If $ y = (\tan^{-1} x)^2 $,then $ (x^2 + 1)^2 y_2 + 2x(x^2 + 1) y_1 $ is equal to

If $y=ax^{n+1}+b x^{-n}$,then $x^2 \frac{d^2 y}{d x^2}=$

For $y=\sin ^{-1}\left\{\frac{5 x+12 \sqrt{1-x^{2}}}{13}\right\} ;|x| \leq 1$,if $a\left(1-x^{2}\right) y_{2}+b x y_{1}=0$ then $(a, b)=$

Let $f$ be a twice differentiable function such that $f^{\prime \prime}(x) = -f(x)$,$f^{\prime}(x) = g(x)$,and $h(x) = (f(x))^2 + (g(x))^2$. If $h(5) = 1$,then the value of $h(10)$ is

If $y=2 \sin x+3 \cos x$ and $y+A \frac{d^2 y}{d x^2}=B$,then the values of $A$ and $B$ are respectively:

If $f(x) = \sin x + \cos x$,then $f\left(\frac{\pi}{4}\right) f^{(iv)}\left(\frac{\pi}{4}\right)$ is equal to