There are 4 men| Permutations and Combinations|JEE Main 2024

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JEE Main 2024

04-04-2024

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There are 4 men and 5 women in Group A, and 5 men and 4 women in Group B. If 4 persons are selected from each group, then the number of ways of selecting 4 men and 4 women is .....

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QJEE Main 20242024

The magnetic field in a plane electromagnetic wave is $...

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A hydrogen atom in ground state is given an energy of 10.2 eV. How many spectral lines will be emitted...

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The temperature of a gas is –78° C and the average translational kinetic energy of its molecules is K. The...

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The following figure represents two biconvex lenses $\mathrm{L}_1$ and $\mathrm{L}_2$ having focal length 10 cm and 15 cm respectively. The...

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QJEE Main 20242024

A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of 2:1. After disintegration they...

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Let y=y(x) be the solution of the differential equation $(x+y+2)^2 d x=d y, y(0)=-2$. Let the maximum and minimum values...

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Consider a line L passing through the points $\mathrm{P}(1,2,1)$ and $\mathrm{Q}(2,1,-1)$. If the mirror image of the point $\mathrm{A}(2,2,2)$ in...

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Consider a triangle ABC having the vertices $\mathrm{A}(1,2), \mathrm{B}(\alpha, \beta)$ and $\mathrm{C}(\gamma, \delta)$ and angles $\angle \mathrm{ABC}=\frac{\pi}{6}$ and $...

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QJEE Main 20242024

In a tournament, a team plays 10 matches with probabilities of winning and losing each match as $\frac{1}{3}$ and $\frac{2}{3}$...

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QJEE Main 20242024

There are 4 men and 5 women in Group A, and 5 men and 4 women in Group B. If...

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QJEE Main 20242024

Let 𝐴 be a 2 × 2 symmetric matrix such that $A\left[\begin{array}{l}1 \\ 1\end{array}\right]=\left[\begin{array}{l}3 \\ 7\end{array}\right]$ and the determinant of...

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Consider the function $\mathrm{f}: \mathbb{R} \rightarrow \mathbb{R}$ defined by $f(x)=\frac{2 x}{\sqrt{1+9 x^2}}$. If the composition of $...

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QJEE Main 20242024

Let f: ℝ → ℝ be a thrice differentiable function such that f(0) = 0, f(1) = 1, f(2) =...

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If $\int \operatorname{cosec}^5 x d x=\alpha \cot x \operatorname{cosec} x\left(\operatorname{cosec}^2 x+\frac{3}{2}\right)+\beta \log _e\left|\tan \frac{x}{2}\right|+C$ where $\alpha, \beta \in \mathbb{R}$ and...

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Let $S=\left\{\sin ^2 2 \theta:\left(\sin ^4 \theta+\cos ^4 \theta\right) x^2+(\sin 2 \theta) x+\left(\sin ^6 \theta+\cos ^6 \theta\right)=0\right.$ has real roots...

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Let P the point of intersection of the lines $\frac{x-2}{1}=\frac{y-4}{5}=\frac{z-2}{1}$ and $\frac{x-3}{2}=\frac{y-2}{3}=\frac{z-3}{2}$. Then, the shortest distance of $P$ from the...

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QJEE Main 20242024

Let $y=y(x)$ be the solution of the differential equation $\left(x^2+4\right)^2 d y+\left(2 x^3 y+8 x y-2\right) d x=0$. If $y(0)=$...

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QJEE Main 20242024

Given the inverse trigonometric function assumes principal values only. Let $x, y$ be any two real numbers in $[-1,1]$ such...

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