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JEE MAIN Previous Year Questions (PYQs)

JEE MAIN Exponential Series PYQ

JEE MAIN PYQ
The sum of all the real roots of the equation $({e^{2x}} - 4)(6{e^{2x}} - 5{e^x} + 1) = 0$ is





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

Solution

JEE MAIN PYQ
The number of real roots of the equation ${e^{6x}} - {e^{4x}} - 2{e^{3x}} - 12{e^{2x}} + {e^x} + 1 = 0$ is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (25 February Morning Shift) PYQ

Solution

JEE MAIN PYQ
For $x\ge0$, the least value of $K$ for which $4^{,1+x}+4^{,1-x},\ \dfrac{K}{2},\ 16^{x}+16^{-x}$ are three consecutive terms of an A.P. is:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (5 April Evening Shift) PYQ

Solution

JEE MAIN PYQ
The number of real roots of the equation ${e^{4x}} + 2{e^{3x}} - {e^x} - 6 = 0$ is :





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

Solution

JEE MAIN PYQ
The number of solutions of the equation $e^{\sin x}-2e^{-\sin x}=2$ is:





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

Solution

JEE MAIN PYQ
The sum of all real values of $x$ satisfying the equation $(x^{2} - 5x + 5)^{x^{2} + 4x - 60} = 1$ is :





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

Solution

JEE MAIN PYQ
Let $S=\Big\{x\in\mathbb{R}:(\sqrt3+\sqrt2)^{x}+(\sqrt3-\sqrt2)^{x}=10\Big\}$. Then the number of elements in $S$ is:





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

Solution

JEE MAIN PYQ
$ \text{The equation } e^{4x}+8e^{3x}+13e^{2x}-8e^{x}+1=0,\ x\in\mathbb{R}\ \text{ has:} $





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

Solution

JEE MAIN PYQ
The sum $1+\dfrac{1+3}{2!}+\dfrac{1+3+5}{3!}+\dfrac{1+3+5+7}{4!}+\cdots$ up to $\infty$ terms is equal to





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

Solution

JEE MAIN PYQ
The number of real roots of the equation ${e^{6x}} - {e^{4x}} - 2{e^{3x}} - 12{e^{2x}} + {e^x} + 1 = 0$ is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (25 July Morning Shift) PYQ

Solution

JEE MAIN PYQ
The value of $\displaystyle \frac{1}{1\cdot 50!}+\frac{1}{3\cdot 48!}+\frac{1}{5\cdot 46!}+\cdots+\frac{1}{49\cdot 2!}+\frac{1}{51\cdot 1!}$ is:





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

Solution

JEE MAIN PYQ
The lowest integer which is greater than ${\left( {1 + {1 \over {{{10}^{100}}}}} \right)^{{{10}^{100}}}}$ is ______________.





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (25 July Evening Shift) PYQ

Solution


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