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JEE MAIN Previous Year Questions (PYQs)

JEE MAIN Inequation PYQ

JEE MAIN PYQ
Let $A = \{x \in \mathbb{R} : [x + 3] + [x + 4] \le 3\}$, and $B = \left\{ x \in \mathbb{R} : 3^x \left( \sum_{r=1}^{\infty} \frac{3}{10^r} \right)^{x - 3} < 3^{-3x} \right\}$, where $[\,]$ denotes the greatest integer function. Then,





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (6 April Morning Shift) PYQ

Solution

JEE MAIN PYQ
The number of real roots of the equation $x|x-2|+3|x-3|+1=0$ is:





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

Solution

JEE MAIN PYQ
Let x, y > 0. If x3y2 = 215, then the least value of 3x + 2y is





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

Solution

JEE MAIN PYQ
$A={(\alpha,\beta)\in\mathbb{R}\times\mathbb{R}:\ |\alpha-1|\le 4\ \text{and}\ |\beta-5|\le 6}$ $B={(\alpha,\beta)\in\mathbb{R}\times\mathbb{R}:\ 16(\alpha-2)^2+9(\beta-6)^2\le 144}.$ Then





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

Solution

JEE MAIN PYQ
$S = \{\, x \in [-6,3] \setminus \{-2,2\} \;:\; \dfrac{|x+3|-1}{|x|-2} \geq 0 \,\}$ $T = \{\, x \in \mathbb{Z} \;:\; x^{2} - 7|x| + 9 \leq 0 \,\}$ Then the number of elements in $S \cap T$ is :





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

Solution

JEE MAIN PYQ
Let $S = {x \in \mathbb{R} : x \ge 0 \text{ and } 2\lvert\sqrt{x}-3\rvert + \sqrt{x}(\sqrt{x}-6)+6=0}$. Then $S$ :





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

Solution

JEE MAIN PYQ
Let $f:R \to R$ and $g:R \to R$ be two functions defined by $f(x) = {\log _e}({x^2} + 1) - {e^{ - x}} + 1$ and $g(x) = {{1 - 2{e^{2x}}} \over {{e^x}}}$. Then, for which of the following range of $\alpha$, the inequality $f\left( {g\left( {{{{{(\alpha - 1)}^2}} \over 3}} \right)} \right) > f\left( {g\left( {\alpha -{5 \over 3}} \right)} \right)$ holds ?





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

Solution

JEE MAIN PYQ
Let [x] denote the greatest integer less than or equal to x. Then the domain of $ f(x) = \sec^{-1}(2[x] + 1) $ is:





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

Solution

JEE MAIN PYQ
The equation $x^{2}-4x+[x]+3 = x[x]$, where $[x]$ denotes the greatest integer function, has:





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

Solution

JEE MAIN PYQ
The sum of the squares of the roots of $|x - 2|^2 + |x - 2| - 2 = 0$ and the squares of the roots of $x^2 - 2|x - 3| - 5 = 0$, is:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (8 April Evening Shift) PYQ

Solution

JEE MAIN PYQ
Let $a,b,c,d$ be positive real numbers such that $a+b+c+d=11$. If the maximum value of $a^5 b^3 c^2 d$ is $3750\beta$, then the value of $\beta$ is:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (11 April Evening Shift) PYQ

Solution

JEE MAIN PYQ
The set of all $a\in\mathbb{R}$ for which the equation $x|x-1|+|x+2|+a=0$ has exactly one real root, is:





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

Solution

JEE MAIN PYQ
Let $S$ be the set of positive integral values of $a$ for which $\frac{a x^{2}+2(a+1)x+9a+4}{x^{2}-8x+32}<0,\ \forall x\in\mathbb{R}.$ Then, the number of elements in $S$ is:





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

Solution

JEE MAIN PYQ
If the domain of the function $f(x)=\log_e(4x^2+11x+6)+\sin^{-1}(4x+3)+\cos^{-1}\!\left(\dfrac{10x+6}{3}\right)$ is $(\alpha,\beta]$, then $36|\alpha+\beta|$ is equal to:





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

Solution

JEE MAIN PYQ
The number of real roots of the equation $x|x|-5|x+2|+6=0$ is:





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

Solution

JEE MAIN PYQ
Let $x, y, z$ be positive real numbers such that $x + y + z = 12$ and $x^{3} y^{4} z^{5} = (0.1)(600)^{3}$. Then $x^{3} + y^{3} + z^{3}$ is equal to:





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

Solution

JEE MAIN PYQ
All the pairs $(x,y)$ that satisfy the inequality $2\sqrt{\sin^{2}x-2\sin x+5}\cdot\dfrac{1}{4\sin^{2}y}\le 1$ also satisfy the equation





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

Solution

JEE MAIN PYQ
Let ${S_1} = \left\{ {x \in R - \{ 1,2\} :{{(x + 2)({x^2} + 3x + 5)} \over { - 2 + 3x - {x^2}}} \ge 0} \right\}$ and ${S_2} = \left\{ {x \in R:{3^{2x}} - {3^{x + 1}} - {3^{x + 2}} + 27 \le 0} \right\}$. Then, ${S_1} \cup {S_2}$ is equal to :





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

Solution


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