$A$ frictionless track $ABCDE$ ends in a circular loop of radius $R$. $A$ body slides down the track from point $A$ which is at a height $h = 5 \, cm$. The maximum value of $R$ for the body to successfully complete the loop is .................. $cm$.

The cold junction of a thermocouple is at $0^{\circ} C$. The thermo e.m.f produced in the thermocouple is given by the equation $E = 16T - 0.04T^2$,where $T$ is the temperature of the hot junction. The temperature of inversion and neutral temperature of the thermocouple are:

The displacement equations of sound waves produced by two sources are given by $y_1 = 5 \sin(400 \pi t)$ and $y_2 = 8 \sin(408 \pi t)$, where $t$ is time in seconds. If the waves are produced simultaneously, the number of beats produced per minute is

In a two-slit experiment with monochromatic light,fringes are obtained on a screen placed at some distance from the slits. If the screen is moved by $5 \times 10^{-2} \ m$ towards the slits,the change in fringe width is $3 \times 10^{-5} \ m$. If the separation between the slits is $10^{-3} \ m$,the wavelength of light used is ......... $\mathring{A}$.

Which among the following is a haloalkyne?

Consider the depicted hydrogen $( H )$ in the hydrocarbons given below. The most acidic hydrogen $( H )$ is