List of top Mathematics Questions asked in JEE Main

$L_1: γ^-=(i+2j+3k)+λ(i-j+k)$;
$L_2: γ^-=(4i+5j+6k)+μ(i+j-k)$,
intersect $L_1$ and $L_2$ at P and Q respectively. If $(α, β, γ)$ is the mid point of the line segment PQ, then $2(α, β, γ$) is equal to

The coefficient of $ x^{70} $ in $ x^2 (1+x)^{98} + x^3 (1+x)^{97} + x^4 (1+x)^{96} + \ldots + x^{54} (1+x)^{46} $ is $ ^{99}C_p - ^{46}C_q $.
Then a possible value to $ p + q $ is:

Number of integral terms in the expansion of $ \left( \sqrt{7} z + \frac{1}{6 \sqrt{z}} \right)^{824} $ is equal to ______.

The value $ 9 \int_{0}^{9} \left\lfloor \frac{10x}{x+1} \right\rfloor \, dx $, where $ \left\lfloor t \right\rfloor $ denotes the greatest integer less than or equal to $ t $, is ________.

In a class there are 40 students. 16 passed in Chemistry, 20 passed in Physics, 25 passed in Math. 15 students passed in both Math and Physics.15 students passed in both Math and Chemistry and 10 students passed in both Physics and Chemistry. Find the maximum number of students that passed in all the subjects.

For the following data table

$x_i$	$f_i$
0 - 4	2
4 - 8	4
8 - 12	7
12 - 16	8
16 - 20	6

Find the value of 20M (where M is median of the data)

Let $(\alpha, \beta, y)$ be the foot of perpendicular form the point $(1,2,3)$ on the line $\bigg(\frac{x + 3}{5}$ = $\frac{y - 1}{2}$ = $\frac{z + 4}{3}$ $\bigg)$then $19 (\alpha + \beta + y)$

$\frac{dy}{dx}$ = $\frac{(1-x-y^2)}{y}$ and $x(1)=1$ , then $5x(2)$ is equal to____.

There are 20 lines numbered as 1,2,3,..., 20. And the odd numbered lines intersect at a point and all the even numbered lines are parallel. Find the maximum number of point of intersections

Let $ \alpha = 1^2 + 4^2 + 8^2 + 13^2 + 19^2 + 26^2 + \ldots $ up to 10 terms and $ \beta = \sum_{n=1}^{10} n^4 $. If $ 4\alpha - \beta = 55k + 40 $, then $ k $ is equal to $\_\_\_\_\_\_\_\_\_$.

Let $\overrightarrow{a},\overrightarrow{b}$ and $\overrightarrow{c}$ be three non-zero vectors such that $\overrightarrow{b}$ and $\overrightarrow{c}$ are non-collinear. If $\overrightarrow{a}+5\overrightarrow{b}$ is collinear with $\overrightarrow{c},\overrightarrow{b}+6\overrightarrow{c}$ is collinear with $\overrightarrow{a}$ and $\overrightarrow{a}+ α\overrightarrow{b} + β\overrightarrow{c} = 0$, then α + β is equal to

The portion of the line $ 4x + 5y = 20 $ in the first quadrant is trisected by the lines $ L_1 $ and $ L_2 $ passing through the origin. The tangent of an angle between the lines $ L_1 $ and $ L_2 $ is:

Let $z_1$ and $z_2$ be two complex numbers such that $z_1 + z_2 = 5$ and $z_1^3+z_2^3 =20 +15i$, then the value of $| z_1^4+z_2^4 |$ is equal to

Let $ f(x) = 2^x - x^2, \, x \in \mathbb{R} $. If $ m $ and $ n $ are respectively the number of points at which the curves $ y = f(x) $ and $ y = f'(x) $ intersect the x-axis, then the value of $ m + n $ is

In a △ABC, suppose y = x is the equation of the bisector of the angle B and the equation of the side AC is 2x−y = 2. If 2AB = BC and the points A and B are respectively (4, 6) and (α, β), then α + 2β is equal to:

Let mean and variance of 6 observations a, b, 68, 44, 40, 60 be 55 and 194. If a > b then find a + 3b

Let $A = \begin{bmatrix} 2 & a & 0 \\ 1 & 3 & 1 \\ 0 & 5 & b \end{bmatrix}$. If $A^3 = 4A^2 - A - 21I$, where I is the identity matrix of order $3 \times 3$, then $2a + 3b$ is equal to:

Let $ \alpha = \sum_{k=0}^{n} \left( \frac{\binom{n}{k}}{k+1} \right)^2 $ and $ \beta = \sum_{k=0}^{n-1} \left( \frac{\binom{n}{k} \binom{n}{k+1}}{k+2} \right) $.
If $ 5\alpha = 6\beta $, then $ n $ equals __________.

$^{n-1}C_r = (k^2 - 8) ^{n}C_{r+1}$ if and only if:

If $ A $ denotes the sum of all the coefficients in the expansion of $ (1 - 3x + 10x^2)^n $ and $ B $ denotes the sum of all the coefficients in the expansion of $ (1 + x^2)^n $, then:

If the coefficient of $x^{30}$ in the expansion of $\left(1 + \frac{1}{x}\right)^6 (1 + x^2)^7 (1 - x^3)^8, \, x \neq 0$ is $\alpha$, then $|\alpha|$ equals ____.

\(x_i\)	\(f_i\)
0 - 4	2
4 - 8	4
8 - 12	7
12 - 16	8
16 - 20	6