In a potentiometer, a wire of length $10 \, m$ having resistance $50 \, \Omega$ is used. $A$ battery of $5 \, V$ and a resistor of $450 \, \Omega$ are connected in series to the wire. If an unknown battery of emf $E$ balances the potentiometer at $450 \, cm$, then the value of $E$ is (in $V$)

Two particles of equal mass have velocities $\overrightarrow{v}_1=4 \hat{i} \text{ ms}^{-1}$ and $\overrightarrow{v}_2=4 \hat{j} \text{ ms}^{-1}$. The first particle has an acceleration $\overrightarrow{a}_1=(5 \hat{i}+5 \hat{j}) \text{ ms}^{-2}$ while the acceleration of the other particle is zero. The centre of mass of the two particles moves in a path of

Keto-enol tautomerism is not observed in

$A$ committee of $12$ members is to be formed from $9$ women and $8$ men. The number of committees in which the women are in majority is

The time in seconds required to produce a potential difference of $20 \ V$ across a capacitor of $1000 \ \mu F$ when it is charged at a steady rate of $200 \ \mu C/s$ is:

$A$ particle at the end of a spring executes simple harmonic motion with a period $t_1$,while the corresponding period for another spring is $t_2$. If the period of oscillation with the two springs in series is $T$,then