List of top Mathematics Questions on Calculus asked in IIT JAM PH

Which one of the following functions has a discontinuity in the second derivative at \(x = 0\), where \(x\) is a real variable?
The coefficient of $x^3$ in the Taylor expansion of $\sin(\sin x)$ around $x = 0$ is .............. (Specify your answer up to two digits after the decimal point.)
Let $f(x)=3x^6 - 2x^2 - 8$. Which of the following statements is (are) true?
The integral of the vector \( \mathbf{A}(\rho, \varphi, z) = \frac{40}{\rho} \cos \varphi \hat{\rho} \) (standard notation for cylindrical coordinates is used) over the volume of a cylinder of height \( L \) and radius \( R_0 \), is:
The volume integral of the function \( f(r, \theta, \phi) = r^2 \cos\theta \) over the region \( 0 \leq r \leq 2, 0 \leq \theta \leq \frac{\pi}{3} \) and \( 0 \leq \phi \leq 2\pi \) is: