JEE MAINS PRACTICE · Mathematics
Application of Derivatives
1,090 practice questions for JEE Mains Practice — 427 easy · 432 medium · 231 hard. Every question is graded instantly with a step-by-step solution when you miss it.
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MCQ
Let $h(x)=\min \left(x, x^2\right)$, for every real numbers $x$. Then,
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$A B$ is a diameter of a circle and $C$ is any point on the circumference of the circle. then
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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?
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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
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If $\theta$ is the semi-vertical angle of a cone of maximum volume and given slant height, then $\tan \theta$ is given by
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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
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If $f(x)=x e^{x(1-x)}$, then $f(x)$ is
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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
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If an edge of a cube measure 2 m with a possible error of 0.5 cm . Find the corresponding error in the calculated volume of the cube
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The values of $a$, if $f(x)=2 e^x-a e^{-x}+(2 a+1) x-3$ increases $x$, are in
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The value $P$ such that the length of subtangent and subnormal is equal for the curve $y=e^{P x}+P x$ at the point $(0,1)$ is
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The value of $c$ prescribed by Lagrange's mean value theorem, when $f(x)=\sqrt{x^2-4}, a=2$ and $b=3$, is