The wavelength of ${K_\alpha }$ $X-$rays produced by an $X-$ray tube is $0.76 \ \mathring A$. The atomic number of the anode material of the tube is:

If $\operatorname{cosec} \theta = \frac{p+q}{p-q}$,then $\cot \left(\frac{\pi}{4} + \frac{\theta}{2}\right)$ is equal to

When ${}_{92}U^{238}$ changes into ${}_{82}Pb^{206}$,the number of $\alpha$ and $\beta^-$ particles emitted are:

If $\Delta$ is the area of the triangle formed by the positive $x$-axis and the normal and tangent to the circle $x^2+y^2=4$ at $(1, \sqrt{3})$,then $\Delta$ is equal to

The horizontal acceleration that should be given to a smooth inclined plane of angle $\theta = \sin^{-1}\left(\frac{1}{l}\right)$ to keep an object stationary on the plane, relative to the inclined plane is:

Which of the following bonds is the most polar?