List of top Mathematics Questions asked in JEE Main

All the letters of the word "GTWENTY" are written in all possible ways with or without meaning, and these words are arranged as in a dictionary. The serial number of the word "GTWENTY" is:

Evaluate the limit : $\lim_{x \to \frac{\pi}{2}} \left( \frac{1}{\left( x - \frac{\pi}{2} \right)^3} \int_{\frac{\pi}{2}}^x \cos \left( \frac{1}{t^3} \right) \, dt \right)$

For $ 0 < a < 1 $, the value of the integral \[ \int_{0}^{\frac{\pi}{2}} \frac{dx}{1 - 2a \cos x + a^2} \] is:

The 20^th term from the end of the progression \[ 20, 19, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, \ldots, -129 \frac{1}{4} \] is:

If $\frac{dy}{dx}$= $\frac{(x+y-2)}{(x-y)}$, and y(0) = 2, find y(2)

If $ 2 \tan^2 \theta - 5 \sec \theta = 1 $ has exactly 7 solutions in the interval $\left[ 0, \frac{n\pi}{2} \right],$ for the least value of $ n \in \mathbb{N} $ then $\sum_{k=1}^{n} \frac{k}{2^k}$ is equal to:

The integral $$ \int \frac{x^8 - x^2}{(x^{12} + 3x^6 + 1) \tan^{-1}\left( \frac{x^3 + 1}{x^3} \right)} \, dx $$ is equal to:

Coefficient of x²⁰¹² in (1-x)²⁰⁰⁸(1+x+x²)²⁰⁰⁷ is equal to ___

Four distinct points $ (2k, 3k), (1, 0), (0, 1) $ and $ (0, 0) $ lie on a circle for $ k $ equal to:

If $ (a, b) $ be the orthocenter of the triangle whose vertices are $ (1, 2) $, $ (2, 3) $, and $ (3, 1) $, and $ I_1 = \int_a^b x \sin(4x - x^2) dx $, $ I_2 = \int_a^b \sin(4x - x^2) dx $, then $ 36 \frac{I_1}{I_2} $ is equal to:

If $å= î+2ĵ + k, b = 3(î - ĵ + k), å · c = 3$ and $å \times č = b$, then $å·((xb)-b-č)$=

$\int^1_0\frac{1}{\sqrt{3+x}+\sqrt{1+x}}dx=a+b\sqrt2+c\sqrt3$ then $2a-3b-4c$ is equal to _____.

If $n-1C_r= (k^2-8)^nC_r+1$ Find $k$.

If $f(x)$ = $\begin {bmatrix} Cos x& -sinx & 0\\sinx & cos x& 0\\0&0&1 \end {bmatrix} $Statement I $⇒ f(x).f(y) = f(x+y)$ Statement II $⇒f(-x) =0 $ is invertible

If $lim_{x\rightarrow 0} \frac{\sqrt 1 + \sqrt{1+x^4}-\sqrt 2}{x^4}=A$ and $lim_{x \rightarrow 0} \frac{sin^2x}{\sqrt 2 - \sqrt{1+cosx}}=B$, then $AB^3$ = ____.

How many times 3 comes from 1 to 1000?

10, 30, 68, 130, ___ ,350
find the missing number?

An equation of a plane parallel to the plane $x-2y+2z-5=0$ and at a unit distance from the origin is?

Let A,B,C be 3×3 matrices such that A is symmetric and B and C are skew symmetric. Consider the statements:
(S1) A¹³B²⁶ − B²⁶A¹³ is symmetric.
(S2) A²⁶C¹³ − C¹³A²⁶ is symmetric.Then:

Let $\vec{a}=-\hat{i}-\hat{j}+\hat{k}, \vec{a} \cdot \vec{b}=1$ and $\vec{a} \times \vec{b}=\hat{i}-\hat{j}$. Then $\vec{a}-6 \vec{b}$ is equal to

Let $ \mathbf{a} $ be a non-zero vector parallel to the line of intersection of the two planes described by $ i + j + k $ and $ -i - j - k $. If $ \theta $ is the angle between the vector $ \mathbf{a} $ and the vector $ \mathbf{b} = -2i - 2j + 2k $, and $ \left| \mathbf{a} \right| = 6 $, then ordered pair $ (\mathbf{a} \cdot \mathbf{b}) $ is equal to:

The number of functions $f:\{1,2,3,4\} \rightarrow\{ a \in: Z|a| \leq 8\}$ satisfying $f(n)+\frac{1}{n} f( n +1)=1, \forall n \in\{1,2,3\}$ is

Let f: R→R be a function such that $f(x)=\frac{x^2+2x+1}{x^2+1}$. Then

Let the plane P pass through the intersection of the planes $2 x+3 y-z=2$and $x+2 y+3 z=6,$ and be perpendicular to the plane $2 x+y-z+1=0$If d is the distance of P from the point (-7,1,1), then $d^2$ is equal to :

If the local maximum value of the function f( x )=$(\frac{√3e}{2 sin x} )^{ sin^2x}$ ,$ x ∈ ( 0,\frac{π}{2} )$, is $\frac{k}{e}$, then $(\frac{k}{e})^8+\frac{k^8}{e^5}+k^8 $ is equal to