The following graph represents the $$T$$-$$V$$ curves of an ideal gas (where $$T$$ is the temperature and $$V$$ the volume) at three pressures $$P_1, P_2$$ and $$P_3$$ compared with those of Charles's law represented as dotted lines.

Then the correct relation is :
The velocity $$(v)-$$ time $$(t)$$ plot of the motion of a body is shown below:

The acceleration $$(a)-$$ time $$(t)$$ graph that best suits this motion is :




Choose the correct circuit which can achieve the bridge balance.




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:
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