Q JEE MAIN 2026

For the function $f(x)=\mathrm{e}^{\sin |x|}-|x|, x \in \mathbf{R}$, consider the following statements: Statement I : $f$ is differentiable for all...

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Q JEE Main 2024

If $\log _e y=3 \sin ^{-1} x$, then $(1-x)^2 y^{\prime \prime}-x y^{\prime}$ at $x=\frac{1}{2}$ is equal to :

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Q Jee Main 2024

The function $f(x)=\frac{x}{x^2-6 x-16}, x \in \mathbb{R}-\{-2,8\}$

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Q Jee Main 2024

If the function $\mathrm{f}:(-\infty,-1] \rightarrow(\mathrm{a}, \mathrm{b}]$ defined by $f(x)=e^{x 3-3 x+1}$ is one-one and onto, then the distance of the...

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Q Jee Main 2024

Let $\mathrm{f}: \rightarrow \mathrm{R} \rightarrow(0, \infty)$ be strictly increasing function such that $\lim _{\substack{x \rightarrow \infty \\ f(x)}} \frac{f(7 x)}{2}=1$....

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Q JEE-Main 2024

Let $g(x)=3 f\left(\frac{x}{3}\right)+f(3-x)$ and $f^{\prime \prime}(x)>0$ for all $\mathrm{x} \in(0,3)$. If g is decreasing in $(0, \alpha)$ and increasing in...

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Q JEE Main 2026

Consider the following three statements for the function $f:(0, \infty) \rightarrow \mathbb{R}$ defined by $f(x)=\left|\log _e x\right|-|x-1|$ : (I) $f$...

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Q JEE Advace

Let the function $f: \mathbb{R} \rightarrow \mathbb{R}$ be defined by $$ f(x)=\frac{\sin x}{e^{\pi x}} \frac{\left(x^{2023}+2024 x+2025\right)}{\left(x^2-x+3\right)}+\frac{2}{e^{\pi x}} \frac{\left(x^{2023}+2024 x+2025\right)}{\left(x^2-x+3\right)} $$...

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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...

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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 $f(x) \mathrm{m}^2-2 f^{\prime}(x) \mathrm{m}+f^{\prime \prime}(x)=0$...

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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 $...

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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 $f$...

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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...

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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

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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 $...

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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?

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Q JEE MAIN_2021_

The Boolean expression $(p \wedge q) \Rightarrow((r \wedge q) \wedge p)$ is equivalent to $i$

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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...

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Q JEE MAIN 2019

Let $f(x)=\frac{x}{\sqrt{a^2+x^2}}-\frac{(d-x)}{\sqrt{b^2+(d-x)^2}}, x \in R$ where $a, b$ and $d$ are non-zero real constants. Then :

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Q JEE MAIN 2021

If ' $R$ ' is the least value of ' $a$ ' such that the function $f(x)=x^2+a x+1$ is increasing...

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Q JEE Main 2021

Let $f$ be any continuous function on $[0,2]$ and twice differentiable on $(0,2)$. If $f(0)=0, f(1)=1$ and $f(2)=2$, then

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Q JEE MAIN 2021

The number of distinct real roots of the equation $3 x^4+4 x^3-12 x^2+4=0$ is $\_\_\_\_$ .

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Q JEE MAIN 2019

Let $f:[0,2] \rightarrow R$ be a twice differentiable function such that $f^{\prime \prime}(x)>0$, for all $x \in(0,2)$. If $\phi(x)=f(x)+ \mathrm{f}(2-x)$,...

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Q JEE MAIN_2021_

The number of real roots of the equation $\mathrm{e}^{6 \mathrm{x}}-\mathrm{e}^{4 \mathrm{x}}-2 \mathrm{e}^{3 \mathrm{x}}-12 \mathrm{e}^{2 \mathrm{x}}+\mathrm{e}^{\mathrm{x}}+1=0$ is $i$

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Q JEE MAIN_2021_

Let $f(x)=3 \sin ^4 x+10 \sin ^3 x+6 \sin ^2 x-3, x \in\left[-\frac{\pi}{6}, \frac{\pi}{2}\right]$. Then, $f$ is -

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Q JEE MAIN 2021

Let a be an integer such that all the real roots of the polynomial $2 x^5+5 x^4+10 x^3+10 x^2+10 x+10$...

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Q JEE-MAIN 2021

Let $f:[-1,1] \rightarrow R$ be defined as $f(x)=a x^2+b x+c$ for all $x \in[-1,1]$ where $a, b, c \in R$...

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Q _JEE MAIN_2021

Let $f: R \rightarrow R$ be defined as $...

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Q JEE-MAIN 2021

Consider the function $f: R \rightarrow R$ defined by $$ f(x)=\left\{\begin{array}{cl} \left(2 \sin \left(\frac{1}{x}\right)\right)|x|, & x \neq 0 \\ 0...

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Q JEE MAIN 2021

Let $f$ be a real valued funditon, defined on $R-\{-1$, $1\}$ and given by $$ f(x)=3 \log _e\left|\frac{x-1}{x+1}\right|-\frac{2}{x-1} $$ Then...

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Q JEE MAIN 2021

The function $f(x)=\frac{4 x^3-3 x^2}{6}-2 \sin x+(2 x-1) \cos x:$

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Q JEE MAIN 2021

Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be defined as, $$ f(x)= \begin{cases}-55 x, & \text { if } x4\end{cases} $$ Let...

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Q JEE MAIN 2021

If Rolle's theorem holds for the function $f(x)=x^3-a x^2+b x-4, x \in[1,2]$ with $f^{\prime}\left(\frac{4}{3}\right)=0$, then ordered pair $(a, b)$ is...

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Q JEE MAIN_2022

Let the function $f(x)=2 x^2-$ logex, $x>0$, be decreasing in (0, a) and increasing in (a, 4). A tangent to...

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Q JEE MAIN_2022

The number of distinct real roots of the equation $x^5\left(x^3-x^2-x+1\right)+x\left(3 x^3-4 x^2-2 x+4\right)-1=0$ is

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Q JEE MAIN 2022

Which of the reaction is suitable for concentrating ore by leaching process ?

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Q JEE MAIN 2025

Let the function $f(x)=\frac{x}{3}+\frac{3}{x}+3, x \neq 0$ be strictly increasing in $\left(-\infty, \alpha_1\right) \cup\left(\alpha_2, \infty\right)$ and strictly decreasing in $...

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