An electron gun is placed inside a long solenoid of radius R on its axis. The solenoid has n turns/length and carries a current I. The electron gun shoots an electron along the radius of the solenoid with speed v. If the electron does not hit the surface of the solenoid, maximum possible value of v is (all symbols have their standard meaning) :

Starting at temperature 300 K, one mole of an
ideal diatomic gas ($$\gamma $$ = 1.4) is first compressed
adiabatically from volume V₁ to V₂ = $${{{V_1}} \over {16}}$$. It is
then allowed to expand isobarically to volume 2V₂. If all the processes are the quasi-static then
the final temperature of the gas (in ^oK) is (to the nearest integer) _____.

Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is 1 : 4, the ratio of their diameters is:

An electric field $$\overrightarrow E = 4x\widehat i - \left( {{y^2} + 1} \right)\widehat j$$ N/C
passes through the box shown in figure. The
flux of the electric field through surfaces ABCD
and BCGF are marked as $${\phi _I}$$ and $${\phi _{II}}$$
respectively. The difference between $$\left( {{\phi _I} - {\phi _{II}}} \right)$$ is (in Nm²/C) _______.