If $f(x)=x e^{x(1-x)}$,then $f(x)$ is

$A$ water barrel having water up to a depth $d$ is placed on a table of height $h$. $A$ small hole is made on the wall of the barrel at its bottom. If the stream of water coming out of the hole falls on the ground at a horizontal distance $R$ from the barrel,then the value of $d$ is

Which of the following is non-conducting?

In the Compton scattering process,the incident $X$-radiation is scattered at an angle of $60^{\circ}$. The wavelength of the scattered radiation is $0.22 \ \mathring{A}$. The wavelength of the incident $X$-radiation in $\mathring{A}$ units is:

If $y = 4x - 5$ is tangent to the curve $y^2 = px^3 + q$ at $(2, 3)$,then

If the point $P(1,3)$ undergoes the following transformations successively:
$(i)$ Reflection with respect to the line $y=x$.
(ii) Translation through $3$ units along the positive direction of the $X$-axis.
(iii) Rotation through an angle of $\frac{\pi}{6}$ about the origin in the clockwise direction.
Then,the final position of the point $P$ is