$X$-rays are used in:

The focal length of an equi-convex lens is greater than the radius of curvature of any of the surfaces. Then the refractive index of the material of the lens is

The spleen is a:

Two tuning forks $A$ and $B$ produce $8 \, Hz$ beats when sounded together. $A$ gas column $37.5 \, cm$ long in a pipe closed at one end resonates in its fundamental mode with fork $A$,whereas a column of length $38.5 \, cm$ of the same gas in a similar pipe is required for resonance with fork $B$. The frequencies of these two tuning forks are:

An object of mass $2m$ is projected with a speed of $100 \ m/s$ at an angle $\theta = \sin^{-1}(3/5)$ to the horizontal. At the highest point,the object breaks into two pieces of same mass $m$ and the first one comes to rest. The distance between the point of projection and the point of landing of the bigger piece (in metre) is (Given,$g = 10 \ m/s^2$)

$\sec h^{-1}\left(\frac{1}{2}\right)-\operatorname{cosec} h^{-1}\left(\frac{3}{4}\right)$ is equal to