List of top Questions asked in JEE Main

Statement-I: Melting point of neopentane is greater than that of n-pentane.
Statement-II: Neopentane gives only one mono-substituted product.

Let {an}ⁿ⁼⁰_∞be a sequence such that a₀=a₁=0 and a_n+2=3a_n+1−2a_n+1,∀ n≥0. Then a₂₅a₂₃−2a₂₅a₂₂−2a₂₃a₂₄+4a₂₂a₂₄is equal to

If for the solution curve $ y = f(x) $ of the differential equation \[ \frac{dy}{dx} + (\tan x) y = 2 + \sec^2 x, \quad y(\frac{\pi}{3}) = \sqrt{3}, \] $\text{then}$ $ y(\frac{\pi}{4}) $ is equal to:

Let $ \hat{a} $ be a unit vector perpendicular to the vectors \[ \mathbf{b} = \hat{i} - 2\hat{j} + 3\hat{k} \quad \text{and} \quad \mathbf{c} = 2\hat{i} + 3\hat{j} - \hat{k}, \] $\text{and makes an angle of}$ $ \cos\left( -\frac{1}{3} \right) $ $\text{with the vector}$ $ \hat{i} + \alpha \hat{j} + \hat{k} $. $\text{If}$ $ \hat{a} $ $\text{makes an angle of}$ $ \frac{\pi}{3} $ $\text{with the vector}$ $ \hat{i} + \alpha \hat{j} + \hat{k} $, then the value of $ \alpha $ $\text{is:}$

Match the LIST-I with LIST-II (Redox Reactions).

Choose the correct answer from the options given below:

The number of different 5 digit numbers greater than 50000 that can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, such that the sum of their first and last digits should not be more than 8, is:

The product of all solutions of the equation $e^{5(\log_e x)^2 + 3 = x^8, x > 0}$ , is :

Let $ C_{t-1} = 28, C_t = 56 $ and $ C_{t+1} = 70 $. Let $ A(4 \cos t, 4 \sin t), B(2 \sin t, -2 \cos t) \text{ and } C(3r - n_1, r^2 - n - 1) $ be the vertices of a triangle ABC, where $ t $ is a parameter. If $ (3x - 1)^2 + (3y)^2 = \alpha $ is the locus of the centroid of triangle ABC, then $ \alpha $ equals:

The area (in sq. units) of the region $(x, y) : 0 \leq y \leq 2|x| + 1, 0 \leq y \leq x^2 + 1, |x| \leq 3$ is:

Given below are two statements, one is labelled as Assertion (A) and the other is labelled as Reason (R):
(A) A simple pendulum is taken to a planet of mass and radius, 4 times and 2 times, respectively, than the Earth. The time period of the pendulum remains same on earth and the planet.
(R) The mass of the pendulum remains unchanged at Earth and the other planet.
In light of the above statements, choose the correct answer from the options given below:

A force $ \mathbf{F} = 2\hat{i} + b\hat{j} + \hat{k} $ is applied on a particle and it undergoes a displacement $ \mathbf{r} = \hat{i} - 2\hat{j} - \hat{k} $. What will be the value of $ b $, if the work done on the particle is zero?

Two long parallel wires X and Y, separated by a distance of 6 cm, carry currents of 5 A and 4 A, respectively, in opposite directions as shown in the figure. Magnitude of the resultant magnetic field at point P at a distance of 4 cm from wire Y is $ 3 \times 10^{-5} $ T. The value of $ x $, which represents the distance of point P from wire X, is$ \_\_\_\_\_$ cm. (Take permeability of free space as $ \mu_0 = 4\pi \times 10^{-7} $ SI units.)

Let $ A $ be a set defined as $ A = \{ 2, 3, 6, 9 \} $. Find the number of singular matrices of order $ 2 \times 2 $ such that elements are from the set $ A $.

Identify the characteristics of an adiabatic process in a monatomic gas. (A) Internal energy is constant. (B) Work done in the process is equal to the change in internal energy. (C) The product of temperature and volume is a constant. (D) The product of pressure and volume is a constant. (E) The work done to change the temperature from $ T_1 $ to $ T_2 $ is proportional to $ (T_2 - T_1) $. Choose the correct answer from the options given below:

Consider the last electron of an element having atomic number $9$ and choose the correct option.

In an electromagnetic system, the quantity representing the ratio of electric flux and magnetic flux has dimension of $\mathrm{M}^{\mathrm{B}} \mathrm{L}^{\mathrm{O}} \mathrm{T}^{\mathrm{B}} \mathrm{A}^{\mathrm{S}}$, where value of 'Q' and 'R' are

If the system of equations \[ x + 2y - 3z = 2 \] \[ 2x + \lambda y + 5z = 5 \] \[ 4x + 3y + \mu z = 33 \] has infinite solutions, then $ \lambda + \mu $ is equal to

If the sum, $ \sum_{r=1}^9 \frac{r+3}{2r} \cdot \binom{9}{r} $ is equal to $ \alpha \cdot \left( \frac{3}{2} \right)^9 - \beta $, then the value of $ (\alpha + \beta)^2 $ is equal to:

Find the value of the integral: \[ \int_0^e \log_e x \, dx \]

Which of the following quantity has the same dimensions as $ \sqrt{\frac{\mu_0}{\epsilon_0}} $?

If $$ f(x) = \int \frac{1}{x^{1/4} (1 + x^{1/4})} \, dx, \quad f(0) = -6, \text{ then } f(1) \text{ is equal to:} $$

0.5 g of an organic compound gives 1.46 g CO$_2$ and 0.9 g H$_2$O. Find the percentage composition of carbon.

A convex lens (f = 30 cm) is in contact with a concave lens (f = -20 cm). An object is placed on the left side at a distance of 20 cm. Find the image distance.

Power of point source is 450 watts. Radiation pressure on a perfectly reflecting surface at a distance of 2 meters is:

Consider two statements:
Statement 1: $ \lim_{x \to 0} \frac{\tan^{-1} x + \ln \left( \frac{1+x}{1-x} \right) - 2x}{x^5} = \frac{2}{5} $
Statement 2: $ \lim_{x \to 1} x \left( \frac{2}{1-x} \right) = e^2 \; \text{and can be solved by the method} \lim_{x \to 1} \frac{f(x)}{g(x) - 1} $