The average energy possessed by an oscillator at a temperature 300 K is (Boltzmann constant $=1.38 \times 10^{-23} \mathrm{JK}^{-1}$ )

A wave is given by $y=5 \times 10^{-3} \sin \left(12.5 \pi x-\frac{\pi}{2} t\right)$. Then its wavelength and time period are respectively ( $y$ and $x$ are in metres and $t$ is in seconds)

A tuning fork $A$ of frequency 250 Hz and another tuning fork $B$ of frequency $x$ produced 5 beats per second when vibrated together. If the fork $B$ is waxed and vibrated together with $A$, then 3 beats per second are produced. Then, $x=$

A convex lens forms a real image of a point object placed on its principal axis. If the upper half of the lens is painted black, then