The sum of all values of $$\theta $$ $$ \in $$$$\left( {0,{\pi \over 2}} \right)$$ satisfying
sin² 2$$\theta $$ + cos⁴ 2$$\theta $$ = $${3 \over 4}$$ is -

Two guns A and B can fire bullets at speeds 1 km/s and 2 km/s respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bullets fired by the two guns, on the ground is -

A heat source at T = 10³ K is connected to another heat reservoir at T = 10² K by a copper slab which is 1 mthick. Given that the thermal conductivity of copper is 0.1 WK^–1m^–1, the energy flux through it in the steady state is -

A satellite is moving with a constant speed v in circular orbit around the earth. An object of mass ‘m’ is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of ejection, the kinetic energy of the object is -