List of top Questions asked in JEE Main

Reaction A(g) → 2B(g) + C(g) is a first-order reaction. It was started with pure A.
The following table shows the pressure of the system at different times:

Which of the following options is incorrect?

A light source of wavelength $ \lambda $ illuminates a metal surface, and electrons are ejected with a maximum kinetic energy of 2 eV. If the same surface is illuminated by a light source of wavelength $ \frac{\lambda}{2} $, then the maximum kinetic energy of ejected electrons will be (The work function of the metal is 1 eV).

A body of mass $m$ is suspended by two strings making angles $\theta_{1}$ and $\theta_{2}$ with the horizontal ceiling with tensions $\mathrm{T}_{1}$ and $\mathrm{T}_{2}$ simultaneously. $\mathrm{T}_{1}$ and $\mathrm{T}_{2}$ are related by $\mathrm{T}_{1}=\sqrt{3} \mathrm{~T}_{2}$. the angles $\theta_{1}$ and $\theta_{2}$ are

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: In photoelectric effect, on increasing the intensity of incident light the stopping potential increases. Reason R: Increase in intensity of light increases the rate of photoelectrons emitted, provided the frequency of incident light is greater than threshold frequency.

An alternating current is represented by the equation, $\mathrm{i}=100 \sqrt{2} \sin (100 \pi \mathrm{t})$ ampere. The RMS value of current and the frequency of the given alternating current are

Two liquids A and B have $\theta_{\mathrm{A}}$ and $\theta_{\mathrm{B}}$ as contact angles in a capillary tube. If $K=\cos \theta_{\mathrm{A}} / \cos \theta_{\mathrm{B}}$, then identify the correct statement:

Let $ y = f(x) $ be the solution of the differential equation\[\frac{dy}{dx} + \frac{xy}{x^2 - 1} = \frac{x^6 + 4x}{\sqrt{1 - x^2}}, \quad -1 < x < 1\] such that $ f(0) = 0 $. If \[6 \int_{-1/2}^{1/2} f(x)dx = 2\pi - \alpha\] then $ \alpha^2 $ is equal to ______.

For a $ 3 \times 3 $ matrix $ M $, let trace(M) denote the sum of all the diagonal elements of $ M $. Let $ A $ be a $ 3 \times 3 $ matrix such that $ |A| = \frac{1}{2} $ and $ \text{trace}(A) = 3 $. If $ B = \text{adj}(\text{adj}(2A)) $, then the value of $ |B| + \text{trace}(B) $ equals:

An object of mass 1000 g experiences a time-dependent force $ \vec{F} = (2t \hat{i} + 3t^2 \hat{j}) \, \text{N} $. The power generated by the force at time $ t $ is:

Let $A = \{ z \in \mathbb{C} : |z - 2 - i| = 3 \}$, $B = \{ z \in \mathbb{C} : \text{Re}(z - iz) = 2 \}$, and $S = A \cap B$. Then $\sum_{z \in S} |z|^2$ is equal to

In a hydrogen-like ion, the energy difference between the 2nd excitation energy state and ground is 108.8 eV. The atomic number of the ion is:

In a group of 3 girls and 4 boys, there are two boys $ B_1 $ and $ B_2 $. The number of ways in which these girls and boys can stand in a queue such that all the girls stand together, all the boys stand together, but $ B_1 $ and $ B_2 $ are not adjacent to each other, is:

If the system of linear equations: \[ x + y + 2z = 6, \] \[ 2x + 3y + az = a + 1, \] \[ -x - 3y + bz = 2b, \] where $ a, b \in \mathbb{R} $, has infinitely many solutions, then $ 7a + 3b $ is equal to:

If $10 \sin^4 \theta + 15 \cos^4 \theta = 6$, then the value of $\frac{27 \csc^6 \theta + 8 \sec^6 \theta}{16 \sec^8 \theta}$ is:

Consider the equation $x^2 + 4x - n = 0$, where $n \in [20, 100]$ is a natural number. Then the number of all distinct values of $n$, for which the given equation has integral roots, is equal to

Two projectiles are fired from the ground with the same initial speeds from the same point at angles $ (45^\circ + \alpha) $ and $ (45^\circ - \alpha) $ with the horizontal direction. The ratio of their times of flights is:

The length of the latus-rectum of the ellipse, whose foci are $(2, 5)$ and $(2, -3)$ and eccentricity is $\frac{4}{5}$, is

If \[ \lim_{x \to \infty} \left( \frac{e}{1 - e} \left( \frac{1}{e} - \frac{x}{1 + x} \right) \right)^x = \alpha, \] then the value of \[ \frac{\log_e \alpha}{1 + \log_e \alpha} \] equals:

In the following circuit, the reading of the ammeter will be: (Take Zener breakdown voltage = 4 V)

Let the three sides of a triangle are on the lines $ 4x - 7y + 10 = 0,\quad x + y = 5,\quad 7x + 4y = 15 $.
Then the distance of its orthocentre from the orthocentre of the triangle formed by the lines $ x = 0,\quad y = 0,\quad x + y = 1 $ is

The sum of all values of $ \theta \in [0, 2\pi] $ satisfying $ 2\sin^2\theta = \cos 2\theta $ and $ 2\cos^2\theta = 3\sin\theta $ is:

The value of $\int_{-1}^{1} \frac{(1 + \sqrt{|x| - x})e^x + (\sqrt{|x| - x})e^{-x}}{e^x + e^{-x}} \, dx$ is equal to

Consider two vectors $\vec{u} = 3\hat{i} - \hat{j}$ and $\vec{v} = 2\hat{i} + \hat{j} - \lambda \hat{k}$, $\lambda>0$. The angle between them is given by $\cos^{-1} \left( \frac{\sqrt{5}}{2\sqrt{7}} \right)$. Let $\vec{v} = \vec{v}_1 + \vec{v}_2$, where $\vec{v}_1$ is parallel to $\vec{u}$ and $\vec{v}_2$ is perpendicular to $\vec{u}$. Then the value $|\vec{v}_1|^2 + |\vec{v}_2|^2$ is equal to

If $\int e^x \left( \frac{x \sin^{-1} x}{\sqrt{1-x^2}} + \frac{\sin^{-1} x}{(1-x^2)^{3/2}} + \frac{x}{1-x^2} \right) dx = g(x) + C$, where C is the constant of integration, then $g\left( \frac{1}{2} \right)$equals:

Let $ P(4, 4\sqrt{3}) $ be a point on the parabola $ y^2 = 4ax $ and PQ be a focal chord of the parabola. If M and N are the foot of the perpendiculars drawn from P and Q respectively on the directrix of the parabola, then the area of the quadrilateral PQMN is equal to: