List of top Statistics Questions on Calculus asked in CUET (PG)

If $f(1)=1$ and $f^{\prime}(1)=-1$, then the value of $\frac{d}{dx}[\frac{f(x^{3})}{x~f(x^{2})}]$ at $x=1$ is equal to

The function $f(x)=|x^{2}+x-6|$ is not differentiable at $x=a$ and $x=b$ then $(b-a)^{2}$ equals

The value of \(\lim_{x \to 1} \frac{x^3-1}{x-1}\) is

If \(f'(x) = 3x^2 - \frac{2}{x^2}\), \(f(1) = 0\) then, \(f(x)\) is

For Lagrange's mean value theorem, the value of 'c' for the function \(f(x) = px^2+qx+r, p\neq 0\) in the interval \([1, b]\) and \(c \in ]1, b[\), is:

The value of \( \lim_{h \to 0} \left(\frac{1}{h} \int_{4}^{4+h} e^{t^2} dt \right) \) is

The volume of the solid for the region enclosed by the curves \(X = \sqrt{Y}\), \(X = \frac{Y}{4}\) revolve about x-axis, is

The area of the surface generated by revolving the curve \(X = \sqrt{9-Y^2}, -2 \leq Y \leq 2\) about the y-axis, is