JEE MAINS PRACTICE · Mathematics
Application of Derivatives
446 practice questions for JEE Mains Practice — 227 easy · 199 medium · 20 hard. Every question is graded instantly with a step-by-step solution when you miss it.
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MCQ
The triangle formed by the tangent to the curve $f(x)=x^2+b x-b$ at the point $(1,1)$ and the coordinate axes lies in the first quadrant. If its area is 2 , then the value of $b$ is
MCQ
$A B$ is a diameter of a circle and $C$ is any point on the circumference of the circle. then
MCQ
If $\theta$ is the semi-vertical angle of a cone of maximum volume and given slant height, then $\tan \theta$ is given by
MCQ
A man 1.6 m high walks at the rate of $30 \mathrm{~m} / \mathrm{min}$ away from a lamp which is 4 m above ground. How fast is the man's shadow lengthening?
MCQ
The curve, for which the area of the triangle formed by $X$-axis, the tangent line at any poin $P$ and line $O P$ is equal to $a^2$, is given by
MCQ
If $f(x)=x e^{x(1-x)}$, then $f(x)$ is
MCQ
Let $h(x)=\min \left(x, x^2\right)$, for every real numbers $x$. Then,
MCQ
If $f(x)=\left\{\begin{aligned} \sin \left(\frac{\pi x}{2}\right), & \text { if } x \lt 1 \\ 3-2 x, & \text { if } x \geq 1\end{aligned}\right.$, then $f(x)$ has
MCQ
A function $f(x)=\frac{x^2-3 x+2}{x^2+2 x-3}$ is
MCQ
The approximate value of $(1.0002)^{3000}$ is
MCQ
The function $x^x$ is increasing, when
MCQ
If $f^{\prime}(x)\gt0 \forall x \in R, f^{\prime}(3)=0$ and $g(x)=f\left(\tan ^2 x-2 \tan x+4\right), 0 \lt x \lt \frac{\pi}{2}$, then $g(x)$ is increasing in