The atomic numbers of Vanadium $(V)$,Chromium $(Cr)$,Manganese $(Mn)$,and Iron $(Fe)$ are $23, 24, 25$,and $26$ respectively. Which of these elements will have the highest second ionization enthalpy?

If the roots of the equations $px^2 + 2qx + r = 0$ and $qx^2 - 2\sqrt{pr}x + q = 0$ are real,then

Percentage of gold in $14$ carat gold is (in $\%$)

$A$ very small hole in an electric furnace is used for heating metals. The hole nearly acts as a black body. The area of the hole is $200 ~mm^2$. To keep a metal at $727^{\circ} C$,the heat energy flowing through this hole per second,in joules,is $\left(\sigma = 5.67 \times 10^{-8} ~W m^{-2} K^{-4}\right)$.

The resistance of a bulb filament is $100\, \Omega$ at a temperature of $100\, ^oC$. If its temperature coefficient of resistance is $0.005\, (^oC)^{-1}$,at what temperature will its resistance become $200\, \Omega$?

The solution of the differential equation $\frac{dy}{dx} = \frac{y}{x} + \frac{\phi(y/x)}{\phi'(y/x)}$ is