List of top Mathematics Questions asked in JEE Main

If the area of the region $\{ (x, y) : |x - 5| \leq y \leq 4\sqrt{x} \}$ is $A$, then $3A$ is equal to

The sum of the infinite series $ \cot^{-1} \left( \frac{7}{4} \right) + \cot^{-1} \left( \frac{19}{4} \right) + \cot^{-1} \left( \frac{39}{4} \right) + \cot^{-1} \left( \frac{67}{4} \right) + ... $ is:

Let the line $ L $ pass through $ (1, 1, 1) $ and intersect the lines $ \frac{x - 1}{2} = \frac{y + 1}{3} = \frac{z - 1}{4} $ and $ \frac{x - 3}{1} = \frac{y - 4}{2} = \frac{z}{1}. $ Then, which of the following points lies on the line $ L $?

Let $ A = \left\{ x \in (0, \pi) \mid - \log\left(\frac{2}{\pi}\right)\sin x + \log\left(\frac{2}{\pi}\right)\cos x = 2 \right\} $ and

\[ B = \left\{ x \geq 0 : \sqrt{x}(\sqrt{x - 4}) - 3\sqrt{x - 2} + 6 = 0 \right\}. \]

Then $ n(A \cup B) $ is equal to:

The number of rational terms in the binomial expansion of $ \left( 5^{1/2} + 7^{1/8} \right)^{1016} $ is:

Let $ a_1, a_2, a_3, ... $ be a G.P. of increasing positive numbers. If $ a_3 a_5 = 729 $ and $ a_2 + a_4 = \frac{111}{4} $, then $ 24(a_1 + a_2 + a_3) $ is equal to

The area of the region enclosed by the curves $ y = e^x $, $ y = |e^x - 1| $, and the y-axis is:

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:

Let $A = \{1, 6, 11, 16, \ldots\}$ and $B = \{9, 16, 23, 30, \ldots\}$ be the sets consisting of the first 2025 terms of two arithmetic progressions. Then $n(A \cup B)$ is

Let $L_1: \frac{x-1}{1} = \frac{y-2}{-1} = \frac{z-1}{2}$ and $L_2: \frac{x+1}{-1} = \frac{y-2}{2} = \frac{z}{1}$ be two lines. Let $L_3$ be a line passing through the point $(\alpha, \beta, \gamma)$ and be perpendicular to both $L_1$ and $L_2$. If $L_3$ intersects $L_1$, then $\left| 5\alpha - 11\beta - 8\gamma \right|$ equals:

Let the ellipse $ E_1 : \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 $, $ a>b $ and $ E_2 : \frac{x^2}{A^2} + \frac{y^2}{B^2} = 1 $, $ A<B $, have the same eccentricity $ \frac{1}{\sqrt{3}} $. Let the product of their lengths of latus rectums be $ \frac{32}{\sqrt{3}} $ and the distance between the foci of $ E_1 $ be 4. If $ E_1 $ and $ E_2 $ meet at A, B, C, and D, then the area of the quadrilateral ABCD equals:

If the components of $ \vec{a} = \alpha \hat{i} + \beta \hat{j} + \gamma \hat{k} $ along and perpendicular to $ \vec{b} = 3\hat{i} + \hat{j} - \hat{k} $ respectively are $ \frac{16}{11} (3\hat{i} + \hat{j} - \hat{k}) $ and $ \frac{1}{11} (-4\hat{i} - 5\hat{j} - 17\hat{k}) $, then $ \alpha^2 + \beta^2 + \gamma^2 $ is equal to:

Let the mean and variance of the observations $ 2, 3, 3, 4, 5, 7, a, b $ be 4 and 2, respectively. Then, the mean deviation about the mode of the observation is:

If the equation of a circle is $ 4x^2 + 4y^2 - 12x + 8y = 0 $, what is the radius of the circle?

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

Two parabolas have the same focus $ (4, 3) $ and their directrices are the x-axis and the y-axis, respectively. If these parabolas intersect at points A and B, then $ (AB)^2 $ is equal to:

What is the sum of the infinite series $ S = \sum_{n=0}^{\infty} \frac{1}{3^n} $?

If $ A $ and $ B $ are the points of intersection of the circle $ x^2 + y^2 - 8x = 0 $ and the hyperbola $ \frac{x^2}{9} - \frac{y^2}{4} = 1 $, and a point $ P $ moves on the line $ 2x - 3y + 4 = 0 $, then the centroid of $ \triangle PAB $ lies on the line:

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:

The area of the region enclosed by the curves $ y = x^2 - 4x + 4 $ and $ y^2 = 16 - 8x $ is:

Let $ y^2 = 12x $ be the parabola and $ S $ its focus. Let $ PQ $ be a focal chord of the parabola such that $ (SP)(SQ) = \frac{147}{4} $. Let $ C $ be the circle described by taking $ PQ $ as a diameter. If the equation of the circle $ C $ is: \[ 64x^2 + 64y^2 - \alpha x - 64\sqrt{3}y = \beta, \] then $ \beta - \alpha $ is equal to:

Let $ \alpha_1 $ and $ \beta_1 $ be the distinct roots of $ 2x^2 + (\cos\theta)x - 1 = 0, \ \theta \in (0, 2\pi) $. If $ m $ and $ M $ are the minimum and the maximum values of $ \alpha_1 + \beta_1 $, then $ 16(M + m) $ equals:

Let the line $ x + y = 1 $ meet the circle $ x^2 + y^2 = 4 $ at the points A and B. If the line perpendicular to AB and passing through the midpoint of the chord AB intersects the circle at C and D, then the area of the quadrilateral ABCD is equal to:

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:

Three defective oranges are accidentally mixed with seven good ones and on looking at them, it is not possible to differentiate between them. Two oranges are drawn at random from the lot. If $ x $ denotes the number of defective oranges, then the variance of $ x $ is: