A particle having a mass of 10^$$-$$2 kg carries a charge of 5 $$ \times $$ 10^$$-$$8 C. The particle is given an initial horizontal velocity of 10⁵ m s^$$-$$1 in the presence of electric field $$\overrightarrow E $$ and magnetic field $$\overrightarrow B $$. To keep the particle moving in a horizontal direction, it is necessary that
(1)  $$\overrightarrow B $$ should be perpendicular to the direction of velocity and $$\overrightarrow E $$ should be along the direction of velocity

(2)  Both $$\overrightarrow B $$ and $$\overrightarrow E $$ should be along the direction of velocity

(3)  Both $$\overrightarrow B $$ and $$\overrightarrow E $$ are mutually perpendicular and perpendicular to the direction of velocity.

(4)  $$\overrightarrow B $$ should be along the direction of velocity and $$\overrightarrow E $$ should be perpendicular to the direction of velocity

Which one of the following pairs of statements is possible ?

The electric field at a distance $${{3R} \over 2}$$ from the centre of a charged conducting spherical shell of radius R is E. The electric field at a distance $${R \over 2}$$ from the centre of the sphere is

Two parallel metal plates having charges +Q and $$-$$Q face each other at a certain distance between them. If the plates are now dipped in kerosene oil tank, the electric field between the plates will

A monatomic gas at pressure P₁ and volume V₁ is compressed adiabatically to $${{1 \over 8}^{th}}$$ of its original volume. What is the final pressure of the gas?