A single slit of width $a$ is illuminated by a monochromatic light of wavelength $600 \mathrm{~nm}$. The value of ' $a$ ' for which first minimum appears at $\theta=30^{\circ}$ on the screen will be :

The position vector of a particle related to time $t$ is given by

$\vec{r}=\left(10 t \hat{i}+15 t^{2} \hat{j}+7 \hat{k}\right) m$

The direction of net force experienced by the particle is :

A body is released from a height equal to the radius $(\mathrm{R})$ of the earth. The velocity of the body when it strikes the surface of the earth will be

(Given $g=$ acceleration due to gravity on the earth.)

A vector in $x-y$ plane makes an angle of $30^{\circ}$ with $y$-axis. The magnitude of $\mathrm{y}$-component of vector is $2 \sqrt{3}$. The magnitude of $x$-component of the vector will be :