the average emf $\left(\mathrm{in} \mathrm{mV}\right)$. in the coil during intervals when the coil rotates from
i. $0°$ to $90°$ position
ii. $90°$ to $180°$ position
ii. $180°$ to $270°$ position
iv. $270°$ to $360°$ position

Two position vectors are given by \(\overrightarrow{r_1}=(1,1,1)\) and \(\overrightarrow{r_2}=(1,-1,1)\). The unit vector in the direction of \(\overrightarrow{r_1} \times \overrightarrow{r_2}\)

The amount of heat that must be supplied to $35 \mathrm{g}$ of oxygen at room temperature to raise its temperature by $80 °\mathrm{C}$ at constant volume is (molecular mass of oxygen is $32$ and $\mathrm{R}=8.3 \mathrm{J} {\mathrm{mol}}^{-1} {\mathrm{K}}^{-1}$)

A motor boat is moving in a river with velocity \(\overrightarrow{\mathrm{v}}=7 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}-5 \hat{\mathrm{k}} \mathrm{ms}^{-1}\). If the flow of water offers resistive force \(\vec{F}=9 \hat{i}+3 \hat{j}-3 \hat{k} \quad N\), then the power of the boat is

A short bar magnet placed in a horizontal plane has its axis aligned along north-south direction. Null points are found on the axis of the magnet at \(20 \mathrm{~cm}\) from the centre of magnet. The earth's magnetic field at the place is \(B\) and angle of dip is \(0^{\circ}\). If the total magnetic field on the normal bisector of the magnet \(20 \mathrm{~cm}\) from the centre of the magnet is \(0.6 \mathrm{G}\), then the magnitude of \(B\) is.

Assertion (A): When plane of coil is perpendicular to magnetic field, magnetic flux linked with the coil is minimum, but induced $emf$ is zero
Reason $\left(\mathbf{R}\right):\varphi =nAB\cos \theta$ and $e=\frac{d\varphi }{dt}$

If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are vectors such that $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=0$ and $\left|\overrightarrow{a}\right|=7, \left|\overrightarrow{b}\right|=5, \left|\overrightarrow{c}\right|=3$ then angle between vector $\overrightarrow{b}$ and$\overrightarrow{c}$ is

\(\frac{1}{\sin 1^{\circ} \sin 2^{\circ}}+\frac{1}{\sin 2^{\circ} \sin 3^{\circ}}+\frac{1}{\sin 3^{\circ} \sin 4^{\circ}}+\ldots+\frac{1}{\sin 89^{\circ} \sin 90^{\circ}}=\)

Thermodynamically most stable allotrope of carbon is

The general formula of the compound formed when a metal \((M)\) of group 1 reacts with non-metal \((X)\) of group 16 is

Using the standard electrode potentials given below identify the correct statements from the following.
\[
\begin{aligned}
\mathrm{Fe}^{2+}+2 e^{-} \longrightarrow \mathrm{Fe} ; E^{\circ} & =-0.44 \mathrm{~V} \\
\mathrm{Cu}^{2+}+2 e^{-} \longrightarrow \mathrm{Cu} ; E^{\circ} & =+0.34 \mathrm{~V} \\
\mathrm{Ag}^{+}+e^{-} \longrightarrow \mathrm{Ag} ; E^{\circ} & =+0.80 \mathrm{~V}
\end{aligned}
\]
(i) Copper can displace iron from \(\mathrm{FeSO}_4\) solution.
(ii) Iron can displace copper from \(\mathrm{CuSO}_4\) solution.
(iii) Silver can displace copper from \(\mathrm{CuSO}_4\) solution.
(iv) Iron can displace silver from \(\mathrm{AgNO}_3\) solution.

The magnitude of magnetic field at \(O\) due to a current carrying loop as shown in the figure is, where \(O\) is the centre of two circular portions with radii \(1 \mathrm{~cm}\) and \(2 \mathrm{~cm}\) respectively is
(Take, the value of current \(I=\frac{1.2}{\pi} \mathrm{A}\) )