The compound formed on heating chlorobenzene with chloral in the presence of concentrated sulphuric acid is:

$A$ block rests on a rough inclined plane making an angle of $30^{\circ}$ with the horizontal. The coefficient of static friction between the block and the plane is $0.8$. If the frictional force on the block is $10 \, N$,the mass of the block (in $kg$) is (take $g = 10 \, m/s^2$)

Let $\overline{a}=2 \hat{i}+\hat{j}-2 \hat{k}$ and $\overline{b}=\hat{i}+\hat{j}$. Let $\overline{c}$ be a vector such that $|\overline{c}-\overline{a}|=3$,$|(\overline{a} \times \overline{b}) \times \overline{c}|=3$,and the angle between $\overline{c}$ and $\overline{a} \times \overline{b}$ is $30^{\circ}$. Then $\overline{a} \cdot \overline{c}$ is equal to

Which of the following has the largest population in a food chain?

$A$ diode detector is used to detect an amplitude-modulated wave of $60\%$ modulation by using a capacitor of capacity $250 \text{ pF}$ in parallel with a load resistance of $100 \text{ k}\Omega$. Find the maximum modulation frequency which could be detected by it.

The position vectors of $P$ and $Q$ are respectively $\overrightarrow{a}$ and $\overrightarrow{b}$. If $R$ is a point such that $\overrightarrow{PR}=5 \overrightarrow{PQ}$, then the position vector of $R$ is