$A$ lead shot of $1\, mm$ diameter falls through a long column of glycerine. The variation of its velocity $v$ with distance covered is represented by

Which of the following is the most primitive ancestor of humans?

$A$ Zener diode,having a breakdown voltage equal to $15\, V$,is used in a voltage regulator circuit as shown in the figure. The current through the Zener diode is.....$mA$.

If $y=\sin (\log _e x)$,then $x^2 \frac{d^2 y}{d x^2}+x \frac{d y}{d x}$ is equal to

$A$ load of $1 ~kg$ weight is attached to one end of a steel wire of area of cross-section $3 ~mm^2$ and Young's modulus $10^{11} ~N/m^2$. The other end is suspended vertically from a hook on a wall,then the load is pulled horizontally and released. When the load passes through its lowest position,the fractional change in length is $(g = 10 ~m/s^2)$.

$A$ man is admitted to a hospital. He is suffering from an abnormally low body temperature,loss of appetite,and extreme thirst. His brain scan would probably show a tumour in