List of top Mathematics Questions asked in JEE Main

If there are 19 and 16 points on two distinct parallel lines \(L_{1}\) and \(L_{2}\), respectively, then the total number of triangles that can be formed using these points as vertices, is :
If \(\sqrt{-24-10 i}=\alpha+i \beta\), \(i=\sqrt{-1}\), \(\alpha, \beta \in \mathbf{R}\), then \(\alpha^{2}+\beta^{2}\) is equal to :
Let \(a, b, c\) be positive real numbers such that \(a, 7, c, b\) are in an arithmetic progression. If \(ab=3(a+b)\), then the largest value of \(b\) is :
If the system of equations \(x+2 y+3 a z=4\), \(2 x+3 y+4 z=1\), \(3 x+7 y+2 z=b\) has infinitely many solutions, then \(b-40 a\) is equals to :
The product of all real solutions of the equation \((3+2 \sqrt{2})^{x^{4}-15}+(3-2 \sqrt{2})^{x^{4}-15}=6\) is :
If the domain of the function \(f(x)=\frac{1}{\log _{10}(1-2 x)}+\sqrt{2 x+1}\) is \([\alpha, \beta)-\{0\}\), then \(20\left(\alpha^{2}+\beta^{2}\right)\) equals :
Let \(A=\{1,2,3,4,5,6,7,8,9,10,11,12\}\). Let \(R\) be a relation on \(A\) defined by \(xRy\) if and only if \(2x=3y\). Let \(l\) and \(m\) be the minimum number of elements required to be added in \(R\) to make it reflexive and symmetric relations, respectively. Then \(l+m\) is equal to :
Consider a sphere of volume \(36\pi\). Then the height of the cone of maximum volume that can be inscribed in the sphere is
Let \(y=y(x)\) be the solution of the differential equation \(x\dfrac{dy}{dx}+y+xy\cot x=x,\ \dfrac{\pi}{4}\le x\le\dfrac{3\pi}{4}\), \(y\left(\dfrac{\pi}{4}\right)=0\). Then \(6y\left(\dfrac{3\pi}{4}\right)\) equals ________.
The mean and standard deviation of four numbers are given by \(10\) and \(\dfrac{5\sqrt{2}}{2}\), respectively. If a fifth number \(15\) is added to the data set, then the variance of the new data set is
Let \(R\) be a relation on the set \(A=\{1,2,3,4,\ldots,10\}\) given by \(xRy\) if and only if \(x\) divides \(y\). Let \(m\) be the number of elements in \(R\) and \(n\) be the number of minimum elements required to be added in \(R\) to make it a symmetric relation. Then \(m+n\) is equal to

The shortest distance between the curves $ y^2 = 8x $ and $ x^2 + y^2 + 12y + 35 = 0 $ is:

Let the three sides of a triangle ABC be given by the vectors $$ 2\hat{i} - \hat{j} + \hat{k}, \quad \hat{i} - 3\hat{j} - 5\hat{k}, \quad \text{and} \quad 3\hat{i} - 4\hat{j} - 4\hat{k}. $$ Let G be the centroid of the triangle ABC. Then $$ 6 \left( |\vec{AG}|^2 + |\vec{BG}|^2 + |\vec{CG}|^2 \right) \text{ is equal to}$$ _______
The number of natural numbers, between 212 and 999, such that the sum of their digits is 15, is _____.
If a curve $ y = y(x) $ passes through the point $ \left(1, \frac{\pi}{2}\right) $ and satisfies the differential equation $$ (7x^4 \cot y - e^x \csc y) \frac{dx}{dy} = x^5, \quad x \geq 1, \text{ then at } x = 2, \text{ the value of } \cos y \text{ is:} $$
Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be a thrice differentiable odd function satisfying $f^{\prime}(x) \geq 0, f^{\prime\prime}(x)=f(x), f(0)=0, f^{\prime}(0)=3$. Then $9 f\left(\log _e 3\right)$ is equal to __________ .
The value of $ \cot^{-1} \left( \frac{\sqrt{1 + \tan^2(2)} - 1}{\tan(2)} \right) - \cot^{-1} \left( \frac{\sqrt{1 + \tan^2 \left( \frac{1}{2} \right)} + 1}{\tan \left( \frac{1}{2} \right)} \right) $ is equal to:
Let \( L_1 : \frac{x - 1}{3} = \frac{y - 1}{-1} = \frac{z + 1}{0} \) and \( L_2 : \frac{x - 2}{2} = \frac{y}{0} = \frac{z + 4}{\alpha} \), where \( \alpha \in \mathbb{R} \), be two lines which intersect at the point \( B \). If \( P \) is the foot of the perpendicular from the point \( A(1, 1, -1) \) on \( L_2 \), then the value of \( 26 \alpha (PB)^2 \) is:
For a \( 3 \times 3 \) matrix \( M \), let trace(M) denote the sum of all the diagonal elements of \( M \). Let \( A \) be a \( 3 \times 3 \) matrix such that \( |A| = \frac{1}{2} \) and \( \text{trace}(A) = 3 \). If \( B = \text{adj}(\text{adj}(2A)) \), then the value of \( |B| + \text{trace}(B) \) equals:
Let the foci of a hyperbola be \( (1, 14) \) and \( (1, -12) \). If it passes through the point \( (1, 6) \), then the length of its latus-rectum is:
Let \( (2, 3) \) be the largest open interval in which the function \( f(x) = 2 \log_e (x - 2) - x^2 + ax + 1 \) is strictly increasing, and \( (b, c) \) be the largest open interval, in which the function \( g(x) = (x - 1)^3 (x + 2 - a)^2 \) is strictly decreasing. Then \( 100(a + b - c) \) is equal to:
The sum of all values of \( \theta \in [0, 2\pi] \) satisfying \( 2\sin^2\theta = \cos 2\theta \) and \( 2\cos^2\theta = 3\sin\theta \) is:

If $ A = \begin{pmatrix} 2 & 2 + p & 2 + p + q \\ 4 & 6 + 2p & 8 + 3p + 2q \\ 6 & 12 + 3p & 20 + 6p + 3q \end{pmatrix} $, then the value of $ \det(\text{adj}(\text{adj}(3A))) = 2^m \cdot 3^n $, then $ m + n $ is equal to:

Let $ A = \{-3, -2, -1, 0, 1, 2, 3\} $ and $ R $ be a relation on $ A $ defined by $ xRy $ if and only if $ 2x - y \in \{0, 1\} $. Let $ l $ be the number of elements in $ R $. Let $ m $ and $ n $ be the minimum number of elements required to be added in $ R $ to make it reflexive and symmetric relations, respectively. Then $ l + m + n $ is equal to:

Let the focal chord PQ of the parabola $ y^2 = 4x $ make an angle of $ 60^\circ $ with the positive x-axis, where P lies in the first quadrant. If the circle, whose one diameter is PS, $ S $ being the focus of the parabola, touches the y-axis at the point $ (0, \alpha) $, then $ 5\alpha^2 $ is equal to: