If the length of a stretched string is shortened by $40 \%$ and the tension is increased by $44 \%$,then the ratio of the final and initial fundamental frequencies is :

$A$ particle of charge '$q$' and mass '$m$' moves in a circular orbit of radius '$r$' with angular speed '$\omega$'. The ratio of the magnitude of its magnetic moment to that of its angular momentum depends on

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

The integrating factor of the differential equation $x \log x \frac{dy}{dx} + y = 2 \log x$ is given by

For $k=1, 2, 3$, the box $B_k$ contains $k$ red balls and $(k+1)$ white balls. Let $P(B_1)=\frac{1}{2}$, $P(B_2)=\frac{1}{3}$, and $P(B_3)=\frac{1}{6}$. $A$ box is selected at random and a ball is drawn from it. If a red ball is drawn, then the probability that it has come from box $B_2$ is:

As the switch $S$ is closed in the circuit shown in the figure,the current passing through it is ................ $A$.