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JEE MAIN Previous Year Questions (PYQs)

JEE MAIN Logarithms And Indices PYQ

JEE MAIN PYQ
If $\log_e a,\ \log_e b,\ \log_e c$ are in an A.P. and $\log_e a-\log_e 2b,\ \log_e 2b-\log_e 3c,\ \log_e 3c-\log_e a$ are also in an A.P., then $a:b:c$ is equal to:





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

Solution

JEE MAIN PYQ
If for x $\in$ $\left( {0,{\pi \over 2}} \right)$, log10sinx + log10cosx = $-$1 and log10(sinx + cosx) = ${1 \over 2}$(log10 n $-$ 1), n > 0, then the value of n is equal to :





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

Solution

JEE MAIN PYQ
For three positive integers $p, q, r$, $x^{p q^{2}} = y^{q r} = z^{p^{2} r}$ and $r = pq + 1$ such that $3,\ 3\log_{y}x,\ 3\log_{z}y,\ 7\log_{x}z$ are in A.P. with common difference $\dfrac{1}{2}$. Then $r - p - q$ is equal to:





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

Solution

JEE MAIN PYQ
The number of integral solutions $x$ of $\log _{\left(x+\frac{7}{2}\right)}\left(\frac{x-7}{2 x-3}\right)^{2} \geq 0$ is :





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

Solution

JEE MAIN PYQ
The sum of all the solutions of the equation $(8)^{2x}-16\cdot(8)^x+48=0$ is:





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

Solution

JEE MAIN PYQ
If (27)999 is divided by 7, then the remainder is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2017 (8 April Morning Shift) PYQ

Solution

JEE MAIN PYQ
The inverse of $y = {5^{\log x}}$ is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (17 March Morning Shift) PYQ

Solution

JEE MAIN PYQ
Let $y=\log_e!\left(\dfrac{1-x^2}{1+x^2}\right)$, with $-1




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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (29 January Evening Shift) PYQ

Solution

JEE MAIN PYQ
If $\log_e a,;\log_e b,;\log_e c$ are in an A.P. and $\log_e a-\log_e(2b),;\log_e(2b)-\log_e(3c),;\log_e(3c)-\log_e a$ are also in an A.P., then $a:b:c$ is equal to:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (29 January Evening Shift) PYQ

Solution

JEE MAIN PYQ
The sum of all real values of $x$ satisfying the equation $2^{(x-1)(x^{2} + 5x - 50)} = 1$ is:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2017 (9 April Morning Shift) PYQ

Solution

JEE MAIN PYQ
The largest $n \in \mathbb{N}$ such that $3^n$ divides $50!$ is:





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

Solution

JEE MAIN PYQ
The sum of the roots of the equation:- $x + 1 - 2{\log _2}(3 + {2^x}) + 2{\log _4}(10 - {2^{ - x}}) = 0$, is :





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

Solution

JEE MAIN PYQ
If the fractional part of the number $\left\{\dfrac{2^{403}}{15}\right\}$ is $\dfrac{k}{15}$, then $k$ 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 product of all solutions of the equation $e^{5(\log_e x)^2+3}=x^8,\ x>0$, is:





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

Solution


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