An alternating voltage $E = 200 \sqrt{2} \sin(100 t)$ is connected to a $1 \mu F$ capacitor through an $AC$ ammeter. The reading of the ammeter shall be: (in $\text{ mA}$)

Let $\overrightarrow{a}=a_1 \hat{i}+a_2 \hat{j}+a_3 \hat{k}$.
Assertion $(A)$: The identity $|\overrightarrow{a} \times \hat{i}|^2+|\overrightarrow{a} \times \hat{j}|^2+|\overrightarrow{a} \times \hat{k}|^2=2|\overrightarrow{a}|^2$ holds for $\overrightarrow{a}$.
Reason $(R)$: $\overrightarrow{a} \times \hat{i}=a_3 \hat{j}-a_2 \hat{k}$, $\overrightarrow{a} \times \hat{j}=a_1 \hat{k}-a_3 \hat{i}$, and $\overrightarrow{a} \times \hat{k}=a_2 \hat{i}-a_1 \hat{j}$.
Which of the following is correct?

The magnifying power of a telescope is $9$. When it is adjusted for parallel rays,the distance between the objective and the eye-piece is found to be $20\, cm$. The focal lengths of the two lenses are

$A$ photon collides with a stationary hydrogen atom in the ground state inelastically. The energy of the colliding photon is $10.2 \, eV$. After a time interval of the order of a microsecond,another photon collides with the same hydrogen atom inelastically with an energy of $15 \, eV$. What will be observed by the detector?

The magnetic flux through a circuit of resistance $R$ changes by an amount $\Delta \phi$ in time $\Delta t$. Then the total quantity of electric charge $Q$ passing during this time through any point of the circuit is given by:

$Br_2 + 2X^{-} \to 2Br^{-} + X_2$
$Cl_2 + 2Y^{-} \to 2Cl^{-} + Y_2$
The incorrect match regarding the above reactions is: