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

If $a > 0$ and $\lim _{x \rightarrow a} \frac{a^x - x^a}{x^x - a^a} = -1$,then $a$ is equal to

$A$ thin hollow sphere of mass $m$ is completely filled with a liquid of mass $m$. When the sphere rolls with a velocity $v$,the kinetic energy of the system is (neglect friction).

Which of the following pairs of animals represents jawless fishes?

The magnetic field $(B)$ inside a long solenoid having $n$ turns per unit length and carrying current $I$ when an iron core is kept in it is ($\mu_0 = $ permeability of vacuum,$\chi = $ magnetic susceptibility).

Passage cells are thin-walled cells found in