$A$ particle of mass $200\,g$ executes a simple harmonic motion. The restoring force is provided by a spring of spring constant $80\,N/m$. The time period is .... $sec$.

Which of the following molecules has the highest dipole moment?

$A$ 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: In the condition of obstructive jaundice,large amounts of unabsorbed fats are eliminated out of the body.
Reason: Entry of bile into the small intestine is prevented during obstructive jaundice.

If two soap bubbles of different radii are connected by a tube, then

The numbers $a_n = 6^n - 5n$ for $n = 1, 2, 3, \ldots$ when divided by $25$ leave the remainder: