$A$ single slit of width $0.20 \, mm$ is illuminated with light of wavelength $500 \, nm$. The observing screen is placed $80 \, cm$ from the slit. The width of the central bright fringe will be.....$mm$

Let the relation $R$ be defined on the set of natural numbers $N$ by $a R b$ if $3 a + 2 b = 27$. Then $R$ is:

$\int_0^{\pi / 2} \sin ^8 x \cos ^2 x \, dx$ is equal to

Two cylinders $A$ and $B$ fitted with pistons contain equal number of moles of an ideal monoatomic gas at $400 ~K$. The piston of $A$ is free to move while that of $B$ is held fixed. Same amount of heat energy is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $42 ~K$, the rise in temperature of the gas in $B$ is (in $~K$)

Which variety of rice is an example of a naturally occurring mutation?

The direction cosines of the line making angles $\frac{\pi}{4}, \frac{\pi}{3}$ and $\theta$ $\left(0 < \theta < \frac{\pi}{2}\right)$ respectively with $x, y$ and $z$ axes, are