Skip to main content
Yukti Vault

Calculus

Differentiation and its Application: JEE Main & Advanced PYQs

559 previous year questions on Differentiation and its Application from JEE Main and JEE Advanced papers, each with its exam and year, an answer and a solution.

Practice this chapter

Questions 551-559 of 559

  1. The shortest distance between the line $y-x=1$ and the curve $x=y^{2}$ is
  2. If $f$ and $g$ are differentiable functions in $[0,1]$ satisfying $f(0)=2=g(1)$, $g(0)=0$ and $f(1)=6$, then for some $c\in\,]0,1[$
  3. The normal to the curve, $x^{2}+2xy-3y^{2}=0$, at $(1,1)$
  4. The intercepts on $x$-axis made by tangents to the curve, $y=\int_0^x|t|\,dt$, $x\in\mathbb{R}$, which are parallel to the line $y=2x$, are equal to :
  5. A wire of length $2$ units is cut into two parts which are bent respectively to form a square of side $=x$ units and a circle of radius $=r$ units. If the sum of the …
  6. Let $f(x)$ be a polynomial of degree $5$ such that $x=\pm1$ are its critical points. If $\lim_{x\to0}\left(2+\frac{f(x)}{x^3}\right)=4$, then which one of the following …
  7. If $2y=\left(\cot^{-1}\left(\frac{\sqrt3\cos x+\sin x}{\cos x-\sqrt3\sin x}\right)\right)^2$, $x\in\left(0,\frac\pi2\right)$, then $\frac{dy}{dx}$ is equal to
  8. The sum of all the local minimum values of the twice differentiable function $f:\mathbf{R}\to\mathbf{R}$ defined by $f(x)=x^3-3x^2-\dfrac{3f''(2)}{2}x+f''(1)$ is :
  9. Let a function $g:[0,4]\to\mathbf{R}$ be defined as $g(x)=\begin{cases}\max\limits_{0\le t\le x}\{t^3-6t^2+9t-3\}, & 0\le x\le 3\\ 4-x, & 3<x\le 4\end{cases}$, then the …

Other chapters