JEE MAIN Differentibility Previous Year Question Paper and Solution with PDF

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JEE MAIN Previous Year Questions (PYQs)

JEE MAIN Differentibility PYQ

Qus : 1 JEE MAIN PYQ

The value of $\log_{e}2 \, \dfrac{d}{dx}\!\big(\log_{\cos x} \csc x\big)$ at $x=\tfrac{\pi}{4}$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (26 July Evening Shift) PYQ

Solution

Qus : 2 JEE MAIN PYQ

Let f : R $ \to $ R be a function defined by f(x) = max {x, x²}. Let S denote the set of all points in R, where f is not differentiable.Then :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 6 September 2020 (Evening) PYQ

Solution

Qus : 3 JEE MAIN PYQ

Let $S={(\lambda,\mu)\in\mathbb{R}\times\mathbb{R}: f(t)=(\lvert\lambda\rvert e^{\lvert t\rvert}-\mu)\cdot\sin(2\lvert t\rvert),\ t\in\mathbb{R},\text{ is a differentiable function}}$. Then $S$ is a subset of :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Morning Shift) PYQ

Solution

Qus : 4 JEE MAIN PYQ

Let $K$ be the set of all real values of $x$ where the function $f(x)=\sin|x|-|x|+2(x-\pi)\cos|x|$ is not differentiable. Then the set $K$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (11 January Evening Shift) PYQ

Solution

Qus : 5 JEE MAIN PYQ

Let $S={t\in\mathbb{R}: f(x)=|x-\pi|,(e^{|x|}-1)\sin|x|\ \text{is not differentiable at }t}$. Then the set $S$ is equal to

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (Offline) PYQ

Solution

Qus : 6 JEE MAIN PYQ

Let $S$ be the set of all points in $(-\pi,\pi)$ at which the function $f(x)=\min\{\sin x,\cos x\}$ is not differentiable. Then $S$ is a subset of which of the following?

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (12 January Morning Shift) PYQ

Solution

Qus : 7 JEE MAIN PYQ

$ \text{The number of points where the function } f:\mathbb{R}\to\mathbb{R},\quad f(x)=|x-1|\cos|x-2|\sin|x-1|+(x-3),|x^{2}-5x+4|,\ \text{is NOT differentiable, is:} $

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (29 July Morning Shift) PYQ

Solution

Qus : 8 JEE MAIN PYQ

Let f, g : R $\to$ R be two real valued functions defined as $f(x) = \left\{ {\matrix{ { - |x + 3|} & , & {x < 0} \cr {{e^x}} & , & {x \ge 0} \cr } } \right.$ and $g(x) = \left\{ {\matrix{ {{x^2} + {k_1}x} & , & {x < 0} \cr {4x + {k_2}} & , & {x \ge 0} \cr } } \right.$, where k₁ and k₂ are real constants. If (gof) is differentiable at x = 0, then (gof) ($-$ 4) + (gof) (4) is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (26 June Morning Shift) PYQ

Solution

Qus : 9 JEE MAIN PYQ

The function $f(x)=2x+3\,x^{1/3},\ x\in\mathbb{R},$ has

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (29 January Evening Shift) PYQ

Solution

Qus : 10 JEE MAIN PYQ

Let the functions f : R $ \to $ R and g : R $ \to $ R be defined as :$f(x) = \left\{ {\matrix{ {x + 2,} & {x < 0} \cr {{x^2},} & {x \ge 0} \cr } } \right.$ and $g(x) = \left\{ {\matrix{ {{x^3},} & {x < 1} \cr {3x - 2,} & {x \ge 1} \cr } } \right.$ Then, the number of points in R where (fog) (x) is NOT differentiable is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (16 March Morning Shift) PYQ

Solution

Qus : 11 JEE MAIN PYQ

Let f(x) = min {1, 1 + x sin x}, 0 $\le$ x $\le$ 2$\pi $. If m is the number of points, where f is not differentiable and n is the number of points, where f is not continuous, then the ordered pair (m, n) is equal to

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (26 June Evening Shift) PYQ

Solution

Qus : 12 JEE MAIN PYQ

Let $$ f(x)= \begin{cases} x^{2}\sin\!\left(\dfrac{1}{x}\right), & x\ne 0,\\[6pt] 0, & x=0 \end{cases} $$ Then at $x=0$:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (24 January Morning Shift) PYQ

Solution

Qus : 13 JEE MAIN PYQ

Let $f(x)=15-|x-10|,\ x\in\mathbb{R}$. Then the set of all values of $x$ at which the function $g(x)=f(f(x))$ is not differentiable is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (9 April Morning Shift) PYQ

Solution

Qus : 14 JEE MAIN PYQ

If $f(x) = \left\{ {\matrix{ {{1 \over {|x|}}} & {;\,|x|\, \ge 1} \cr {a{x^2} + b} & {;\,|x|\, < 1} \cr } } \right.$ is differentiable at every point of the domain, then the values of a and b are respectively :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (18 March Morning Shift) PYQ

Solution

Qus : 15 JEE MAIN PYQ

Let $g(x)$ be a linear function and $ f(x)= \begin{cases} g(x), & x\le 0,\\[2mm] \left(\dfrac{1+x}{2+x}\right)^{\tfrac{1}{x}}, & x>0 \end{cases} $ is continuous at $x=0$. If $f'(1)=f(-1)$, then the value $g(3)$ is

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (31 January Morning Shift) PYQ

Solution

Qus : 16 JEE MAIN PYQ

The function $f(x) = \left| {{x^2} - 2x - 3} \right|\,.\,{e^{\left| {9{x^2} - 12x + 4} \right|}}$ is not differentiable at exactly :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (31 August Morning Shift) PYQ

Solution

Qus : 17 JEE MAIN PYQ

Let $f:R \to R$ be a function defined by :

$f(x) = \left\{ {\matrix{ {\max \,\{ {t^3} - 3t\} \,t \le x} & ; & {x \le 2} \cr {{x^2} + 2x - 6} & ; & {2 < x < 3} \cr {[x - 3] + 9} & ; & {3 \le x \le 5} \cr {2x + 1} & ; & {x > 5} \cr } } \right.$

where [t] is the greatest integer less than or equal to t. Let m be the number of points where f is not differentiable and $I = \int\limits_{ - 2}^2 {f(x)\,dx} $. Then the ordered pair (m, I) is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (29 June Morning Shift) PYQ

Solution

Qus : 18 JEE MAIN PYQ

Let $[x]$ denote the greatest integer function and $f(x)=\max\{\,1+x+[x],\ 2+x,\ x+2[x]\,\},\ 0\le x\le 2.$ Let $m$ be the number of points in $[0,2]$, where $f$ is not continuous and $n$ be the number of points in $(0,2)$, where $f$ is not differentiable. Then $(m+n)^2+2$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (15 April Morning Shift) PYQ

Solution

Qus : 19 JEE MAIN PYQ

Consider the function $f:(0,\infty)\to\mathbb{R}$ defined by $f(x)=e^{-|\log_e x|}$. If $m$ and $n$ are respectively the number of points at which $f$ is not continuous and $f$ is not differentiable, then $m+n$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (31 January Evening Shift) PYQ

Solution

Qus : 20 JEE MAIN PYQ

Let $f(x) = \left| {x - 2} \right|$ and g(x) = f(f(x)), $x \in \left[ {0,4} \right]$. Then
$\int\limits_0^3 {\left( {g(x) - f(x)} \right)} dx$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 4 September 2020 (Morning) PYQ

Solution

Qus : 21 JEE MAIN PYQ

Let $f:\mathbb{R}\to\mathbb{R}$ be differentiable at $c\in\mathbb{R}$ and $f(c)=0$. If $g(x)=|f(x)|$, then at $x=c$, $g$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (10 April Morning Shift) PYQ

Solution

Qus : 22 JEE MAIN PYQ

If the function

f(x) = $\left\{ {\matrix{ { - x} & {x < 1} \cr {a + {{\cos }^{ - 1}}\left( {x + b} \right),} & {1 \le x \le 2} \cr } } \right.$

is differentiable at x = 1, then ${a \over b}$ is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (9 April Morning Shift) PYQ

Solution

Qus : 23 JEE MAIN PYQ

Let $f$ be a differentiable function from $\mathbb{R}$ to $\mathbb{R}$ such that $|f(x)-f(y)|\le 2|x-y|^{3/2}$ for all $x,y\in\mathbb{R}$. If $f(0)=1$, then $\displaystyle \int_{0}^{1} f^{2}(x)\,dx$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (9 January Evening Shift) PYQ

Solution

Qus : 24 JEE MAIN PYQ

The number of real roots of the equation $5+\lvert 2^{x}-1\rvert=2^{x},(2^{x}-2)$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (10 April Evening Shift) PYQ

Solution

Qus : 25 JEE MAIN PYQ

Let $f(x)=\left|2x^{2}+5|x|-3\right|,\; x\in\mathbb{R}$. If $m$ and $n$ denote the number of points where $f$ is not continuous and not differentiable respectively, then $m+n$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (1 February Evening Shift) PYQ

Solution

Qus : 26 JEE MAIN PYQ

If the function.

$g\left( x \right) = \left\{ {\matrix{ {k\sqrt {x + 1} ,} & {0 \le x \le 3} \cr {m\,x + 2,} & {3 < x \le 5} \cr } } \right.$

is differentiable, then the value of $k+m$ is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2015 (Offline) PYQ

Solution

Qus : 27 JEE MAIN PYQ

Let $f\left( x \right) = \left\{ {\matrix{ {\max \left\{ {\left| x \right|,{x^2}} \right\}} & {\left| x \right| \le 2} \cr {8 - 2\left| x \right|} & {2 < \left| x \right| \le 4} \cr } } \right.$

Let S be the set of points in the interval (– 4, 4) at which f is not differentiable. Then S

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (10 January Morning Shift) PYQ

Solution

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