$A$ tuning fork vibrating with a sonometer having $20 \, cm$ wire produces $5$ beats per sec. The beat frequency does not change if the length of the wire is changed to $21 \, cm$. The frequency of the tuning fork must be ..... $Hz$.

The angle between the lines represented by $(\sin^2 \alpha) y^2 - 2xy(\cos^2 \alpha) + (\cos^2 \alpha - 1) x^2 = 0$ is

Which organ in an adult human causes the least damage if removed?

If the function $y = \sin^{-1} x$, then $(1 - x^2) \frac{d^2 y}{d x^2}$ is equal to

Two thick wires and two thin wires,all of the same material and same length,form a square in three different ways $P$,$Q$,and $R$ as shown in the figure. With the current connection shown,the magnetic field at the centre of the square is zero in which cases?

The figure shows the variation of $R$,$X_L$,and $X_C$ with frequency $f$ in a series $LCR$ circuit. For which frequency point is the circuit inductive?