Let y = y(x) be the solution of the differential equation,
$${{2 + \sin x} \over {y + 1}}.{{dy} \over {dx}} = - \cos x$$, y > 0,y(0) = 1.
If y($$\pi $$) = a and $${{dy} \over {dx}}$$ at x = $$\pi $$ is b, then the ordered pair (a, b) is equal to :

In a reactor, 2 kg of ₉₂U²³⁵ fuel is fully used up in 30 days. The energy released per fission is 200 MeV. Given that the Avogadro number, N = 6.023 $$ \times $$ 10²⁶ per kilo mole and 1 eV = 1.6 × 10^–19 J. The power output of the reactor is close to

A spherical mirror is obtained as shown in the figure from a hollow glass sphere. If an object is positioned in front of the mirror, what will be the nature and magnification of the image of the object?
(Figure drawn as schematic and not to scale)

Consider four conducting materials copper, tungsten, mercury and aluminium with resistivity $$\rho $$_C, $$\rho $$_T, $$\rho $$_M and $$\rho $$_A respectively. Then :