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JEE MAIN Previous Year Questions (PYQs)

JEE MAIN Application Of Derivatives PYQ

JEE MAIN PYQ
If $m$ is the minimum value of $k$ for which the function $f(x)=x\sqrt{kx-x^{2}}$ is increasing in the interval $[0,3]$ and $M$ is the maximum value of $f$ in $[0,3]$ when $k=m$, then the ordered pair $(m,M)$ is equal to:





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

Solution

JEE MAIN PYQ
A helicopter is flying along the curve given by $y - x^{3/2} = 7,\ (x \ge 0)$. A soldier positioned at the point $\left(\dfrac{1}{2},\,7\right)$ wants to shoot down the helicopter when it is nearest to him. Then this nearest distance is –





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

Solution

JEE MAIN PYQ
A spherical chocolate ball has a layer of ice-cream of uniform thickness around it. When the thickness of the ice-cream layer is 1 cm , the ice-cream melts at the rate of $81 \mathrm{~cm}^3 / \mathrm{min}$ and the thickness of the ice-cream layer decreases at the rate of $\frac{1}{4 \pi} \mathrm{~cm} / \mathrm{min}$. The surface area (in $\mathrm{cm}^2$ ) of the chocolate ball (without the ice-cream layer) is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (23 January Evening Shift) PYQ

Solution

JEE MAIN PYQ
The remainder when $\big((64)^{(64)}\big)^{(64)}$ is divided by $7$ is:





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

Solution

JEE MAIN PYQ
The real number $k$ for which the equation $2x^{3}+3x+k=0$ has two distinct real roots in $[0,1]$





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2013 (Offline) PYQ

Solution

JEE MAIN PYQ
The surface area of a balloon of spherical shape being inflated, increases at a constant rate. If initially, the radius of balloon is 3 units and after 5 seconds, it becomes 7 units, then its radius after 9 seconds is :





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

Solution

JEE MAIN PYQ
Consider a curve $y=y(x)$ in the first quadrant as shown in the figure. Let the area $A_{1}$ be twice the area $A_{2}$. Then the normal to the curve perpendicular to the line $2x-12y=15$ does NOT pass through the point:





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

Solution

JEE MAIN PYQ
For the function $f(x) = 4{\log _e}(x - 1) - 2{x^2} + 4x + 5,\,x > 1$, which one of the following is NOT correct?





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

Solution

JEE MAIN PYQ
Consider the region $R = {(x, y) : x \le y \le 9 - \dfrac{11}{3}x^2, , x \ge 0}$. The area of the largest rectangle of sides parallel to the coordinate axes and inscribed in $R$ is





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (24 January Morning Shift) PYQ

Solution

JEE MAIN PYQ
The maximum area (in sq. units) of a rectangle having its base on the $x$-axis and its other two vertices on the parabola $y=12-x^{2}$, such that the rectangle lies inside the parabola, is:





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

Solution

JEE MAIN PYQ
Water is being filled at the rate of 1 cm3 / sec in a right circular conical vessel (vertex downwards) of height 35 cm and diameter 14 cm. When the height of the water level is 10 cm, the rate (in cm2 / sec) at which the wet conical surface area of the vessel increases is





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (25 June Evening Shift) PYQ

Solution

JEE MAIN PYQ
$ \text{Let } f(x)=3^{(x^{2}-2)^{3}+4},; x\in\mathbb{R}. \text{ Then which of the following statements are true?} $ $P: x=0 \text{ is a point of local minima of } f$ $Q: x=\sqrt{2} \text{ is a point of inflection of } f$ $R: f' \text{ is increasing for } x>\sqrt{2}$





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

Solution

JEE MAIN PYQ
Consider a cuboid of sides 2x, 4x and 5x and a closed hemisphere of radius r. If the sum of their surface areas is a constant k, then the ratio x : r, for which the sum of their volumes is maximum, is :





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

Solution

JEE MAIN PYQ
If the function $f(x)=2x^{3}-9ax^{2}+12a^{2}x+1,;a>0$ has a local maximum at $x=\alpha$ and a local minimum at $x=\alpha^{2}$, then $\alpha$ and $\alpha^{2}$ are the roots of the equation:





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

Solution

JEE MAIN PYQ
Let $f(x)=ax^{3}+bx^{2}+cx+41$ be such that $f(1)=40,; f'(1)=2$ and $f''(1)=4$. Then $a^{2}+b^{2}+c^{2}$ is equal to:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (9 April Morning Shift) PYQ

Solution

JEE MAIN PYQ
The area (in sq. units) of the region $A={(x,y):\dfrac{y^{2}}{2}\le x\le y+4}$ is:





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

Solution

JEE MAIN PYQ
If the surface area of a cube is increasing at a rate of 3.6 cm2/sec, retaining its shape; then the rate of change of its volume (in cm3/sec),when the length of a side of the cube is 10 cm, is :





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

Solution

JEE MAIN PYQ

A wire of length 22 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into an equilateral triangle. Then, the length of the side of the equilateral triangle, so that the combined area of the square and the equilateral triangle is minimum, is :






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

Solution

JEE MAIN PYQ
The maximum volume (in $\mathrm{m}^3$) of the right circular cone having slant height $3\,\mathrm{m}$ is:





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

Solution

JEE MAIN PYQ
A water tank has the shape of an inverted right circular cone, whose semi-vertical angle is $\tan^{-1}\left(\dfrac{1}{2}\right)$. Water is poured into it at a constant rate of $5$ cubic meter per minute. The rate (in m/min) at which the level of water is rising at the instant when the depth of water in the tank is $10\text{ m}$, is:





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

Solution

JEE MAIN PYQ
If $\theta$ denotes the acute angle between the curves $y=10-x^{2}$ and $y=2+x^{2}$ at a point of their intersection, then $|\tan\theta|$ is equal to:





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

Solution

JEE MAIN PYQ
The minimum distance of a point on the curve $y = x^{2} - 4$ from the origin is :





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

Solution

JEE MAIN PYQ
A spherical iron ball of radius $10\ \text{cm}$ is coated with a layer of ice of uniform thickness that melts at a rate of $50\ \text{cm}^3/\text{min}$. When the thickness of the ice is $5\ \text{cm}$, the rate at which the thickness (in cm/min) of the ice decreases is:





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

Solution

JEE MAIN PYQ
Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be a twice differentiable function such that $f(x+y)=f(x) f(y)$ for all $x, y \in \mathbf{R}$. If $f^{\prime}(0)=4 \mathrm{a}$ and $f$ satisfies $f^{\prime \prime}(x)-3 \mathrm{a} f^{\prime}(x)-f(x)=0, \mathrm{a}>0$, then the area of the region $\mathrm{R}=\{(x, y) \mid 0 \leq y \leq f(a x), 0 \leq x \leq 2\}$ is :





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

Solution

JEE MAIN PYQ
A wire of length $20 \mathrm{~m}$ is to be cut into two pieces. A piece of length $l_{1}$ is bent to make a square of area $A_{1}$ and the other piece of length $l_{2}$ is made into a circle of area $A_{2}$. If $2 A_{1}+3 A_{2}$ is minimum then $\left(\pi l_{1}\right): l_{2}$ is equal to :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (31 January Morning Shift) PYQ

Solution

JEE MAIN PYQ
The shortest distance between the point $\left(\dfrac{3}{2},\,0\right)$ and the curve $y=\sqrt{x},\ (x>0)$, is:





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

Solution

JEE MAIN PYQ
A $2,\text{m}$ ladder leans against a vertical wall. If the top of the ladder begins to slide down the wall at the rate of $25,\text{cm/sec}$, then the rate (in $\text{cm/sec}$) at which the bottom of the ladder slides away from the wall on the horizontal ground when the top of the ladder is $1,\text{m}$ above the ground is:





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

Solution


JEE MAIN

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