List of top Mathematics Questions asked in JEE Main

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: 
If the equation of the parabola with vertex $\left(\frac{3}{2},\, 3\right)$ and the directrix $x + 2y = 0$ is
$$ ax^2 + by^2 - cxy - 30x - 60y + 225 = 0, $$ then $\alpha + \beta + \gamma$ 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:
The number of natural numbers, between 212 and 999, such that the sum of their digits is 15, 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:
Evaluate the integral \( I = \int_0^\pi \frac{4 \cos^2 x + \sin^2 x}{8x} \, dx \).
Let a circle \( C \) with radius \( r \) passes through four distinct points \( (0, 0), (k, 3k), (2, 3), (-1, 5) \), such that \( k \neq 0 \), then \( (10k + 2r^2) \) is equal to:

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

and \( f(0) = \frac{5}{4} \), then the value of \[ 12 \left( y \left( \frac{\pi}{4} \right) - \frac{1}{e^2} \right) \] equals to:

If \( \alpha + i\beta \) and \( \gamma + i\delta \) are the roots of the equation \( x^2 - (3-2i)x - (2i-2) = 0 \), \( i = \sqrt{-1} \), then \( \alpha\gamma + \beta\delta \) is equal to:
If \( y = y(x) \) is the solution of the differential equation, \[ \sqrt{4 - x^2} \frac{dy}{dx} = \left( \left( \sin^{-1} \left( \frac{x}{2} \right) \right)^2 - y \right) \sin^{-1} \left( \frac{x}{2} \right), \] where \( -2 \leq x \leq 2 \), and \( y(2) = \frac{\pi^2 - 8}{4} \), then \( y^2(0) \) is equal to:
The domain of the function \[ f(x) = \frac{1}{\sqrt{10 + 3x - x^2}} + \frac{1}{\sqrt{x + |x|}} \] is \( (a, b) \). Then \( (1 + a^2) + b^2 \) is:
If \( \theta \in \left[ -\frac{7\pi}{6}, \frac{4\pi}{3} \right] \), then the number of solutions of the equation \[ \sqrt{3} \csc^2 \theta - 2 (\sqrt{3} - 1) \csc \theta - 4 = 0 \] is:
If \[ \lim_{x \to 0} \frac{\cos(2x) + a \cos(4x) - b}{x^4} \] is finite, then \( a + b = \) __.
Total number of terms in an A.P. are even. Sum of odd terms is 24 and sum of even terms is 30. Last term exceeds the first term by \( \frac{21}{2} \). Find the total number of terms.
Let \( a_1, a_2, a_3, \dots \) be an A.P. and \( \sum_{k=1}^{12} a_{2k-1} = -\frac{72}{5} a_1 \) and \( \sum_{k=1}^{n} a_k = 0 \). Then the value of \( n \) is: