List of top Mathematics Questions asked in JEE Main

Let the value of $p$, such that the sum of the squares of the roots of the quadratic equation \[ x^2+(7-p)x+4=p \] has the least value, be $\alpha$, and the corresponding roots be $\beta$ and $\gamma$. Then $\alpha^3+\beta^3+\gamma^3$ equals \underline{\hspace{2cm}.}

Let $25^x+25^{-x},\ \dfrac{\alpha}{3},\ 20^{1+x}+20^{1-x}$, where $x,\alpha\in\mathbb{R}$, be the first three terms of an A.P. of increasing terms. For the least value of $\alpha$, the sum of its first $10$ terms is _____

If the circles \[ x^2+y^2-2x-8y+17=r \quad \text{and} \quad x^2+y^2-26x-18y+234=0 \] intersect at exactly one point, then the sum of all possible values of $r$ is _______

Let $\vec a = 2\hat i + 3\hat j + 5\hat k$, $\vec b = \hat i - \hat j + 3\hat k$ and $\vec c$ be a vector such that \[ \vec a \cdot \vec c = 104 \quad \text{and} \quad \vec a \times \vec c = \vec c \times \vec b. \] Then $\vec b \cdot \vec c$ is equal to ______

Let $ x = -1 $ and $ x = 2 $ be the critical points of the function $ f(x) = x^3 + ax^2 + b \log|x| + 1 $, where $ x \neq 0 $. Let $ m $ and $ M $ be the absolute minimum and maximum values of $ f $ in the interval $ \left[-2, -\frac{1}{2}\right] $. Then, $ |M + m| $ is equal 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:

Let the curve $z(1 + i) +$ $\overline{z(1 - i) = 4}$, z $\in$$ \mathbb{C}$, divide the region $|z - 3| \leq 1$ into two parts of areas $ \alpha $ and $ \beta $. Then $ |\alpha - \beta| $ equals:}

If $ \sum_{r=0}^5 \frac{{}^{11}C_{2r+1}}{2r+2} = \frac{m}{n} $, gcd(m, n) = 1, then $ m - n $ is equal to:

Let $ (1 + x + x^2)^{10} = a_0 + a_1 x + a_2 x^2 + ... + a_{20} x^{20} $. If $ (a_1 + a_3 + a_5 + ... + a_{19}) - 11a_2 = 121k $, then k is equal to _______

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

If the sum, $ \sum_{r=1}^9 \frac{r+3}{2r} \cdot \binom{9}{r} $ is equal to $ \alpha \cdot \left( \frac{3}{2} \right)^9 - \beta $, then the value of $ (\alpha + \beta)^2 $ is equal to:

The sum of all rational terms in the expansion of $ \left( 2 + \sqrt{3} \right)^8 $ is

The number of solutions of the equation \[ \left( \frac{9}{x} - \frac{9}{\sqrt{x}} + 2 \right) \left( \frac{2}{x} - \frac{7}{\sqrt{x}} + 3 \right) = 0 \] is:

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:

The number of 6-letter words, with or without meaning, that can be formed using the letters of the word "MATHS" such that any letter that appears in the word must appear at least twice is:

Group A consists of 7 boys and 3 girls, while group B consists of 6 boys and 5 girls. The number of ways, 4 boys and 4 girls can be invited for a picnic if 5 of them must be from group A and the remaining 3 from group B, is equal to:

If all the words with or without meaning made using all the letters of the word "KANPUR" are arranged as in a dictionary, then the word at 440^th position in this arrangement is:

There are 12 points in a plane in which 5 are collinear such that no three of them are in a straight line. Then, the number of triangles that can be formed from any 3 vertices from 12 points.

There are 12 points in a plane in which 5 are collinear such that no three of them are in a straight line. Then the number of triangles that can be formed from any 3 vertices from 12 points.

If the number of seven-digit numbers, such that the sum of their digits is even, is $ m \cdot n \cdot 10^a $; $ m, n \in \{1, 2, 3, ..., 9\} $, then $ m + n $ is equal to

The number of 6-letter words, with or without meaning, that can be formed using the letters of the word MATHS such that any letter that appears in the word must appear at least twice, is $ 4 \_\_\_\_\_$.

The number of sequences of ten terms, whose terms are either 0 or 1 or 2, that contain exactly five 1’s and exactly three 2’s, is equal to:

Let $$ E: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1, \quad a > b \quad \text{and} \quad H: \frac{x^2}{A^2} - \frac{y^2}{B^2} = 1. $$ Let the distance between the foci of $E$ and the foci of $H$ be $2\sqrt{3}$. If $a - A = 2$, and the ratio of the eccentricities of $E$ and $H$ is $\frac{1}{3}$, then the sum of the lengths of their latus rectums is equal to:

Let the ellipse $ 3x^2 + py^2 = 4 $ pass through the centre $ C $ of the circle $ x^2 + y^2 - 2x - 4y - 11 = 0 $ of radius $ r $. Let $ f_1, f_2 $ be the focal distances of the point $ C $ on the ellipse. Then $ 6f_1 f_2 - r $ is equal to