A charged particle carrying charge 1 $$\mu $$C is moving
with velocity $$\left( {2\widehat i + 3\widehat j + 4\widehat k} \right)$$ ms^–1. If an external
magnetic field of $$\left( {5\widehat i + 3\widehat j - 6\widehat k} \right)$$× 10^–3 T exists in the region where the particle is moving then the
force on the particle is $$\overrightarrow F $$ × 10^–9 N. The vector $$\overrightarrow F $$ is :

A satellite is moving in a low nearly circular orbit around the earth. Its radius is roughly equal to that of the earth’s radius R_e . By firing rockets attached to it, its speed is instantaneously increased in the direction of its motion so that it become $$\sqrt {{3 \over 2}} $$ times larger. Due to this the farthest distance from the centre of the earth that the satellite reaches is R. Value of R is :

A cricket ball of mass 0.15 kg is thrown vertically up by a bowling machine so that it rises to a maximum height of 20 m after leaving the machine. If the part pushing the ball applies a constant force F on the ball and moves horizontally a distance of 0.2 m while launching the ball, the value of F (in N) is (g = 10 ms^–2) ____.

A balloon filled with helium (32^oC and 1.7 atm.) bursts. Immediately afterwards the expansion of helium can be considered as