List of top Questions asked in JEE Main- 2024

Let \( L \) denote the line in the \( xy \)-plane with \( x \) and \( y \) intercepts as 2 and 1 respectively. If the image of the point \( (-1,-3) \) in this line is \( \left(\frac{\alpha}{5}, \frac{\beta}{5}\right) \), then \( \alpha+\beta \) is equal to ________

There are two bags. The first bag contains 3 white and 4 red balls and the second bag contains 4 white and 3 red balls. Two balls are drawn at random from the first bag and are put into the second bag without noticing their colours. Then two balls are drawn from the second bag. If the probability that one ball is white and the other is red is \( \frac{x}{y} \), where \( \frac{x}{y} \) is in the simplest form, then value of \( (2x-y) \) is ________

Which of the following is a shell structure?

Let \( y=y(x) \) be the solution of differential equation \( \sin x \frac{dy}{dx}+y\cos x=4x \). If \( y\left(\frac{\pi}{2}\right)=0 \) and \( y\left(-\frac{\pi}{6}\right)=\frac{\alpha}{\beta}\pi^{2} \), where \( \alpha \) and \( \beta \) are co-prime numbers, then value of \( (\alpha+\beta) \) is ________

The value of \( \int_{1}^{5} f(x)\, dx \), where \( f(x)=|x-1|+|x-2|+|x-3| \) is ________

If \( \alpha,\beta,\gamma \) are the angles of a triangle, then the value of the determinant \( \begin{vmatrix}\cot\alpha&\cot\beta&\cot\gamma\\1&1&1\\\sin^{2}\alpha&\sin^{2}\beta&\sin^{2}\gamma\end{vmatrix} \) is equal to ________

If \( r^{\text{th}} \) term in the expansion of \( \left(\sqrt[3]{\frac{a}{\sqrt{b}}}+\sqrt{\frac{b}{\sqrt[3]{a}}}\right)^{21} \) contains equal powers of \( a \) and \( b \), then value of \( r \) is ________

If \( y=\tan^{-1}\left(\frac{3x}{1+54x^{2}}\right)+\tan^{-1}\left(\frac{3x}{1+18x^{2}}\right) \), then \( \frac{dy}{dx} \) at \( x=0 \) is ________

Let \( \alpha \) and \( \beta \) be the roots of the equation \( x^{2}-6x-2=0 \), with \( \alpha>\beta \). If \( a_{n}=\alpha^{n}-\beta^{n} \) for \( n\geq1 \), then the value of \( \frac{a_{10}-2a_{8}}{3a_{9}} \) is equal to ________

The projection vector of \(\vec{a}=\hat{i}-3 \hat{j}-3 \hat{k}\) on \(\vec{b}=3 \hat{i}-4 \hat{j}\) is

Given \( |\vec{a}|=|\vec{b}|=1 \) and \( |\vec{a}+\vec{b}|=\sqrt{3} \). If \( \vec{c} \) is a vector such that \( \vec{c}-\vec{a}-2\vec{b}=3(\vec{a}\times\vec{b}) \), then \( \vec{c}\cdot\vec{b} \) is equal to

\( \cot^{-1}7+\cot^{-1}8+\cot^{-1}5= \)

The value of \( \sec 15^{\circ}-\sqrt{3}\,\operatorname{cosec} 15^{\circ} \) is

The shortest distance between the lines \(\vec{r}=(\hat{i}+2 \hat{j}+3 \hat{k})+\lambda(\hat{i}-3 \hat{j}+2 \hat{k})\) and \(\vec{r}=(4 \hat{i}+5 \hat{j}+6 \hat{k})+\mu(2 \hat{i}+3 \hat{j}+\hat{k})\) is :

If \( A \) and \( B \) are two events such that \( P(A\cup B)=\frac{5}{8} \) and \( P(A'\cup B')=\frac{3}{4} \), then \( P(A')+P(B')= \)

The vertices of a triangle \(OAB\) are \((0,0)\), \((a, 0)\) and \((0, b)\) respectively. The distance between its orthocentre and circumcentre is

\(\int \frac{\mathrm{d} x}{\sin ^{2} x \cos ^{2} x}\) is equal to

The point diametrically opposite to the point \((-1,1)\) on the circle \(x^{2}+y^{2}-x-4 y+1=0\) is

If \(\lim_{x \to 1} \frac{x^{5}-1}{x-1}=\lim_{x \to k} \frac{x^{3}-k^{3}}{x^{2}-k^{2}}\), then \(k\) is equal to

The solution of differential equation \(\left(x+2 y^{3}\right) \frac{d y}{d x}=y\) is

Let \(f:[0, \pi] \rightarrow \mathbb{R}\) be a function defined by \(f(x)=\begin{cases}x+\sqrt{2}\, a \sin x, & 0 \leq x<\frac{\pi}{4} \\ 2 x \cot x+b, & \frac{\pi}{4} \leq x \leq \frac{\pi}{2} \\ a \cos 2 x-b \sin x, & \frac{\pi}{2}<x \leq \pi\end{cases}\)
If \(f\) is continuous for \(0 \leq x \leq \pi\), then \(a^{2}+140 b^{2}\) is equal to

Combine Musical Instruments like Guitar, Microphone (mic), Drums, Tabla, Keyboard, etc. into a 3D Abstract Sculpture, using different colors to represent various Texture and Instruments. You can scale each object to any size of your choice. Apply the effect of light and shadow on your Sculpture.
OR
Considering yourself as one of the spectators, draw a beautiful sketch of a Football stadium where a match is going on.

Draw a proportionate sketch of the image given below in detail. Sketch this using Black and White medium only.

Identify the building material primarily used for cladding in Lotus Temple :

Match List I with List II

Choose the correct answer from the options given below: