List of top Questions asked in JEE Main

Consider the following elements In, Tl, Al, Pb, and Ge. The most stable oxidation states of elements with highest and lowest first ionisation enthalpies, respectively, are:

The velocity-time graph of an object moving along a straight line is shown in the figure. What is the distance covered by the object between $ t = 0 $ to $ t = 4s $?

Let $ P_n = \alpha^n + \beta^n $, $ P_{10} = 123 $, $ P_9 = 76 $, $ P_8 = 47 $, and $ P_1 = 1 $. The quadratic equation whose roots are $ \frac{1}{\alpha} $ and $ \frac{1}{\beta} $ is:

The expression given below shows the variation of velocity $ v $ with time $ t $: \[ v = At^2 + \frac{Bt}{C + t}. \] The dimension of $ ABC $ is:

Number of functions $ f: \{1, 2, \dots, 100\} \to \{0, 1\} $, that assign 1 to exactly one of the positive integers less than or equal to 98, is equal to:

Suppose that the number of terms in an A.P. is $ 2k, k \in \mathbb{N} $. If the sum of all odd terms of the A.P. is 40, the sum of all even terms is 55, and the last term of the A.P. exceeds the first term by 27, then $ k $ is equal to:

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).

Let $ f(x) = \frac{x - 5}{x^2 - 3x + 2} $. If the range of $ f(x) $ is $ (-\infty, \alpha) \cup (\beta, \infty) $, then $ \alpha^2 + \beta^2 $ equals to.

If the domain of the function $ f(x) = \frac{1}{\sqrt{3x + 10 - x^2}} + \frac{1}{\sqrt{x + |x|}} $ is $ (a, b) $, then $ (1 + a)^2 + b^2 $ is equal to:

What is the shape of the $ \text{ClO}_2^- $ ion according to VSEPR theory?

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 :

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?

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 $.

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: