The equation of the circle passing through the point $(1, 2)$ and through the points of intersection of $x^2+y^2-4x-6y-21=0$ and $3x+4y+5=0$ is given by

If $x$ is numerically so small that $x^2$ and higher powers of $x$ can be neglected,then $\left(1+\frac{2 x}{3}\right)^{3 / 2} \cdot(32+5 x)^{-1 / 5}$ is approximately equal to

Light of wavelength $2475 \, Å$ is incident on barium. Photoelectrons emitted describe a circle of radius $100 \, cm$ in a magnetic field of flux density $\frac{1}{\sqrt{17}} \times 10^{-5} \, T$. The work function of the barium is ............. $eV$ (given $\frac{e}{m} = 1.7 \times 10^{11} \, C/kg$).

An inductance of $1 \ H$ is connected in series with an $AC$ source of $220 \ V$ and $50 \ Hz$. The inductive reactance (in ohm) is (in $\pi$)

In a cyclic process,the work done by the system is

The maximum tension a rope can withstand is $60 ~kg-wt$. The ratio of maximum acceleration with which two boys of masses $20 ~kg$ and $30 ~kg$ can climb up the rope at the same time is