List of top Questions asked in JEE Main

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

Consider a disc of mass 5 kg, radius 2 m, rotating with angular velocity of 10 rad/s about an axis perpendicular to the plane of rotation. An identical disc is kept gently over the rotating disc along the same axis. The energy dissipated so that both the discs continue to rotate together without slipping is \( \_\_\_\_ \) J.

A LCR circuit is at resonance for a capacitor C, inductance L and resistance R. Now the value of resistance is halved keeping all other parameters same. The current amplitude at resonance will be now:

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

Let $A = \begin{bmatrix} 2 & -1 \\ 1 & 1 \end{bmatrix}$. If the sum of the diagonal elements of $A^{13}$ is $3^n$, then $n$ is equal to _____.

\(\text{Let } S = \{x \in \mathbb{R} : (\sqrt{3} + \sqrt{2})^x + (\sqrt{3} - \sqrt{2})^x = 10\}\).Then the number of elements in \( S \) is:

Consider the function \( f : \mathbb{R} \to \mathbb{R} \) defined by \[ f(x) = \frac{2x}{\sqrt{1 + 9x^2}}. \] If the composition of \( f \), \[ (f \circ f \circ f \circ \dots \circ f)(x) \quad \text{(10 times)} = \frac{2^{10}x}{\sqrt{1 + 9\alpha x^2}}, \] then the value of \( \sqrt{3\alpha + 1} \) is equal to \( \dots \).

If \( 2 \tan^2 \theta - 5 \sec \theta = 1 \) has exactly 7 solutions in the interval \(\left[ 0, \frac{n\pi}{2} \right],\) for the least value of \( n \in \mathbb{N} \) then \(\sum_{k=1}^{n} \frac{k}{2^k}\) is equal to:

A block is simply released from the top of an inclined plane as shown in the figure above. The maximum compression in the spring when the block hits the spring is :

The value of \[ \lim_{x \to 0} 2 \left( \frac{1 - \cos x \sqrt{\cos 2x} \, \sqrt[3]{\cos 3x} \ldots \sqrt[10]{\cos 10x}}{x^2} \right) \] is _____.

Let \( S \) be the set of positive integral values of \( a \) for which \[ \frac{a x^2 + 2(a + 1)x + 9a + 4}{x^2 - 8x + 32} < 0, \quad \forall x \in \mathbb{R}. \] Then, the number of elements in \( S \) is:

Total number of electrons present in \( (\pi^*) \) molecular orbitals of \( \text{O}_2 \), \( \text{O}_2^+ \), and \( \text{O}_2^- \) is __________ .

IUPAC name of following hydrocarbon (X) is :

A galvanometer (G) of $2 \, \Omega$ resistance is connected in the given circuit. The ratio of charge stored in $C_1$ and $C_2$ is:

A heavy iron bar, of weight W is having its one end on the ground and the other on the shoulder of a person. The bar makes an angle \(\theta\) with the horizontal. The weight experienced by the person is:

If the function \( f(x) = \begin{cases} \frac{1}{|x|}, & |x| \geq 2 \\ ax^2 + 2b, & |x| < 2 \end{cases} \) is differentiable on \( \mathbb{R} \), then \( 48 (a + b) \) is equal to \(\_\_\_\_\_\_\_\_\_\).

Two insulated circular loop A and B radius ‘a’ carrying a current of ‘I’ in the anti clockwise direction as shown in figure. The magnitude of the magnetic induction at the centre will be :

The incorrect statement about Glucose is :

A body falling under gravity covers two points A and B separated by 80 m in 2s. The distance of upper point A from the starting point is ________ m (use g = 10 ms^–2)

While preparing crystals of Mohr's salt, dil. \(H_2SO_4\) is added to a mixture of ferrous sulphate and ammonium sulphate, before dissolving this mixture in water, dil. \(H_2SO_4\) is added here to:

If three letters can be posted to any one of the 5 different addresses, then the probability that the three letters are posted to exactly two addresses is:

Consider a $\triangle ABC$ where $A(1, 2, 3)$, $B(-2, 8, 0)$, and $C(3, 6, 7)$. If the angle bisector of $\angle BAC$ meets the line $BC$ at $D$, then the length of the projection of the vector $\overrightarrow{AD}$ on the vector $\overrightarrow{AC}$ is:

The position vectors of the vertices \( A, B \) and \( C \) of a triangle are \[ 2\mathbf{i} - 3\mathbf{j} + 3\mathbf{k}, \quad 2\mathbf{i} + 2\mathbf{j} + 3\mathbf{k} \quad \text{and} \quad -\mathbf{i} + \mathbf{j} + 3\mathbf{k} \] respectively. Let \( l \) denote the length of the angle bisector \( AD \) of \( \angle BAC \) where \( D \) is on the line segment \( BC \). Then \( 2l^2 \) equals:

If \[ S(x) = (1 + x) + 2(1 + x)^2 + 3(1 + x)^3 + \ldots + 60(1 + x)^{60}, \, x \neq 0, \] and \[ (60)^2 S(60) = a(b)^b + b, \] where $a, b \in \mathbb{N}$, then $(a + b)$ is equal to ________.

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