Which of the following statements is correct for the peroxide ion $(O_2^{2-})$?
$A.$ It has completely filled antibonding molecular orbitals.
$B.$ It is diamagnetic.
$C.$ It has a bond order of $1$.
$D.$ It is isoelectronic with Neon.

$\int \frac{d x}{7+5 \cos x}$ is equal to

$A$ reversible engine converts one-sixth of the heat supplied into work. When the temperature of the sink is reduced by $62^{\circ} C$,the efficiency of the engine is doubled. The temperatures of the source and sink are

If tangents are drawn from any point on the circle $x^2+y^2=25$ to the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$,then the angle between the tangents is

Assertion : In the purely resistive element of a series $LCR$ $AC$ circuit,the maximum value of $rms$ current increases with an increase in the angular frequency of the applied $emf$.
Reason : $I_{\max} = \frac{\varepsilon_{\max}}{Z}$,where $Z = \sqrt{R^2 + (\omega L - \frac{1}{\omega C})^2}$ and $I_{\max}$ is the peak current in a cycle.

$A$ ball at rest is dropped from a height of $12 ~m$. It loses $25 \%$ of its kinetic energy on striking the ground and bounces back to a height '$h$'. Then the value of '$h$' is: (in $~m$)