$A$ car is moving at a speed of $40 \, m/s$ on a circular track of radius $400 \, m$. This speed is increasing at the rate of $3 \, m/s^2$. The acceleration of the car is ....... $m/s^2$.

If $\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c}$ are three vectors such that $\overrightarrow{a}=\overrightarrow{b}+\overrightarrow{c}$ and the angle between $\overrightarrow{b}$ and $\overrightarrow{c}$ is $\frac{\pi}{2}$,then:

Four numbers are chosen at random from $\{1, 2, 3, \ldots, 40\}$. The probability that they are not consecutive is:

The angle between the lines $x \cos \alpha_1 + y \sin \alpha_1 = p_1$ and $x \cos \alpha_2 + y \sin \alpha_2 = p_2$ is:

If $y=3x$ is a tangent to a circle with centre $(1,1)$,then the other tangent drawn through $(0,0)$ to the circle is

In the $NO_3^-$ ion,what are the number of bond pairs and lone pairs of electrons on the $N$ atom,respectively?