MCQ
If $F(x) = \frac{1}{{{x^2}}}\int_4^x {(4{t^2} - 2F'(t))\,dt,} $ then $F'(4)$ equals
- A$32$
- B$\frac{{32}}{3}$
- ✓$\frac{{32}}{9}$
- DNone of these
$\therefore \,\,F'(x) = \frac{1}{{{x^2}}}\left( {4{x^2} - 2F'(x)} \right) - \frac{2}{{{x^3}}}\int_4^x {(4{t^2} - 2F'(t))dt} $
==> $F'(4) = \frac{1}{{16}}[64 - 2F'(4)] - 0 $
$\Rightarrow F'(4) = \frac{{32}}{9}$.
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.