If $y = \cos^{-1}\left(\frac{a^2-x^2}{a^2+x^2}\right) + \sin^{-1}\left(\frac{2ax}{a^2+x^2}\right)$, then $\frac{dy}{dx}$ is equal to

$A$ hollow sphere of radius $R$ is filled completely with an ideal liquid of density $\rho$. The sphere is moving horizontally with an acceleration $2g$,where $g$ is the acceleration due to gravity. If the minimum pressure of the liquid is $P_0$,then find the pressure at the centre of the sphere.

Let $A(3-i)$ and $B(2+i)$ be two points in the Argand plane. If the point $P$ represents the complex number $z=x+iy$,which satisfies $|z-3+i|=|z-2-i|$,then the locus of the point $P$ is

The 'Golden Rice' variety is enriched with which of the following?

The de-Broglie wavelength of a particle moving with a velocity of $2.25 \times 10^8 \ m/s$ is equal to the wavelength of a photon. The ratio of the kinetic energy of the particle to the kinetic energy of the photon is: (in $/8$)

The most important feature of all living systems is to