Which one of the following metallic hydroxides does not dissolve in sodium hydroxide solution?

The time constant of an inductance coil is $3 \text{ ms}$. When a $90 \Omega$ resistance is joined in series,the time constant becomes $0.5 \text{ ms}$. The inductance and the resistance of the coil are:

$A$ gas at the temperature $250\, K$ is contained in a closed vessel. If the gas is heated through $1\, K$, then the percentage increase in its pressure will be .... $\%$

Match the items given in Column $I$ with those in Column $II$ and select the correct option given below:
Column $I$ | Column $II$
$a$. $p \land q$ | $i$. $p \to q$
$b$. $p \lor q$ | $ii$. $\sim p \lor \sim q$
$c$. $\sim(p \land q)$ | $iii$. $\sim p \lor q$
$d$. $p \to q$ | $iv$. $\sim p \land \sim q$

$A$ 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?

Assertion $(A)$: $A$ particle of mass $m$ dropped into a hole made along the diameter of the Earth from one end to the other executes simple harmonic motion.
Reason $(R)$: Gravitational force between any two particles is inversely proportional to the square of the distance between them.