For a plane electromagnetic wave, the magnetic field at a point x and time t is

$$\overrightarrow B \left( {x,t} \right)$$ = $$\left[ {1.2 \times {{10}^{ - 7}}\sin \left( {0.5 \times {{10}^3}x + 1.5 \times {{10}^{11}}t} \right)\widehat k} \right]$$ T

The instantaneous electric field $$\overrightarrow E $$ corresponding to $$\overrightarrow B $$ is :
(speed of light c = 3 × 10⁸ ms^–1)

Given the masses of various atomic particles
m_p = 1.0072 u, m_n = 1.0087 u, m_e = 0.000548 u,
$${m_{\overline v }}$$ = 0, m_d = 2.0141 u, where p $$ \equiv $$ proton, n $$ \equiv $$ neutron,
e $$ \equiv $$ electron, $$\overline v $$ $$ \equiv $$ antineutrino and d $$ \equiv $$ deuteron. Which of the following process is allowed by momentum and energy conservation?

Two planets have masses M and 16 M and their radii are $$a$$ and 2$$a$$, respectively. The separation between the centres of the planets is 10$$a$$. A body of mass m is fired from the surface of the larger planet towards the smaller planet along the line joining their centres. For the body to be able to reach at the surface of smaller planet, the minimum firing speed needed is :

Consider the force F on a charge 'q' due to a uniformly charged spherical shell of radius R carrying charge Q distributed uniformly over it. Which one of the following statements is true for F, if 'q' is placed at distance r from the centre of the shell?