List of top Mathematics Questions asked in JEE Main

The system of linear equations
$x + y + z = 6$
$2x + 5y + az = 36$
$x + 2y + 3z = b$
has

Let $y=y(x)$ be a differentiable function in the interval $(0,\infty)$ such that $y(1)=2$, and \[ \lim_{t\to x}\left(\frac{t^2y(x)-x^2y(t)}{x-t}\right)=3 \text{ for each } x>0. \] Then $2y(2)$ is equal to

The number of $3\times2$ matrices $A$, which can be formed using the elements of the set $\{-2,-1,0,1,2\}$ such that the sum of all the diagonal elements of $A^{T}A$ is $5$, is

Find the value of \[ \frac{6}{3^{26}} + 10\cdot\frac{1}{3^{25}} + 10\cdot\frac{2}{3^{24}} + \cdots + 10\cdot\frac{2^{24}}{3^{1}} : \]

If \[ \int (\cos x)^{-5/2}(\sin x)^{-11/2}\,dx = \frac{p_1}{q_1}(\cot x)^{9/2} + \frac{p_2}{q_2}(\cot x)^{5/2} + \frac{p_3}{q_3}(\cot x)^{1/2} - \frac{p_4}{q_4}(\cot x)^{-3/2} + C, \] where \(C\) is the constant of integration, then find the value of \[ \frac{15\,p_1p_2p_3p_4}{q_1q_2q_3q_4}. \]

Let \( A = \{2, 3, 5, 7, 11\} \) and a relation \( R \) is defined as \[ R = \{(x, y) : x, y \in A, 2x \leq 3y\}. \] Then the minimum number of elements to be added to relation \( R \) such that \( R \) becomes symmetric is:

The area of the region \[ A = \{(x,y) : 4x^2 + y^2 \le 8 \;\text{and}\; y^2 \le 4x\} \] is

If the system of linear equations \[ \begin{cases} 3x + y + \beta z = 3 \\ 2x + \alpha y - z = 1 \\ x + 2y + z = 4 \end{cases} \] has infinitely many solutions, then the value of \(22\beta - 9\alpha\) is:

The number of values of \( x \) satisfying \( \tan^{-1}(4x) + \tan^{-1}(6x) = \frac{\pi}{6} \) and \( x<\left[ \frac{-1}{2\sqrt{6}} , \frac{1}{2\sqrt{6}} \right] \) is:

The least value of $(\cos^2 \theta - 6\sin \theta \cos \theta + 3\sin^2 \theta + 2)$ is

Maximum value of $n$ for which $40^n$ divides $60!$ is

If \[ I(x) = 3\int \frac{dx}{(4x+6)\sqrt{4x^2 + 8x + 3}}, \quad I(0) = \frac{\sqrt{3}}{4}, \] then find \( I(1) \):

The area of the region enclosed between the circles $x^2 + y^2 = 4$ and $x^2 + (y - 2)^2 = 4$ is:

A bag contains 'k' red balls and (10 - k) black balls. If 3 balls are drawn at random and they are found to be black then the probability that bag has 9 black balls & 1 red ball is

If \( a, b, c \) are in A.P. where \( a + b + c = 1 \) and \( a, 2b, c \) are in G.P., then the value of \( 9(a^2 + b^2 + c^2) \) is equal to:

If \[ f(x) = \begin{cases} \dfrac{a|x| + x^2 - 2(\sin|x|)(\cos|x|)}{x}, & x \ne 0, \\ b, & x = 0, \end{cases} \] is continuous at \( x = 0 \), then \( a + b \) is equal to.

Let \( C_r \) denote the coefficient of \( x^r \) in the binomial expansion of \( (1+x)^n \), where \( n \in \mathbb{N} \) and \( 0 \le r \le n \). If \[ P_n = C_0 - C_1 + \frac{2^2}{3} C_2 - \frac{2^3}{4} C_3 + \cdots + \frac{(-2)^n}{n+1} C_n, \] then the value of \[ \sum_{n=1}^{25} \frac{1}{2n} P_n \] equals

If \( (f(x))^2 = 25 + \int_0^x \left[ (f(x))^2 + (f'(x))^2 \right] \, dx \), find the mean of \( f(\ln 1) + f(\ln 2) + \dots + f(\ln 625) \):

The sum of all the elements in the range of
\[ f(x)=\operatorname{sgn}(\sin x)+\operatorname{sgn}(\cos x) +\operatorname{sgn}(\tan x)+\operatorname{sgn}(\cot x), \]
where
\[ x\neq \frac{n\pi}{2},\ n\in\mathbb{Z}, \]
and
\[ \operatorname{sgn}(t)= \begin{cases} 1, & t>0 \\ -1, & t<0 \end{cases} \]
is:

Let \( \mathbf{a} = \sqrt{2} \hat{i} \) and \( \mathbf{b} = 5\hat{j} + \hat{k} \). If \( \mathbf{c} = \mathbf{a} \times \mathbf{b} \) and \( \mathbf{c} \) lies in the \( y \)-\( z \) plane such that \( |\mathbf{c}| = 2 \), then the maximum value of \( |\mathbf{c} \cdot \mathbf{d}| \) is equal to:

If sum of first 4 terms of an A.P. is 6 and sum of first 6 terms is 4, then sum of first 12 terms of an A.P. is

If the probability distribution is given by, \[ \begin{array}{|c|c|c|c|c|} \hline x & 0 & 1 & 2 & 3 \\ \hline p(n) & 8a-1 \, /30 & 4a-1 \, /30 & 2a+1 \, /30 & b \\ \hline \end{array} \] If it is given that \( \sigma^2 + \mu^2 = 2 \), where \( \sigma \) is the standard deviation and \( \mu \) is the mean of the distribution, then \( \frac{a}{b} \) is: