$A$ mixture of $2\, \text{moles}$ of helium gas (atomic mass $= 4\, \text{amu}$) and $1\, \text{mole}$ of argon gas (atomic mass $= 40\, \text{amu}$) is kept at $300\, \text{K}$ in a container. The ratio of the $r.m.s.$ speeds $\left( \frac{v_{\text{rms}}(\text{helium})}{v_{\text{rms}}(\text{argon})} \right)$ is

$A$ light wave enters from medium $1$ to medium $2$. Its velocity in the $2^{nd}$ medium is double that of the $1^{st}$ medium. For total internal reflection to occur,the angle of incidence must be greater than which of the following values?

Identify the correct gland on the basis of the following characteristics:
$(I)$ It is located on the dorsal side of the forebrain.
$(II)$ It plays a very important role in the regulation of the $24$-hour rhythm of our body.
$(III)$ It helps in maintaining the body temperature.
$(IV)$ Its hormone influences metabolism as well as defense capability.

$A$ point object is placed at a distance of $10\,cm$ and its real image is formed at a distance of $20\,cm$ from a concave mirror. If the object is moved by $0.1\,cm$ towards the mirror,the image will shift by about:

Power delivered by the $ac$ source of the circuit becomes maximum when

If $x = \sqrt{\frac{2+\sqrt{3}}{2-\sqrt{3}}}$,then $x^2(x-4)^2$ is equal to: