If $f(x) = 10 \cos x + (13 + 2x) \sin x$, then $f''(x) + f(x)$ is equal to

If $\log _e y=3 \sin ^{-1} x$,then $(1-x^2) y^{\prime \prime}-x y^{\prime}$ at $x=\frac{1}{2}$ is equal to :

If $y = \sqrt{\sin x + \sqrt{\sin x + \sqrt{\sin x + \dots \infty}}}$,then the value of $\frac{d^2 y}{d x^2}$ at the point $(\pi, 1)$ is

Let $f(x) = x^{3} + x^{2}f^{\prime}(1) + 2x f^{\prime\prime}(2) + f^{\prime\prime\prime}(3)$, where $x \in R$. Then the value of $f^{\prime}(5)$ is:

If the function $y = \sin^{-1} x$,then $\left(1-x^2\right) \frac{d^2 y}{d x^2}$ is equal to

Let $f(x)$ be a twice differentiable function such that $f''(x) = -f(x)$, $f'(x) = g(x)$, and $h(x) = \{f(x)\}^2 + \{g(x)\}^2$. If $h(5) = 11$, then $h(10)$ is equal to ...