The alum used for purifying water is

The angular resolution of a $10\,cm$ diameter telescope at a wavelength of $5000\,\mathring{A}$ is of the order of:

In a $CE$ transistor amplifier,the audio signal voltage across the collector resistance of $2\,k\Omega$ is $2\,V$. If the base resistance is $1\,k\Omega$ and the current amplification of the transistor is $100$,the input signal voltage is

The solution of $x \frac{dy}{dx} = y + x e^{y/x}$ with $y(1) = 0$ is

In Young's double slit experiment,the $y$-coordinates of the central maximum and the $10^{th}$ maximum are $2\, cm$ and $5\, cm$ respectively. When the $YDSE$ apparatus is immersed in a liquid of refractive index $\mu = 1.5$,what will be the new $y$-coordinates?

For a binomial variate $X$ with parameters $n=5$ and $p=\frac{3}{4}$,if $\alpha=\frac{1}{9} P(X \geq 3)$ and $\beta=P(X \leq 2)$,then $256(\beta-\alpha)=$