List of top Mathematics Questions on Calculus asked in CBSE CLASS XII

If $y = \sin^{-1} x$, then $(1 - x^2) \frac{d^2y}{dx^2}$ is equal to :
If $f: \mathbb{R} \to \mathbb{R}$ is defined as $f(x) = 2x - \sin x$, then $f$ is:
Find the value of \( a \) for which } \( f(x) = \sqrt{3} \sin x - \cos x - 2ax + 6 \) \(\text{ is decreasing in } \mathbb{R}\).
A spherical ball has a variable diameter $\frac{5}{2}(3x + 1)$. The rate of change of its volume w.r.t. $x$, when $x = 1$, is:
If $f(x) = 2x + \cos x$, then $f(x)$ :
The function \( f(x) = x^2 - 4x + 6 \) is increasing in the interval:
The area of the shaded region (figure) represented by the curves \( y = x^2 \), \( 0 \leq x \leq 2 \), and the y-axis is given by:
The area of the shaded region
Find: \[ J = \int \frac{\sqrt{x^2 + 1} \left[ \log(x^2 + 1) - 2 \log x \right]}{x^2} \, dx \]
Show that the derivative of \( \tan^{-1} (\sec x + \tan x) \) with respect to \( x \) is equal to \( \frac{1}{2} \) for \( \left( -\frac{\pi}{2}<x<\frac{\pi}{2} \right) \).
Find the values of \( a \) for which \( f(x) = \sin x - ax + b \) is increasing on \( \mathbb{R} \).
The function \( f(x) = kx - \sin x \) is strictly increasing for:
Derivative of \( e^2x \) with respect to \( e^x \) is:
The function \( f(x) = kx - \sin x \) is strictly increasing for: