$A$ nucleus $_Z{X^A}$ emits an $\alpha$-particle with velocity $v$. The recoil speed of the daughter nucleus is

If $a > 0$ and $b^2 - 4ac = 0$,then the curve $y = ax^2 + bx + c$

$A$ flask of volume $10^3 \text{ cc}$ is completely filled with mercury at $0 \ ^\circ\text{C}$. The coefficient of cubical expansion of mercury is $180 \times 10^{-6} / ^\circ\text{C}$ and that of glass is $40 \times 10^{-6} / ^\circ\text{C}$. If the flask is now placed in boiling water at $100 \ ^\circ\text{C}$,how much mercury (in $\text{cc}$) will overflow?

Total number of secondary amines (excluding stereoisomers) possible with the molecular formula $C_5H_{13}N$ is

$\int \frac{x-1}{(x+1) \sqrt{x(x^2+x+1)}} dx = $

Heartbeat increases due to the stimulation of .......