Explanation

(d)
Given, $y = x^{2} + x - 1$
$\therefore\ \ \ \ \ \frac{dy}{dx} = 2x + 1$
At (1, 1), $\frac{dy}{dx} = 3 = m$
$\therefore$ Length of tangent,
$A = \left| \frac{y_{1}\sqrt{1 + m^{2}}}{m} \right| = \left| \frac{1\sqrt{1 + 9}}{3} \right| = \frac{\sqrt{10}}{3}$
Length of subtangent, $B = \left| \frac{y_{1}}{m} \right| = \frac{1}{3}$
Length of normal,
$C = \left| y_{1}\sqrt{1 + m^{2}} \right| = \left| 1\sqrt{1 + 9} \right| = \sqrt{10}$
And length of subnormal, $D = \left| y_{1}m \right| = 3$
Now, increasing order is$B,\ A,\ D,\ C$.