Explanation

(d)
Given, $\ \ y = x^{2}$
$\ \ \ \frac{dy}{dx} = 2x$
${\ \ \ m}_{1} = \left( \frac{dy}{dx} \right)_{(1,1)}$
$and\ \ \ \ \ y^{2} = x$
$\Rightarrow \ \$ $2y\frac{dy}{dx} = 1$
$\Rightarrow \ \ \frac{dy}{dx} = \frac{1}{2y}$
$\ m_{2} = \left( \frac{dy}{dx} \right)_{(1,1)} = \frac{1}{2}$
If $\theta$ be the angle between the two curves
$\therefore\ \ \ \tan{\theta = \left| \frac{m_{1} - m_{2}}{1 + m_{1} + m_{2}} \right|} = \left| \frac{2 - \frac{1}{2}}{1 + 2 \times \frac{1}{2}} \right| = \frac{3}{4}$
$\Rightarrow \ \theta = \tan^{- 1}\left( \frac{3}{4} \right)$