List of top Mathematics Questions asked in JEE Main

The sum of all values of $ \alpha $, for which the points whose position vectors are:

\[ \mathbf{r_1} = \hat{i} - 2\hat{j} + 3\hat{k}, \quad \mathbf{r_2} = 2\hat{i} - 3\hat{j} + 4\hat{k}, \quad \mathbf{r_3} = (\alpha+1)\hat{i} + 2\hat{k}, \quad \mathbf{r_4} = \hat{j} + 2\hat{k} \]

are coplanar, is equal to:

If $\vec{a}$, $\vec{b}$, $\vec{c}$ are three non-zero vectors and $\hat{n}$ is a unit vector perpendicular to $\vec{c}$ such that $\vec{a}$=$\alpha \vec{b}$-$\hat{n}$, $\alpha \neq 0$ and $\vec{b}$ .$ \vec{c}$=12, then |$\vec{c} \times(\vec{a} \times \vec{b})$| is equal to:

Eight persons are to be transported from city A to city B in three cars of different makes. If each car can accommodate at most three persons, then the number of ways in which they can be transported is:

If the number of words, with or without meaning, which can be made using all the letters of the word MATHEMATICS in which C and S do not come together, is (6!)k , is equal to

If ²ⁿC₃: ⁿC₃= 10, then $\frac{n^{2}+3n}{n^{2}-3n+4}$ is equal to

Let $ f(x) = 2x^n + \lambda $, where $ \lambda \in \mathbb{R} $ and $ n \in \mathbb{N} $ . Given that $ f(4) = 133 $ and $ f(5) = 255 $, What is the sum of all the positive integer divisors of $ f(3) - f(2) $?

Using all the letters of the word MATHS, then rank of the word THAMS is:

Find out the rank of MONDAY in English dictionary if all alphabets are arranged in order?

Rank of the word PUBLIC is?

The number of ways to distribute 20 chocolates among three students such that each student gets atleast one chocolate is

Find all the four letter words with two vowels and 2 consonants from the word UNIVERSE?

If ${ }^{2 n+1} P _{n-1}:{ }^{2 n-1} P _n=11: 21$, then $n^2+n+15$ is equal to :

Using the number 1, 2, 3 ... 7, total numbers of 7 digit number which does not contain string 154 or 2367 is (Repetition is not allowed)

The total number of six digit numbers, formed using the digits 4,5,9 only and divisible by 6 , is __

If ${ }^{2 n+1} P _{n-1}:{ }^{2 n-1} P _n=11: 21$, then $n^2+n+15$ is equal to :

The number of five-digit numbers, greater than 40000 and divis ible by 5, which can be formed using the digits 0, 1, 3, 5, 7, and 9 without repetition, is equal to:

In an examination, 5 students have been allotted their seats as per their roll numbers. The number of ways, in which none of the students sit on the allotted seat, is:

All the letters of the word PUBLIC are written in all possible orders and these words are written as in a dictionary with serial numbers. Then the serial number of the word PUBLIC is:

The number of ways of giving 20 distinct oranges to 3 children such that each child gets at least one orange is______

The number of triplets $ (x, y, z) $, where $ x, y, z $ are distinct non-negative integers satisfying $ x + y + z = 15 $, is:

The equations of two sides of a variable triangle are $x-0$ and $y=3$, and its third side is a tangent to the parabola $y^2=6 x$. The locus of its circumcentre is:

Let the foci of the ellipse $\frac{x^2}{16}+\frac{y^2}{7}=1$ and the hyperbola $\frac{x^2}{144}-\frac{y^2}{\alpha}=\frac{1}{25}$ coincide Then the length of the latus rectum of the hyperbola is:-

A parabola with focus (3, 0) and directrix x = –3. Points P and Q lie on the parabola and their ordinates are in the ratio 3 : 1. The point of intersection of tangents drawn at points P and Q lies on the parabola

Let $ H_n : \frac{x^2}{1 + n} + \frac{y^2}{3 + n} = 1, n \in \mathbb{N} $. Let $ k $ be the smallest even value of $ n $ such that the eccentricity of $ H_n $ is a rational number. If $ l $ is the length of the latus rectum of $ H_k $, then 21 $ l $ is equal to:

Let $z=1+i$ and $z_1=\frac{1+i \bar{z}}{\bar{z}(1-z)+\frac{1}{z}}$ Then $\frac{12}{\pi} \arg \left(z_1\right)$ is equal to________