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?

In the figure shown, the current in the 10 V battery is close to :

A student measuring the diameter of a pencil of circular cross-section with the help of a vernier scale records the following four readings 5.50 mm, 5.55 mm, 5.45 mm, 5.65 mm. The average of these four readings is 5.5375 mm and the standard deviation of the data is 0.07395 mm. The average diameter
of the pencil should therefore be recorded as :