If the points $(1,2)$ and $(3,4)$ lie on the same side of the straight line $3x - 5y + a = 0$,then $a$ lies in the set

Which of the following is the most stable carbocation?

$A$ nucleus at rest undergoes $\alpha-$ decay according to the equation ${}_{92}^{226}X \to Y + \alpha$. At $t = 0$,the emitted $\alpha-$ particle enters a region of space where a uniform magnetic field $\vec{B} = B_0 \hat{i}$ and an electric field $\vec{E} = E_0 \hat{i}$ exist. The $\alpha-$ particle enters the region with velocity $\vec{v} = v_0 \hat{j}$ at $x = 0$. After a time $t = \sqrt{3} \times 10^7 \frac{m_{\alpha}}{q_{\alpha} E_0}$,the particle is found to have twice its initial speed. What is the initial speed $v_0$ of the $\alpha-$ particle?

The bonds between $P$ atoms and $Cl$ atoms in $PCl_5$ are likely to be

If a gas is compressed isothermally,then the r.m.s. velocity of the molecules

When a non-volatile solute is added to a solvent,the vapor pressure of the solvent decreases by $10 \ mm \ Hg$. The mole fraction of the solute in the solution is $0.2$. If the vapor pressure is to be decreased by $20 \ mm \ Hg$,what will be the mole fraction of the solvent?