List of top Questions asked in JEE Main

The major products from the following reaction sequence are product A and product B.
The total sum of \(\pi\) electrons in product A and product B are ______ (nearest integer)

Let the foci of a hyperbola $ H $ coincide with the foci of the ellipse $ E : \frac{(x - 1)^2}{100} + \frac{(y - 1)^2}{75} = 1 $ and the eccentricity of the hyperbola $ H $ be the reciprocal of the eccentricity of the ellipse $ E $. If the length of the transverse axis of $ H $ is $ \alpha $ and the length of its conjugate axis is $ \beta $, then $ 3\alpha^2 + 2\beta^2 $ is equal to:

The acceleration due to gravity on the surface of earth is g. If the diameter of earth reduces to half of its original value and mass remains constant, then acceleration due to gravity on the surface of earth would be:
Let \( z \) be a complex number such that the real part of \[ \frac{z - 2i}{z + 2i} \] is zero. Then, the maximum value of \( |z - (6 + 8i)| \) is equal to:
A train is moving with a speed of 12 m/s on rails which are 1.5 m apart. To negotiate a curve radius of 400 m, the height by which the outer rail should be raised with respect to the inner rail is (Given, \( g = 10 \, \text{m/s}^2 \)):
A proton moving with a constant velocity passes through a region of space without any change in its velocity. If \( \vec{E} \) and \( \vec{B} \) represent the electric and magnetic fields respectively, then the region of space may have:
(A) \( \vec{E} = 0, \vec{B} = 0 \) 
(B) \( \vec{E} = 0, \vec{B} \neq 0 \) 
(C) \( \vec{E} \neq 0, \vec{B} = 0 \) 
(D) \( \vec{E} \neq 0, \vec{B} \neq 0 \) 
Choose the most appropriate answer from the options given below:
If the refractive index of the material of a prism is \(cot\bigg(\frac{A}{2}\bigg)\), where A is the angle of the prism, then the angle of minimum deviation will be:
If \(\alpha\) satisfies the equation \(x^2 + x + 1 = 0\) and \((1 + \alpha)^7 = A + B \alpha + C \alpha^2\), \(A, B, C \geq 0\), then \(5(3A - 2B - C)\) is equal to ______.

\(\lim_{x \to 0} \frac{e - (1 + 2x)^{\frac{1}{2x}}}{x} \quad \text{is equal to:}\)

Frequency of the de-Broglie wave of the electron in Bohr's first orbit of the hydrogen atom is ______ \( \times 10^{13} \, \text{Hz} \) (nearest integer).
Given:\(R_H\) (Rydberg constant) = \(2.18 \times 10^{-18} \, \text{J}\)\(h\) \((\)Planck's constant)= \(6.6 \times 10^{-34}\)\(\text{J.s}\)
Let \[ \int_{0}^{x} \sqrt{1 - (y'(t))^2} \, dt = \int_{0}^{x} y(t) \, dt, \quad 0 \leq x \leq 3, \, y \geq 0, \, y(0) = 0. \] Then, at \( x = 2 \), \( y'' + y + 1 \) is equal to:
Consider the line $L$ passing through the points $(1, 2, 3)$ and $(2, 3, 5)$. The distance of the point $$ \left( \frac{11}{3}, \frac{11}{3}, \frac{19}{3} \right) $$ from the line $L$ along the line $$ \frac{3x - 11}{2} = \frac{3y - 11}{1} = \frac{3z - 19}{2} $$ is equal to: 
Given below are two statements:
Statement (I): Viscosity of gases is greater than that of liquids. 
Statement (II): Surface tension of a liquid decreases due to the presence of insoluble impurities. 
In the light of the above statements, choose the most appropriate answer from the options given below:
Position of an ant \( S \) (in meters) moving in the Y-Z plane is given by \( S = 2t \hat{j} + 5t \hat{k} \) (where \( t \) is in seconds). The magnitude and direction of velocity of the ant at \( t = 1 \, s \) will be:
Let \( f(x) = x^3 + x^2 f'(1) + x f''(2) + f'''(3) \), \( x \in \mathbb{R} \). Then \( f'(10) \) is equal to ______.
Let the set of all \( a \in \mathbb{R} \) such that the equation \(\cos 2x + a \sin x = 2a - 7\) has a solution be \([p, q]\) and \( r = \tan 9^\circ - \tan 27^\circ - \frac{1}{\cot 63^\circ + \tan 81^\circ} \), then \( pqr \) is equal to ______.
Let the area of the region \(\{(x, y) : x - 2y + 4 \geq 0, x + 2y^2 \geq 0, x + 4y^2 \leq 8, y \geq 0\}\) be \(\frac{m}{n}\), where \( m \) and \( n \) are coprime numbers. Then \( m + n \) is equal to ______.
A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses required and let \(a=P(X=3), b=P(X≥3)\), and \(( c = P(X \geq 6|X>3).\) Then \(\frac{b+c}{a}\) is equals to ____.
The major product of the following reaction is P.
Number of oxygen atoms present in product 'P' is _______ (nearest integer).
9.3 g of pure aniline upon diazotisation followed by coupling with phenol gives an orange dye. The mass of orange dye produced (assume 100% yield/ conversion) is ________g. (nearest integer)
If \( 8 = 3 + \frac{1}{4}(3 + p) + \frac{1}{4^2}(3 + 2p) + \frac{1}{4^3}(3 + 3p) + \ldots \infty \), then the value of \( p \) is ______.
Number of molecules from the following which can exhibit hydrogen bonding is ______. (nearest integer)
Let for a differentiable function \(f : (0, \infty) \rightarrow \mathbb{R}\), \(f(x) - f(y) \geq \log_e \left( \frac{x}{y} \right) + x - y, \quad \forall \; x, y \in (0, \infty).\) 
Then \(\sum_{n=1}^{20} f'\left(\frac{1}{n^2}\right)\) is equal to ____.
If the solution of the differential equation \((2x + 3y - 2) \, dx + (4x + 6y - 7) \, dy = 0, \quad y(0) = 3,\) is  \(\alpha x + \beta y + 3 \log_e |2x + 3y - \gamma| = 6,\) then \(\alpha + 2\beta + 3\gamma\) is equal to ____.
Time required for 99.9% completion of a first order reaction is _____ time the time required for completion of 90% reaction.(nearest integer).