$A$ hollow insulated conducting sphere is given a positive charge of $10\,\mu C$. What will be the electric field at the centre of the sphere if its radius is $2\,m$?

The population of an insect species shows an explosive increase in numbers during the rainy season,followed by its disappearance at the end of the season. What does this show?

For positive numbers $x, y, \text{ and } z$,the numerical value of the determinant $\left| \begin{array}{ccc} 1 & \log_x y & \log_x z \\ \log_y x & 1 & \log_y z \\ \log_z x & \log_z y & 1 \end{array} \right|$ is

$A$ father with $8$ children takes them $3$ at a time to the Zoological gardens,as often as he can without taking the same $3$ children together more than once. The number of times he will go to the garden is

Match the following lists:

List-$I$	List-$II$
$A$. Ethane	$1$. $2$ $sp$ carbons
$B$. Ethylene	$2$. $6$ $sp^2$ carbons
$C$. Acetylene	$3$. $2$ $sp^3$ carbons
$D$. Benzene	$4$. $2$ $sp^2$ carbons
	$5$. $1$ $sp$ and $1$ $sp^2$ carbons

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