$A$ glass convex lens is of refractive index $1.55$ with both faces of same radius of curvature. What will be the radius of curvature if the focal length is to be $20 \text{ cm}$ (in $\text{ cm}$)?

One litre of oxygen at a pressure of $1 ~atm$ and two litres of nitrogen at a pressure of $0.5 ~atm$ are introduced into a vessel of volume $1 ~L$. If there is no change in temperature,the final pressure of the mixture of gas (in $atm$) is

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.

The instantaneous angular position of a point on a rotating wheel is given by the equation $\theta(t) = 2t^3 - 6t^2$. The torque on the wheel becomes zero at $t = \dots \text{sec}$.

Which of the following acids has the lowest $pK_a$ value?

The hydroxides and carbonates of sodium and potassium are easily soluble in water,while the corresponding salts of magnesium and calcium are sparingly soluble in water. Explain.