List of top Mathematics Questions asked in JEE Main

Two biased dice are rolled. Out of which one die contains 1, 1, 2, 2, 3, 3, and another die contains 1, 2, 2, 3, 3, 4. Then the probability of getting a sum of 4 or 5 is:

For positive integers $ n $, if $ 4 a_n = \frac{n^2 + 5n + 6}{4} $ and $$ S_n = \sum_{k=1}^{n} \left( \frac{1}{a_k} \right), \text{ then the value of } 507 S_{2025} \text{ is:} $$

If $ f(x) = \frac{2^x}{2^x + \sqrt{2}} $, $x \in \mathbb{R}$, then $ \sum_{k=1}^{81} f\left(\frac{k}{82}\right) $ is equal to:

If $ \theta \in [-2\pi,\ 2\pi] $, then the number of solutions of $$ 2\sqrt{2} \cos^2\theta + (2 - \sqrt{6}) \cos\theta - \sqrt{3} = 0 $$ is:

All five letter words are made using all the letters A, B, C, D, E and arranged as in an English dictionary with serial numbers. Let the word at serial number $ n $ be denoted by $ W_n $. Let the probability $ P(W_n) $ of choosing the word $ W_n $ satisfy $ P(W_n) = 2P(W_{n-1}) $, $ n>1 $. If $ P(CDBEA) = \frac{2^\alpha}{2^\beta - 1} $, $ \alpha, \beta \in \mathbb{N} $, then $ \alpha + \beta $ is equal to :

Bag $ B_1 $ contains 6 white and 4 blue balls, Bag $ B_2 $ contains 4 white and 6 blue balls, and Bag $ B_3 $ contains 5 white and 5 blue balls. One of the bags is selected at random and a ball is drawn from it. If the ball is white, then the probability that the ball is drawn from Bag $ B_2 $ is:

The number of non-empty equivalence relations on the set $\{1,2,3\}$ is :

The function $ f: (-\infty, \infty) \to (-\infty, 1) $, defined by \[ f(x) = \frac{2^x - 2^{-x}}{2^x + 2^{-x}}, \] is:

The term independent of $ x $ in the expansion of $$ \left( \frac{x + 1}{x^{3/2} + 1 - \sqrt{x}} \cdot \frac{x + 1}{x - \sqrt{x}} \right)^{10} $$ for $ x>1 $ is:

The focus of the parabola $ y^2 = 4x + 16 $ is the center of the circle $ C $ with radius 5. If the values of $ \lambda $, for which $ C $ passes through the point of intersection of the lines $ 3x - y = 0 $ and $ x + \lambda y = 4 $, are $ \lambda_1 $ and $ \lambda_2 $, $ \lambda_1 <\lambda_2 $, then $ 12\lambda_1 + 29\lambda_2 $ is equal to:

The radius of the smallest circle which touches the parabolas $ y = x^2 + 2 $ and $ x = y^2 + 2 $ is

Let $( f(x) =$ $\int_0^{x^2 \frac{t^2 - 8t + 15}{e^t} dt}$, $x \in \mathbb{R}$. Then the numbers of local maximum and local minimum points of $ f $, respectively, are:

If $ \frac{1}{1^4} + \frac{1}{2^4} + \frac{1}{3^4} + ... \infty = \frac{\pi^4}{90}, $ $ \frac{1}{1^4} + \frac{1}{3^4} + \frac{1}{5^4} + ... \infty = \alpha, $ $ \frac{1}{2^4} + \frac{1}{4^4} + \frac{1}{6^4} + ... \infty = \beta, $ then $ \frac{\alpha}{\beta} $ is equal to:

A line passes through the origin and makes equal angles with the positive coordinate axes. It intersects the lines $ L_1 : 2x + y + 6 = 0 $ and $ L_2 : 4x + 2y - p = 0 $, $ p>0 $, at the points A and B, respectively. If $ AB = \frac{9}{\sqrt{2}} $ and the foot of the perpendicular from the point A on the line $ L_2 $ is M, then $ \frac{AM}{BM} $ is equal to

The line $ L_1 $ is parallel to the vector $ \mathbf{a} = -3\hat{i} + 2\hat{j} + 4\hat{k} $ and passes through the point $ (7, 6, 2) $, and the line $ L_2 $ is parallel to the vector $ \mathbf{b} = 2\hat{i} + \hat{j} + 3\hat{k} $ and passes through the point $ (5, 3, 4) $. The shortest distance between the lines $ L_1 $ and $ L_2 $ is:

What is the solution to the differential equation $ \frac{dy}{dx} = \frac{y}{x} $ with the initial condition $ y(1) = 2 $?

In an arithmetic progression, if $ S_{40} = 1030 $ and $ S_{12} = 57 $, then $ S_{30} - S_{10} $ is equal to:

If the probability that the random variable X takes the value x is given by $ P(X = x) = k(x + 1)3^{-x} $, $ x = 0, 1, 2, 3, ... $, where k is a constant, then $ P(X \ge 3) $ is equal to

Let the points $ \left( \frac{11}{2}, \alpha \right) $ lie on or inside the triangle with sides $ x + y = 11 $, $ x + 2y = 16 $, and $ 2x + 3y = 29 $. Then the product of the smallest and the largest values of $ \alpha $ is equal to:

The system of equations \[ x + y + z = 6, \] \[ x + 2y + 5z = 9, \] \[ x + 5y + \lambda z = \mu, \] has no solution if:

The number of ways, 5 boys and 4 girls can sit in a row so that either all the boys sit together or no two boys sit together is:

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 $ y = y(x) $ be the solution of the differential equation $ \frac{dy}{dx} + 3(\tan^2 x) y + 3y = \sec^2 x $, with $ y(0) = \frac{1}{3} + e^3 $. Then $ y\left(\frac{\pi}{4}\right) $ is equal to

If the sum of the first 20 terms of the series $$ \frac{4.1}{4 + 3.1^2 + 1^4} + \frac{4.2}{4 + 3.2^2 + 2^4} + \frac{4.3}{4 + 3.3^2 + 3^4} + \frac{4.4}{4 + 3.4^2 + 4^4} + ... $$ is $ \frac{m}{n} $, where $ m $ and $ n $ are coprime, then $ m + n $ is equal to:

Let the length of a latus rectum of an ellipse $ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 $ be 10. If its eccentricity is $ e $, and the minimum value of the function $ f(t) = t^2 + t + \frac{11}{12} $, where $ t \in \mathbb{R} $, then $ a^2 + b^2 $ is equal to: