List of top Mathematics Questions asked in JEE Main

If the set of all solutions of \(|x^2 + x - 9| = |x| + |x^2 - 9|\) is \([\alpha, \beta] \cup [\gamma, \infty)\), then \((\alpha^2 + \beta^2 + \gamma^2)\) is equal to:

The first term of an A.P. of 30 non-negative terms is \(\frac{10}{3}\). If the sum of this A.P. is the cube of its last term, then its common difference is:

The mean and variance of 10 observations are 9 and 34.2, respectively. If 8 of these observations are \( 2, 3, 5, 10, 11, 13, 15, 21 \), then the mean deviation about the median of all the 10 observations is:

If $f(x) = \min \{2x^2 + 3, 6x\} + |x-1| \cos(x^2 - \frac{1}{4})$, then the number of points of non derivability of $f(x)$ is/are

Let $a_1,a_2,a_3,a_4$ be an A.P. of four terms such that each term of the A.P. and its common difference are integers. If $a_1+a_2+a_3+a_4=48$ and $a_1^2a_2a_3a_4+1^4=361$, then the largest term of the A.P. is equal to

Let \( f(x) = \begin{cases} \frac{ax^2 + 2ax + 3}{4x^2 + 4x - 3}, & x \neq -\frac{3}{2}, \frac{1}{2} \\ b, & x = -\frac{3}{2}, \frac{1}{2} \end{cases} \) be continuous at \( x = -\frac{3}{2} \). If \( f(x) = \frac{7}{5} \), then \( x \) is equal to :

Let $\vec{a}=2\hat{i}-\hat{j}-\hat{k}$, $\vec{b}=\hat{i}+3\hat{j}-\hat{k}$ and $\vec{c}=2\hat{i}+\hat{j}+3\hat{k}$. Let $\vec{v}$ be the vector in the plane of $\vec{a}$ and $\vec{b}$, such that the length of its projection on the vector $\vec{c}$ is $\dfrac{1}{\sqrt{14}}$. Then $|\vec{v}|$ is equal to

The number of real solution of equation x$|$x+4$|$+3$|$x+2$|$+10=0 is/are :

The number of critical points of the function} \[ f(x)= \begin{cases} \dfrac{|\sin x|}{x}, & x\neq0\\ 1, & x=0 \end{cases} \] in the interval \((-2\pi,2\pi)\) is equal to:

Find sum up to 8 terms of the series
\[ \frac{1^3}{1}+\frac{1^3+2^3}{1+3}+\frac{1^3+2^3+3^3}{1+3+5}+\cdots \]

If the sum of the first four terms of an A.P. is \(6\) and the sum of its first six terms is \(4\), then the sum of its first twelve terms is

The coefficient of \(x^{48}\) in \[ (1+x) + 2(1+x)^2 + 3(1+x)^3 + \cdots + 100(1+x)^{100} \] is equal to

If \(a_1 = 1\) and for all \(n \ge 1\), \[ a_{n+1} = \frac{1}{2}a_n + \frac{n^2 - 2n - 1}{n^2 (n+1)^2}, \] then the value of \[ \sum_{n=1}^{\infty} \left( a_n - \frac{2}{n^2} \right) \] is equal to:

Let the sum of the first n terms of an A.P. be $3n^2 + 5n$. Then the sum of squares of the first 10 terms of the A.P. is:

Let \( \alpha \) and \( \beta \) respectively be the maximum and the minimum values of the function \( f(\theta) = 4\left(\sin^4\left(\frac{7\pi}{2} - \theta\right) + \sin^4(11\pi + \theta)\right) - 2\left(\sin^6\left(\frac{3\pi}{2} - \theta\right) + \sin^6(9\pi - \theta)\right) \). Then \( \alpha + 2\beta \) is equal to :

The value of the integral $\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{32 \cos^4 x}{1 + e^{\sin x}} dx$ is:

Let the arithmetic mean of \(\frac{1}{a}\) and \(\frac{1}{b}\) be \(\frac{5}{16}\), where \(a>2\). If \(a,4,b\) are in A.P., then the equation \[ ax^2-ax+2(a-2b)=0 \] has:

If $\cot x=\dfrac{5}{12}$ for some $x\in\left(\pi,\dfrac{3\pi}{2}\right)$, then \[ \sin 7x\left(\cos\frac{13x}{2}+\sin\frac{13x}{2}\right) +\cos 7x\left(\cos\frac{13x}{2}-\sin\frac{13x}{2}\right) \] is equal to:

If $A=\{1,2,3,4\}$. A relation from set $A$ to $A$ is defined as $(a,b)\,R\,(c,d)$ such that $2a+3b=3c+4d$. Find the number of elements in the relation.

The letters of the word ``UDAYPUR'' are written in all possible ways with or without meaning and these words are arranged as in a dictionary. The rank of the word ``UDAYPUR'' is

A bag contains 6 blue and 6 green balls. Pairs of balls are drawn without replacement until the bag is empty. The probability that each drawn pair consists of one blue ball and one green ball is:

An equilateral triangle OAB is inscribed in the parabola $y^2 = 4x$ with the vertex O at the vertex of the parabola. Then the minimum distance of the circle having AB as a diameter from the origin is

The number of elements in the relation \[ R=\{(x,y): 4x^2+y^2<52,\; x,y\in\mathbb{Z}\} \] is