If the mass of the bob in a simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is $$\frac{x}{2}$$ times its original time period. Then the value of $$x$$ is:

A simple pendulum oscillating in air has a period of $$\sqrt{3} \mathrm{~s}$$. If it is completely immersed in non-viscous liquid, having density $$\left(\frac{1}{4}\right)^{\text {th }}$$ of the material of the bob, the new period will be :-

The $$x$$ - $$t$$ graph of a particle performing simple harmonic motion is shown in the figure. The acceleration of the particle at $$t=2 \mathrm{~s}$$ is :

Match List-I with List-II

	List-I (x-y graphs)		List-II (Situations)
(a)		(i)	Total mechanical energy is conserved
(b)		(ii)	Bob of a pendulum is oscillating under negligible air friction
(c)		(iii)	Restoring force of a spring
(d)		(iv)	Bob of a pendulum is oscillating along with air friction

Choose the correct answer from the options given below