Permutations & Combinations JEE Main 2025

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JEE MAIN 2025

24-01-2025 SHIFT-1

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The number of 3-digit numbers, that are divisible by 2 and 3, but not divisible by 4 and 9, is

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Showing 18 questions

Q JEE MAIN 20262026

Given below are two statements
Statement I: $\mathrm{H}_2 \mathrm{O}$ molecules move from the chamber 1 to chamber 2 .
Statement II:...

JEE MainChemistryMedium

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QJEE MAIN 20222022

The tangents at the points $A(1,3)$ and $B(1,-1)$ on the parabola $y^2-2 x-2 y=1$ meet at the point $P$. Then...

JEE MainMathematicsEasy

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QJEE MAIN 20222022

If the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ meets the line $\frac{x}{7}+\frac{y}{2 \sqrt{6}}=1$ on the $x$-axis and the line $\frac{x}{7}-\frac{y}{2 \sqrt{6}}=1$ on the $y$-axis,...

JEE MainMathematicsEasy

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QJEE MAIN 20222022

Let a smooth curve $y=f(x)$ be such that the slope of the tangent at any point ( $x, y$ )...

JEE MainMathematicsEasy

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QJEE Main 20222022

Let the point $\mathrm{P}(\alpha, \beta)$ be at a unit distance from each of the two lines $\mathrm{L}_1: 3 \mathrm{x}-4 \mathrm{y}+12=0$,...

JEE MainMathematicsMedium

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QJEE Main 20222022

Let $[t]$ denote the greatest integer less than or equal to $t$. Then the value of the integral $$ \int_{-3}^{101}\left([\sin...

JEE MainMathematicsMedium

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QJEE Main 20222022

If $A$ and $B$ are two events such that $P(A)=\frac{1}{3}, P(B)=\frac{1}{5}$ and $P(A \cup B)=\frac{1}{2}$, then $...

JEE MainMathematicsEasy

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QJEE Main 20222022

$\lim _{n \rightarrow \infty} \frac{1}{2^n}\left(\frac{1}{\sqrt{1-\frac{1}{2^n}}}+\frac{1}{\sqrt{1-\frac{2}{2^n}}}+\frac{1}{\sqrt{1-\frac{3}{2^n}}}+\ldots \ldots+\frac{1}{\sqrt{1-\frac{2^n-1}{2^n}}}\right)$ is equal to

JEE MainMathematicsEasy

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QJEE Main 20222022

$$ \lim _{x \rightarrow \frac{\pi}{4}} \frac{8 \sqrt{2}-(\cos x+\sin x)^7}{\sqrt{2}-\sqrt{2} \sin 2 x} $$ is equal to

JEE MainMathematicsEasy

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QJEE Main 20222022

The sum $\sum_{n=1}^{21} \frac{3}{(4 n-1)(4 n+3)}$ is equal to

JEE MainMathematicsEasy

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QJEE Main 20222022

The remainder when $(11)^{1011}+(1011)^{11}$ is divided by 9 is

JEE MainMathematicsEasy

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QJEE Main 20222022

The number of bijective functions $f:\{1,3,5,7, \ldots, 99\} \rightarrow\{2,4,6,8, \ldots . ., 100\}$ such that $...

JEE MainMathematicsEasy

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QJEE Main 20222022

The number of real values of $\lambda$, such that the system of linear equations $$ \begin{aligned} & 2 x-3 y+5...

JEE MainMathematicsEasy

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QJEE-Main_2026

If the curve $y=f(x)$ passes through the point ( $1, \mathrm{e}$ ) and satisfies the differential equation $...

JEE MainMathematicsEasy

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QJEE Main 20232023

Let $\stackrel{\mathbb{J}}{\mathrm{a}}=4 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}$ and $\stackrel{\mathrm{b}}{\mathrm{b}}=3 \hat{\mathrm{i}}-4 \hat{\mathrm{j}}+5 \hat{\mathrm{k}}$ and $\stackrel{n}{\mathrm{c}}$ is a vector such that $...

JEE MainMathematicsEasy

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QJEE Main 20232023

Let $\alpha_1, \alpha_2, \ldots, \alpha_7$ be the roots of the equation $x^7+3 x^5-13 x^3-15 x=0$ and $...

JEE MainMathematicsEasy

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QJEE-Main_2026

$\lim _{x \rightarrow 2} \frac{\sin \left(x^3-5 x^2+a x+b\right)}{(\sqrt{x-1}-1) \log _e(x-1)}=m$, then $a+b+m$ is equal to :

JEE MainMathematicsMedium

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QJEE Main 20232023

Let $\alpha=8-14 i, \quad A=\left\{z \in C: \frac{\alpha z-\bar{\alpha} \bar{z}}{z^2-(\bar{z})^2-112 i}=1\right\}$ and $B=\{z \in C:|z+3 i|=4\}$ Then $...

JEE MainMathematicsEasy

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