$A$ body of mass $2 \, kg$ slides down a curved track which is a quadrant of a circle of radius $1 \, m$. All the surfaces are frictionless. If the body starts from rest,its speed at the bottom of the track is ................. $m/s$.

$A$ capacitor of capacity $0.1 \mu F$ connected in series to a resistor of $10 M \Omega$ is charged to a certain potential and then made to discharge through the resistor. The time in which the potential will take to fall to half its original value is (Given,$\log _{10} 2=0.3010$ ) (in $~s$)

If $\int \frac{dx}{(1+\sqrt{x}) \sqrt{x-x^2}} = \frac{A \sqrt{x}}{\sqrt{1-x}} + \frac{B}{\sqrt{1-x}} + C$,where $C$ is a real constant,then $A+B$ equals to

Which of the following is a source of rubber?

The given diagram shows an ideal gas taken from state $1$ to $2$ through optional paths $A, B, C$. Let $Q, W$,and $\Delta U$ represent the heat supplied to the gas,work done by the gas,and the change in internal energy of the gas,respectively. Which of the following conditions is true?

Which of the following carbonyl compounds will exhibit enolization?
$(i)$
$(ii)$
$(iii)$
$(iv)$
$(v)$