An electric fan has blades of length $30 \, cm$ as measured from the axis of rotation. If the fan is rotating at $1200 \, r.p.m.$,the acceleration of a point on the tip of the blade is approximately ........ $m/s^2$.

An engine has an efficiency of $1/6$. When the temperature of the sink is reduced by $62^{\circ}C$,its efficiency is doubled. The temperature of the source is ....... $^{\circ}C$.

Which of the following substances does not contain a $-COOH$ group?

If $a, b, c$ are non-coplanar unit vectors such that $a \times (b \times c) = \frac{b + c}{\sqrt{2}}$,then what is the angle between $a$ and $b$?

Identify the correct statements from the following: $(i)$ The cryptozoite ingests food and becomes spherical. $(ii)$ Sporozoites enter the human blood. $(iii)$ Two stages of the life cycle are observed in Plasmodium. $(iv)$ The cryptozoite transforms into cryptomerozoites.

Two equal point charges are fixed at $x = -a$ and $x = +a$ on the $x$-axis. Another point charge $Q$ is placed at the origin. The change in the electrical potential energy of $Q$ when it is displaced by a small distance $x$ along the $x$-axis is approximately proportional to