If $f(x) = \frac{\cos^2 x + \sin^4 x}{\sin^2 x + \cos^4 x}$, for $x \in R$, then $f(2002)$ is equal to

In a thermodynamic process,the pressure of a fixed mass of a gas is changed in such a manner that the gas releases $20 \, J$ of heat when $8 \, J$ of work is done on the gas. If the initial internal energy of the gas was $30 \, J$,then the final internal energy will be ........ $J$.

$A$ galvanometer of resistance $50\,\Omega$ is connected to a battery of $3\,V$ along with a resistance of $2950\,\Omega$ in series. $A$ full-scale deflection of $30$ divisions is obtained in the galvanometer. In order to reduce this deflection to $20$ divisions,the resistance in series should be.......$\Omega$.

$A$ glass capillary tube of inner diameter $0.28 \ mm$ is lowered vertically into water in a vessel. The pressure to be applied on the water in the capillary tube so that the water level in the tube is the same as that in the vessel (in $N/m^2$) is:
(Surface tension of water $= 0.07 \ N/m$,Atmospheric pressure $= 10^5 \ N/m^2$)

An insect crawls up a hemispherical surface very slowly (see figure). The coefficient of friction between the insect and the surface is $\mu = 1/3$. If the line joining the centre of the hemispherical surface to the insect makes an angle $\alpha$ with the vertical,the maximum possible value of $\alpha$ is given by

Ovulation is induced under the influence of which hormone?