JEE MAIN Maxima and Minima Previous Year Question Paper and Solution with PDF

JEE MAIN Previous Year Questions (PYQs)

JEE MAIN Maxima And Minima PYQ

Qus : 1 JEE MAIN PYQ

The sum of the absolute maximum and minimum values of the function $f(x)=\lvert x^{2}-5x+6\rvert-3x+2$ in the interval $[-1,3]$ is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (1 February Evening Shift) PYQ

Solution

Qus : 2 JEE MAIN PYQ

Let $a>0$. If the function $f(x)=6x^3-45ax^2+108a^2x+1$ attains its local maximum and minimum values at the points $x_1$ and $x_2$ respectively such that $x_1x_2=54$, then $a+x_1+x_2$ is equal to

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (4 April Evening Shift) PYQ

Solution

Qus : 3 JEE MAIN PYQ

If $x=-1$ and $x=2$ are extreme points of $f(x)=\alpha\log|x|+\beta x^{2}+x$ then

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2014 (Offline) PYQ

Solution

Qus : 4 JEE MAIN PYQ

The set of all real values of $\lambda $ for which thefunction$f(x) = \left( {1 - {{\cos }^2}x} \right)\left( {\lambda + \sin x} \right),x \in \left( { - {\pi \over 2},{\pi \over 2}} \right)$ has exactly one maxima and exactly oneminima, is :

1
2
3
4
Go to Discussion

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

Solution

Qus : 5 JEE MAIN PYQ

The maximum value of the function $f(x)=3x^{3}-18x^{2}+27x-40$ on the set $S=\{x\in\mathbb{R}: x^{2}+30\le 11x\}$ is :

1
2
3
4
Go to Discussion

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

Solution

Qus : 6 JEE MAIN PYQ

If a right circular cone, having maximum volume, is inscribed in a sphere of radius $3\ \text{cm}$, then the curved surface area (in $\text{cm}^{2}$) of this cone is :

1
2
3
4
Go to Discussion

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

Solution

Qus : 7 JEE MAIN PYQ

Let $x=-1$ and $x=2$ be the critical points of the function $f(x)=x^{3}+ax^{2}+b\log_{e}|x|+1,;x\neq0$. Let $m$ and $M$ respectively be the absolute minimum and the absolute maximum values of $f$ in the interval $\left[-2,-\dfrac{1}{2}\right]$. Then $|M+m|$ is equal to (take $\log_{e}2=0.7$):

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (7 April Morning Shift) PYQ

Solution

Qus : 8 JEE MAIN PYQ

Let $f:\mathbb{R}\to\mathbb{R}$ be a polynomial of degree four having extreme values at $x=4$ and $x=5$. If $\displaystyle \lim_{x\to 0}\frac{f(x)}{x^{2}}=5$, then $f(2)$ is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (7 April Evening Shift) PYQ

Solution

Qus : 9 JEE MAIN PYQ

The sum of absolute maximum and absolute minimum values of the function $f(x) = |2{x^2} + 3x - 2| + \sin x\cos x$ in the interval [0, 1] is :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (24 June Morning Shift) PYQ

Solution

Qus : 10 JEE MAIN PYQ

Let $x, y$ be positive real numbers and $m, n$ positive integers. The maximum value of the expression $\dfrac{x^m y^n}{(1+x^{2m})(1+y^{2n})}$ is :

1
2
3
4
Go to Discussion

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

Solution

Qus : 11 JEE MAIN PYQ

If the minimum value of $f(x)=\dfrac{5x^{2}}{2}+\dfrac{\alpha}{x^{5}},; x>0,$ is $14$, then the value of $\alpha$ is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (28 July Morning Shift) PYQ

Solution

Qus : 12 JEE MAIN PYQ

Let $f(x)$ be a polynomial of degree $4$ having extreme values at $x=1$ and $x=2$. If $\lim_{x\to 0}\left(\dfrac{f(x)}{x^{2}}+1\right)=3$ then $f(-1)$ is equal to :

1
2
3
4
Go to Discussion

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

Solution

Qus : 13 JEE MAIN PYQ

The sum of the absolute maximum and absolute minimum values of the function $$f(x) = \tan^{-1}(\sin x - \cos x)$$ in the interval $[0,\pi]$ is :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (28 July Evening Shift) PYQ

Solution

Qus : 14 JEE MAIN PYQ

Let $f(x) = x^{2} + \dfrac{1}{x^{2}}$ and $g(x) = x - \dfrac{1}{x}$, $x \in \mathbb{R} - {-1,0,1}$. If $h(x) = \dfrac{f(x)}{g(x)}$, then the local minimum value of $h(x)$ is

1
2
3
4
Go to Discussion

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

Solution

Qus : 15 JEE MAIN PYQ

The sum of all local minimum values of the function

$\mathrm{f}(x)=\left\{\begin{array}{lr} 1-2 x, & x<-1 \\ \frac{1}{3}(7+2|x|), & -1 \leq x \leq 2 \\ \frac{11}{18}(x-4)(x-5), & x>2 \end{array}\right.$

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (28 January Morning Shift) PYQ

Solution

Qus : 16 JEE MAIN PYQ

The square tin of side $30\ \text{cm}$ is made into an open-top box by cutting a square of side $x$ from each corner and folding up the flaps. If the volume of the box is maximum, then its surface area (in $\text{cm}^2$) is:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (10 April Morning Shift) PYQ

Solution

Qus : 17 JEE MAIN PYQ

Let $M$ and $m$ be respectively the absolute maximum and the absolute minimum values of the function $f(x) = 2x^{3} - 9x^{2} + 12x + 5$ in the interval $[0, 3]$. Then $M - m$ is equal to :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (16 April Morning Shift) PYQ

Solution

Qus : 18 JEE MAIN PYQ

Let $M$ and $m$ be respectively the absolute maximum and the absolute minimum values of the function $f(x)=2x^{3}-9x^{2}+12x+5$ in the interval $[0,3]$. Then $M-m$ is equal to :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (16 April Morning Shift) PYQ

Solution

Qus : 19 JEE MAIN PYQ

If the function $f(x)=\left(\dfrac1x\right)^{2x},; x>0$ attains its maximum at $x=\dfrac1e$, then:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (6 April Evening Shift) PYQ

Solution

Qus : 20 JEE MAIN PYQ

The sum of the absolute minimum and the absolute maximum values of the function f(x) = |3x $-$ x² + 2| $-$ x in the interval [$-$1, 2] is :

1
2
3
4
Go to Discussion

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

Solution

Qus : 21 JEE MAIN PYQ

Let $f(x) = 2{\cos ^{ - 1}}x + 4{\cot ^{ - 1}}x - 3{x^2} - 2x + 10$, $x \in [ - 1,1]$. If [a, b] is the range of the function f, then 4a $-$ b is equal to :

1
2
3
4
Go to Discussion

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

Solution

Qus : 22 JEE MAIN PYQ

Let $f(x)=4\cos^{3}x+3\sqrt{3}\cos^{2}x-10$. The number of points of local maxima of $f$ in the interval $(0,2\pi)$ is:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (8 April Morning Shift) PYQ

Solution

Qus : 23 JEE MAIN PYQ

If $S_1$ and $S_2$ are respectively the sets of local minimum and local maximum points of the function $f(x)=9x^4+12x^3-36x^2+25,\ x\in\mathbb{R}$, then:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (8 April Morning Shift) PYQ

Solution

Qus : 24 JEE MAIN PYQ

The maximum area of a triangle whose one vertex is at $(0,0)$ and the other two vertices lie on the curve $y=-2x^{2}+54$ at points $(x,y)$ and $(-x,y)$, where $y>0$, is:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (30 January Morning Shift) PYQ

Solution

Qus : 25 JEE MAIN PYQ

The number of critical points of the function $f(x)=(x-2)^{2/3}(2x+1)$ is:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (8 April Morning Shift) PYQ

Solution

Qus : 26 JEE MAIN PYQ

Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in sq. m) of the flower-bed, is :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2017 (Offline) PYQ

Solution

Qus : 27 JEE MAIN PYQ

Let $x=2$ be a local minima of the function $f(x)=2x^{4}-18x^{2}+8x+12,\ x\in(-4,4)$. If $M$ is the local maximum value of the function $f$ in $(-4,4)$, then $M=$

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (25 January Morning Shift) PYQ

Solution

Qus : 28 JEE MAIN PYQ

If m and n respectively are the number of local maximum and local minimum points of the function $f(x) = \int\limits_0^{{x^2}} {{{{t^2} - 5t + 4} \over {2 + {e^t}}}dt} $, then the ordered pair (m, n) is equal to

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (27 June Evening Shift) PYQ

Solution

Qus : 29 JEE MAIN PYQ

If the local maximum value of the function $f(x)=\left(\dfrac{\sqrt{3}e}{2\sin x}\right)^{\sin^{2}x},; x\in\left(0,\dfrac{\pi}{2}\right),$ is $\dfrac{k}{e},$ then $\left(\dfrac{k}{e}\right)^{8}+\dfrac{k^{8}}{e^{5}}+k^{8}$ is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (12 April Morning Shift) PYQ

Solution

Qus : 30 JEE MAIN PYQ

Let $f(x)=(x+3)^2(x-2)^3,\ x\in[-4,4]$. If $M$ and $m$ are the maximum and minimum values of $f$ respectively in $[-4,4]$, then the value of $M-m$ is:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (30 January Evening Shift) PYQ

Solution

Qus : 31 JEE MAIN PYQ

The height of a right circular cylinder of maximum volume inscribed in a sphere of radius $3$ is:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (8 April Evening Shift) PYQ

Solution

Qus : 32 JEE MAIN PYQ

Let the function $f(x)=2x^{3}+(2p-7)x^{2}+3(2p-9)x-6$ have a maxima for some value of $x<0$ and a minima for some value of $x>0$. Then, the set of all values of $p$ is:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (25 January Evening Shift) PYQ

Solution

Qus : 33 JEE MAIN PYQ

If $f(x)$ is a non-zero polynomial of degree $4$, having local extreme points at $x=-1,0,1$, then the set $S={x\in\mathbb{R}: f(x)=f(0)}$ contains exactly:

1
2
3
4
Go to Discussion

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

Solution

Qus : 34 JEE MAIN PYQ

$\displaystyle \max_{0\le x\le \pi}\left\{x-2\sin x\cos x+\frac{1}{3}\sin(3x)\right\}=$

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (13 April Morning Shift) PYQ

Solution

Qus : 35 JEE MAIN PYQ

If the function $f(x) = 2x^3 - 9ax^2 + 12a^2x + 1$, where $a > 0$, attains its local maximum and local minimum values at $p$ and $q$ respectively, such that $p^2 = q$, then $f(3)$ is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (2 April Morning Shift) PYQ

Solution

Qus : 36 JEE MAIN PYQ

Suppose f(x) is a polynomial of degree four,having critical points at –1, 0, 1. If T = {x $ \in $ R | f(x) = f(0)}, then the sum of squares of all the elements of T is :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 3 September 2020 (Evening) PYQ

Solution

Qus : 37 JEE MAIN PYQ

A wire of length $2$ units is cut into two parts which are bent respectively to form a square of side $= x$ units and a circle of radius $= r$ units. If the sum of the areas of the square and the circle so formed is minimum, then:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (Offline) PYQ

Solution

Qus : 38 JEE MAIN PYQ

If $m$ and $M$ are the minimum and the maximum values of $4 + \dfrac{1}{2}\sin^{2} 2x - 2\cos^{4} x,; x \in \mathbb{R}$, then $M - m$ is equal to :

1
2
3
4
Go to Discussion

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

Solution

Qus : 39 JEE MAIN PYQ

If xy⁴ attains maximum value at the point (x, y) on the line passing through the points (50 + $\alpha$, 0) and (0, 50 + $\alpha$), $\alpha$ > 0, then (x, y) also lies on the line :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (30 June Morning Shift) PYQ

Solution

Qus : 40 JEE MAIN PYQ

If xy⁴ attains maximum value at the point (x, y) on the line passing through the points (50 + $\alpha$, 0) and (0, 50 + $\alpha$), $\alpha$ > 0, then (x, y) also lies on the line :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (30 June Morning Shift) PYQ

Solution

Qus : 41 JEE MAIN PYQ

Let m and M respectively be the minimum and the maximum values of $f(x) = {\sin ^{ - 1}}2x + \sin 2x + {\cos ^{ - 1}}2x + \cos 2x,\,x \in \left[ {0,{\pi \over 8}} \right]$. Then m + M is equal to :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (30 June Morning Shift) PYQ

Solution

Qus : 42 JEE MAIN PYQ

If the functions $f(x)=\dfrac{x^{3}}{3}+2bx+\dfrac{a x^{2}}{2}$ and $g(x)=\dfrac{x^{3}}{3}+a x+b x^{2},\ a\ne 2b$ have a common extreme point, then $a+2b+7$ is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (30 January Evening Shift) PYQ

Solution

Qus : 43 JEE MAIN PYQ

If the absolute maximum value of the function $f(x)=\left(x^{2}-2 x+7\right) \mathrm{e}^{\left(4 x^{3}-12 x^{2}-180 x+31\right)}$ in the interval $[-3,0]$ is $f(\alpha)$, then :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (25 July Morning Shift) PYQ

Solution

Qus : 44 JEE MAIN PYQ

The curve $y(x)=a x^{3}+b x^{2}+c x+5$ touches the $x$-axis at the point $\mathrm{P}(-2,0)$ and cuts the $y$-axis at the point $Q$, where $y^{\prime}$ is equal to 3 . Then the local maximum value of $y(x)$ is:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (25 July Morning Shift) PYQ

Solution

Qus : 45 JEE MAIN PYQ

Let $a,b\in\mathbb{R}$, $(a\neq 0)$. If the function $f$ defined as $f(x)= \begin{cases} \dfrac{2x^{2}}{a}, & 0\le x<1 \\ a, & 1\le x<\sqrt{2} \\ \dfrac{2b^{2}-4b}{x^{3}}, & \sqrt{2}\le x<\infty \end{cases}$ is continuous in the interval $[0,\infty)$, then an ordered pair $(a,b)$ is :

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (10 April Morning Shift) PYQ

Solution

Qus : 46 JEE MAIN PYQ

Let $f:\mathbb{R}\to\mathbb{R}$ be defined by $f(x)=\left|,|x+2|-2|x|,\right|$. If $m$ is the number of points of local minima and $n$ is the number of points of local maxima of $f$, then $m+n$ is

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (3 April Evening Shift) PYQ

Solution

Qus : 47 JEE MAIN PYQ

Let $f(x)=\displaystyle \int_{0}^{e^{x^{2}}}\frac{t^{2}-8t+15}{e^{t}}\,dt,\ x\in\mathbb{R}$. Then the numbers of local maximum and local minimum points of $f$, respectively, are:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (22 January Evening Shift) PYQ

Solution

Qus : 48 JEE MAIN PYQ

Let $f(x)$ be a polynomial of degree four having extreme values at $x=1$ and $x=2$. If $\displaystyle \lim_{x\to 0}\left[1+\frac{f(x)}{x^{2}}\right]=3$, then $f(2)$ is equal to :

1
2
3
4
Go to Discussion

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

Solution

Qus : 49 JEE MAIN PYQ

Let the sum of the maximum and the minimum values of the function $f(x)=\dfrac{2x^{2}-3x+8}{2x^{2}+3x+8}$ be $\dfrac{m}{n}$, where $\gcd(m,n)=1$. Then $m+n$ is equal to:

1
2
3
4
Go to Discussion

JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (4 April Morning Shift) PYQ

Feedback

Info.

Information

Aspire's Library

JEE MAIN Previous Year Questions (PYQs)

JEE MAIN Maxima And Minima PYQ

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

JEE MAIN

JEE MAIN

Info.

Confirm Delete

Edit