Two lines $\frac{x-3}{1}=\frac{y+1}{3}=\frac{z-6}{-1}$ and $\frac{x+5}{7}=\frac{y-2}{-6}=\frac{z-3}{4}$ intersect at the point $R$. Then the reflection of $R$ in the $xy$-plane has coordinates:

If $\int \frac{dx}{(1+\sqrt{x}) \sqrt{x-x^2}} = \frac{A \sqrt{x}}{\sqrt{1-x}} + \frac{B}{\sqrt{1-x}} + C$,where $C$ is a real constant,then $A+B$ equals to

$A$ uniform but time-varying magnetic field $B(t)$ exists in a circular region of radius $a$ and is directed into the plane of the paper,as shown. The magnitude of the induced electric field at point $P$ at a distance $r > a$ from the centre of the circular region is:

The value of $\left(\frac{1+\sin \frac{2 \pi}{9}+i \cos \frac{2 \pi}{9}}{1+\sin \frac{2 \pi}{9}-i \cos \frac{2 \pi}{9}}\right)^{3}$ is

The de-Broglie wavelength of the electron in the ground state of the hydrogen atom is . . . . . . $\mathring{A}$ (radius of the first orbit of hydrogen atom $= 0.53 \ \mathring{A}$).

An ideal gas of mass $m$ in a state $A$ goes to another state $B$ via three different processes as shown in the figure. If ${Q_1}, {Q_2}$ and ${Q_3}$ denote the heat absorbed by the gas along the three paths,then