$x = \log \left( \frac{1}{y} + \sqrt{1 + \frac{1}{y^2}} \right) \Rightarrow y$ is equal to

Ionisation enthalpies of $Ce$,$Pr$,and $Nd$ are higher than $Th$,$Pa$,and $U$. Why?

In the following reaction,$X$ and $Y$ respectively are:
$C_2H_5OH \xrightarrow{KMnO_4 / H^{+}} X$
$X \xrightarrow[H_2SO_4 / \Delta]{Y} CH_3COOC_2H_5$

Which of the following electronic configurations is not possible?

$A$ ball is thrown upward with an initial velocity $V_0$ from the surface of the earth. The motion of the ball is affected by a drag force equal to $m \gamma v^2$ (where $m$ is the mass of the ball,$v$ is its instantaneous velocity,and $\gamma$ is a constant). The time taken by the ball to rise to its zenith is:

If $\alpha+\beta=-2$ and $\alpha^3+\beta^3=-56$,then the quadratic equation whose roots are $\alpha$ and $\beta$ is