If $P(1, 2)$,$Q(4, 6)$,$R(5, 7)$,and $S(a, b)$ are the vertices of a parallelogram $PQRS$,then:

Select the correct statement $:-$

The displacement equations of two waves are given as $y_1 = 10 \sin(3\pi t + \pi/3)$ and $y_2 = 5(\sin 3\pi t + \sqrt{3} \cos 3\pi t)$. What is the ratio of their amplitudes?

The time period of a simple pendulum is $T$. When the length is increased by $10 \ cm$,its period is $T_1$. When the length is decreased by $10 \ cm$,its period is $T_2$. Then,the relation between $T, T_1$ and $T_2$ is

$A$ fully charged capacitor $C$ with initial charge $q_0$ is connected to a coil of self-inductance $L$ at $t = 0$. The time at which the energy is stored equally between the electric and the magnetic fields is

The maximum value of $\frac{\log x}{x}, 0 < x < \infty$ is