List of top Mathematics Questions asked in JEE Main

There are 12 points in a plane in which 5 are collinear such that no three of them are in a straight line. Then, the number of triangles that can be formed from any 3 vertices from 12 points.

The integral \[ 80 \int_0^{\frac{\pi}{4}} \frac{(\sin \theta + \cos \theta)}{(9 + 16 \sin 2\theta)} \, d\theta \] is equal to:

If $ \text{Re} \left( \frac{2z + i}{z + i} \right) + \text{Re} \left( \frac{2z - i}{z - i} \right) = 2 $ is a circle of radius $ r $ and centre $ (a, b) $, then $ \frac{15ab}{r^2} $ is equal to:

If two vectors $ \mathbf{a} $ and $ \mathbf{b} $ satisfy the equation:

\[ \frac{|\mathbf{a} + \mathbf{b}| + |\mathbf{a} - \mathbf{b}|}{|\mathbf{a} + \mathbf{b}| - |\mathbf{a} - \mathbf{b}|} = \sqrt{2} + 1, \]

then the value of

\[ \frac{|\mathbf{a} + \mathbf{b}|}{|\mathbf{a} - \mathbf{b}|} \]

is equal to:

If $ f(\theta) = \frac{\tan(\tan(\theta)) - \tan(\sin(\theta))}{\tan(\theta) - \sin(\theta)} $ is continuous at $ \theta = 0 $, then the value of $ f(\theta) $ at $ \theta = 0 $ is equal to.

If a box contains 19 unbiased coins and 1 biased coin with both faces heads, and a coin is randomly chosen from this box and tossed. If the head appears, then the probability that the unbiased coin was selected is:

\[ \int_9^{10} \frac{\sqrt{1 + x^2 + x}}{\sqrt{1 + x^2 - x}} \, dx = \frac{1}{m} \left[ \left( \sqrt{1 + x^2 + x} + x \right)^n \left( n \sqrt{1 + x^2 - x} - x \right) \right] + c \] where $ c $ is the constant of integration and $ m, n \in \mathbb{N} $, then $ m + n $ is ______.

Let $ L_1 : \frac{x - 1}{3} = \frac{y}{4} = \frac{z}{5} $ and $ L_2 : \frac{x - p}{2} = \frac{y}{3} = \frac{z}{4} $. If the shortest distance between $ L_1 $ and $ L_2 $ is $ \frac{1}{\sqrt{6}} $, then the possible value of $ p $ is:

\[ \sum_{k=1}^{n} \left( \alpha^k + \frac{1}{\alpha^k} \right)^2 = 20, \quad \alpha \text{ is one of the roots of } x^2 + x + 1 = 0, \text{ then } n = ? \]

\[ \cot^{-1}\left(\frac{7}{4}\right) + \cot^{-1}\left(\frac{19}{4}\right) + \cot^{-1}\left(\frac{39}{4}\right) + \dots \, \infty \]

If $ \alpha $ and $ \beta $ are negative real roots of the quadratic equation $ x^2 - (p + 2)x + (2p + 9) = 0 $ and $ p \in (\alpha, \beta) $. Then the value of $ \beta^2 - 2\alpha $ is:

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 $.

The area bounded by the curves $ y = 4 - \frac{x^2}{4} $ and $ y = \frac{x - 4}{2} $ (in square units) is:

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

Let the area of the region $$ \{(x, y) : 2y \leq x^2 + 3, \quad y + |x| \leq 3, \quad y \geq |x-1|\} $$ be $ A $. Then $ 6A $ is equal to:

The total number of 10-digit sequences formed by only $ \{0, 1, 2\} $, where 1 should be used at least 5 times and 2 should be used exactly three times, is:

Let there be two A.P.'s with each having 2025 terms. Find the number of distinct terms in the union of the two A.P.'s, i.e., $ A \cup B $, if the first A.P. is $ 1, 6, 11, \dots $ and the second A.P. is $ 9, 16, 23, \dots $.

The integral \[ \int_0^\pi \frac{8x}{4\cos^2 x + \sin^2 x} \, dx \text{ is equal to:} \]

The sum of the series $ 1 + 3 + 5^2 + 7 + 9^2 + \dots $ up to 80 terms is?

Solve $ \int_{-1}^{1} \frac{1+2x}{e^{-x} + e^x} \, dx $.

If the equation of an ellipse $ E $ is $ \frac{x^2}{9} + \frac{y^2}{16} = 1 $, then the length of the latus rectum of $ E $ is?

The distance of the point $ (7, 10, 11) $ from the line $ \frac{x-9}{2} = \frac{y-13}{3} = \frac{z-17}{6} $ along the line is:

Let $ y = f(x) $ be the solution of the differential equation

\[ \frac{dy}{dx} + 3y \tan^2 x + 3y = \sec^2 x \]

such that $ f(0) = \frac{e^3}{3} + 1 $, then $ f\left( \frac{\pi}{4} \right) $ is equal to:

If $ \lim_{x \to 0} \left( \frac{\tan x}{x} \right)^{\frac{1}{x^2}} = p $, then $ 96 \ln p $ is: 32

If $ (1 + x + x^2)^{10} = 1 + a_1 x + a_2 x^2 + \dots $, then $ (a_1 + a_3 + a_5 + \dots + a_{19}) - 11a_2 $ equals to: