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Monotonicity

Get chapter-wise JEE Main & Advanced questions with solutions

Q JEE MAIN 2026
Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be a twice differentiable function such that $f^{\prime \prime}(x)>0$ for all $x \in \mathbf{R}$ and $f^{\prime}(\mathrm{a}-1)=0$, where a is a...
JEE Main Mathematics Easy
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Q JEE MAIN 2026
Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be a twice differentiable function such that the quadratic equation $f(x) \mathrm{m}^2-2 f^{\prime}(x) \mathrm{m}+f^{\prime \prime}(x)=0$ in m , has two...
JEE Main Mathematics Medium
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Q JEE MAIN_2019
Let $f(x)=e^x-x$ and $g(x)=x^2-x, \forall x \in R$. Then the set of all $x \in R$, where the function $h(x)=(\mathrm{fog}) (x)$ is increasing, is i
JEE Main Mathematics Medium
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Q JEE MAIN 2020
Let $f:(-1, \infty) \longrightarrow R$ be defined by $f(0)=1$ and $f(x)=\frac{1}{x} \log _e(1+x), x \neq 0$. Then the function $f$ :
JEE Main Mathematics Easy
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Q JEE MAIN 2020
A spherical iron ball of 10 cm radius is coated with a layer of ice of uniform thickness that melts at a rate of $...
JEE Main Mathematics Easy
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Q JEE MAIN 2020
The number of real roots of the equation,
$e^{4 x}+e^{3 x}-4 e^{2 x}+e^x+1=0$ is
JEE Main Mathematics Easy
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Q JEE MAIN 2020
Let $f$ be any function continuous on $[a, b]$ and twice differentiable on $(a, b)$. If for all $x \in(a, b), f^{\prime}(x)>0$ and $f^{\prime \prime}(x)<0$,...
JEE Main Mathematics Medium
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Q JEE MAIN 2020
Let $f(x)=x \cos ^{-1}(-\sin |x|), x \in\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$, then which of the following is true?
JEE Main Mathematics Medium
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Q JEE MAIN_2021_
The Boolean expression $(p \wedge q) \Rightarrow((r \wedge q) \wedge p)$ is equivalent to $i$
JEE Main Mathematics Medium
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Q JEE MAIN 2020
Let $f:(1,3) \rightarrow R$ be a function defined by $f(x)=\frac{x[x]}{1+x^2}$, where $[x]$ denotes the greatest integer $\leq x$. Then the range of $f$ is
JEE Main Mathematics Medium
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