List of top Questions asked in JEE Main

Let the relations \( R_1 \) and \( R_2 \) on the set
\( X = \{ 1, 2, 3, \dots, 20 \} \) be given by
\( R_1 = \{ (x, y) : 2x - 3y = 2 \} \) and
\( R_2 = \{ (x, y) : -5x + 4y = 0 \} \).
If \( M \) and \( N \) be the minimum number of elements required to be added in \( R_1 \) and \( R_2 \), respectively, in order to make the relations symmetric, then \( M + N \) equals:

Let \( \alpha, \beta \) be the distinct roots of the equation $$ x^2 - (t^2 - 5t + 6)x + 1 = 0, \, t \in \mathbb{R} \, \text{and} \, a_n = \alpha^n + \beta^n. $$ Then the minimum value of \( \frac{a_{2023} + a_{2025}}{a_{2024}} \) is: 

A company has two plants A and B to manufacture motorcycles. 60% motorcycles are manufactured at plant A and the remaining are manufactured at plant B. 80% of the motorcycles manufactured at plant A are rated of the standard quality, while 90% of the motorcycles manufactured at plant B are rated of the standard quality. A motorcycle picked up randomly from the total production is found to be of the standard quality. If p is the probability that it was manufactured at plant B, then 126p is

The shortest distance between the lines
\[\frac{x - 3}{2} = \frac{y + 15}{-7} = \frac{z - 9}{5}\]and
\[\frac{x + 1}{2} = \frac{y - 1}{1} = \frac{z - 9}{-3}\] is:

For \( \alpha, \beta \in \mathbb{R} \) and a natural number \( n \), let \[A_r = \begin{vmatrix} r & 1 & \frac{n^2}{2} + \alpha \\ 2r & 2 & n^2 - \beta \\3r - 2 & 3 & \frac{n(3n - 1)}{2} \end{vmatrix}.\]Then \( 2A_{10} - A_8 \) is:

Let \( C \) be the circle of minimum area touching the parabola \( y = 6 - x^2 \) and the lines \( y = \sqrt{3} |x| \). Then, which one of the following points lies on the circle \( C \)?

The function \( f(x) = \frac{x^2 + 2x - 15}{x^2 - 4x + 9} \), \( x \in \mathbb{R} \) is:

\( \int_{0}^{\pi/4} \frac{\cos^2 x \sin^2 x}{\left( \cos^3 x + \sin^3 x \right)^2} \, dx \) is equal to:

If \( A(3, 1, -1) \), \( B\left(\frac{5}{3}, \frac{7}{3}, \frac{1}{3}\right) \), \( C(2, 2, 1) \), and \( D\left(\frac{10}{3}, \frac{2}{3}, \frac{-1}{3}\right) \) are the vertices of a quadrilateral ABCD, then its area is:

If \( f(x) = \begin{cases} x^3 \sin\left(\frac{1}{x}\right), & x \neq 0 \\ 0, & x = 0 \end{cases} \), then:

A block of mass \(2\) \(kg\) is placed on a disc which is rotating at constant angular velocity \(4\) \(rad/sec\). Find the friction force in (N) between block and disc if block is not sliding.

Find the acceleration of \(2\) \(kg\) block shown in the diagram (neglect friction)

The charge accumulated on the capacitor connected in the following circuit is ____ µC
(Given \( C = 150 \, \mu \text{F} \))

For $x \geq 0$, the least value of $K$, for which $4^{1+x}, 4^{1-x}, \frac{K}{2}, 16^{x}, 16^{-x}$ are three consecutive terms of an A.P. is equal to:

The angle between vector \( \vec{Q} \) and the resultant of \( (2\vec{Q} + 2\vec{P}) \) and \( (2\vec{Q} - 2\vec{P}) \) is:

If \(n-1C_r= (k^2-8)^nC_r+1\) Find \(k\).

If the ratio of centripetal acceleration of two particles moving on the same circular path is \(3: 4\). Find the ratio of their speed.

Find average power in electric circuit if source voltage \((V) = 20\;sin(100\;⍵t)\) and current in the circuit \((I) = 2\;sin\;\bigg(100⍵t + \frac{\pi}{3}\bigg)\)

If the foot is perpendicular from (1, 2, 3) to the line \(\frac{x+1}{2} = \frac{y-2}{5} = \frac{z-1}{1}\) is \(( a, \beta, \gamma)\), then find \(a + \beta + \gamma\)

A point source is emitting sound waves of intensity \( 16 \times 10^{-8} \, Wm^{-2} \) at the origin. The difference in intensity (magnitude only) at two points located at distances of 2 m and 4 m from the origin respectively will be _____ \( \times 10^{-8} \, Wm^{-2} \).

Which of the following is the correct structure for the given IUPAC name?
3-Methylpent-2-enal

If the domain of the function \(f(x)\) = \(\frac{\sqrt{x^2-25}}{(4-x^2)}+ \log(x^2+2x-15)\) is \((-∞, α) ∪ (β, ∞)\), then \(α^2+β^2\) is equal to \(b\)

If \(4 cos\ θ + 5 sin\ θ = 1\), then all possible values of \(tan\ θ\), is/are
Where, \(θ∈(-\frac \pi2,\frac \pi2)\)