The wavelengths of light used in an optical instrument are ${\lambda _1 = 4000 \ \mathring{A}}$ and ${\lambda _2 = 5000 \ \mathring{A}}$. The ratio of their respective resolving powers (corresponding to ${\lambda _1}$ and ${\lambda _2}$) is:

Arsenic drugs are mainly used in the treatment of

For a gas,$\frac{R}{C_{V}}=0.4$,where $R$ is the universal gas constant and $C_{V}$ is the molar specific heat at constant volume. The gas is made up of molecules which are

An electron moves with speed $2 \times 10^5 \ m/s$ along the positive $x$-direction in the presence of a magnetic field of induction $B = (\hat{i} + 4\hat{j} - 3\hat{k}) \ T$. The magnitude of the force experienced by the electron in newtons is (Charge on the electron $= 1.6 \times 10^{-19} \ C$)

$A$ curve passes through the point $\left(1, \frac{\pi}{6}\right)$. Let the slope of the curve at each point $(x, y)$ be $\frac{y}{x}+\sec \left(\frac{y}{x}\right)$,where $x>0$. Then,the equation of the curve is:

Two particles undergo $SHM$ along parallel lines with the same time period $(T)$ and equal amplitudes. At a particular instant,one particle is at its extreme position while the other is at its mean position. They move in the same direction. They will cross each other after a further time: