An oscillator circuit consists of an inductance of $0.5\,mH$ and a capacitor of $20\,\mu F$. The resonant frequency of the circuit is nearly.....$Hz$

If $\frac{x+1}{(2x-1)(3x+1)}=\frac{A}{(2x-1)}+\frac{B}{(3x+1)}$, then $16A+9B$ is equal to

$A$ cricketer can throw a ball to a maximum horizontal distance of $100 \, m$. The speed with which he throws the ball is (to the nearest integer) (in $m/s$).

If $f(x) = \sqrt{ax} + \frac{a^2}{\sqrt{ax}}$,then $f^{\prime}(a)$ is equal to

The primary and secondary coils of a transformer have $50$ and $1500$ turns respectively. If the magnetic flux $\phi$ linked with the primary coil is given by $\phi = \phi_0 + 4t$,where $\phi$ is in webers,$t$ is time in seconds,and $\phi_0$ is a constant,the output voltage across the secondary coil is ...... $volts$.

Identify the incorrect pair from the following: