List of top Mathematics Questions asked in JEE Main

The line passing through the points (5, 1, a) and (3, b, 1)  crosses the yz- plane at the point 0,172,-132 . Then;
If 6th  term in the expansion of [1x8/3+x2log10⁡x]8 is 5600, then x is equal to
In a ΔPQR, if 3sinP + 4cosQ = 6 and 4sinQ + 3cosP = 1, then the angle R is equal to:
If A = {1, 2, 3, 4, 6} and R is a relation on A such that R = {(a, b) : a, b ∈ A and b is exactly divisible by a} then find the number of elements present in the range of R?
If ax2+bx+c=0 and cx2+bx+a=0 (a,b,c∈R) have a common non - real root, then

If ABCD is a parallelogram, vector AB = 2i + 4j - 5k and vector AD = i + 2j + 3k, then the unit vector in the direction of BD is

Find the equation of normal to the curvey=(1+x)y+sin−1⁡(sin2⁡x) at x=0
Let $S$ be the set of all solutions of the equation $\cos ^{-1}(2 x)-2 \cos ^{-1}\left(\sqrt{1-x^2}\right)=\pi$, $x \in\left[-\frac{1}{2}, \frac{1}{2}\right]$ Then $\displaystyle\sum_{x \in S} 2 \sin ^{-1}\left(x^2-1\right)$ is equal to

For x ∈ (0, π), the equation sin x + 2sin2x −sin3x = 3 has 

Let $y=y(x)$ be the solution of the differential equation $\left(x^2-3 y^2\right) d x+3 x y d y=0, y(1)=1$.Then $6 y^2( e )$ is equal to

The value of limx→0∫0x2sec2⁡tdtxsin⁡x is
A function y = f(x) has a second order derivative f''(x) = 6(x - 1).  If its graph passes through the point (2, 1) and at that point the tangent to the graph is y = 3x -5.  then the function is :
The integral ∫sin2⁡xcos2⁡x(sin5⁡x+cos3⁡xsin2⁡x+xcos2⁡x+cos5⁡x)2dx is equal to:
The 315th word in dictionary arranged in order for the word ‘NAGPUR’ is
Find area bounded by $y^2 ≤ 2x$ and $y ≥ 4x – 1$
Given \(f(x) =   \begin{cases}     \frac{tan((a+1)x)+tanx\cdot b}{x}       & \quad x\lt 0\\     3  & \quad x=0\\ \frac{\sqrt{ax+b^2x^2}-\sqrt{ax}}{\sqrt{a}bx\sqrt{x}}  & \quad x\gt 0\end{cases}\) It is a continuous function at x=0, then find \(\frac{b}{a}\)
The value of $\frac{1}{1 ! 50 !}+\frac{1}{3 ! 48 !}+\frac{1}{5 ! 46 !}+\ldots +\frac{1}{49 ! 2 !}+\frac{1}{51 ! 1 !}$ is :
The value of $∫_0^{\frac{\pi}{4}} \frac{dx}{1+tanx} $
Let the vectors \( , , \) represent three coterminous edges of a parallelepiped of volume \( V \). Then the volume of the parallelepiped, whose coterminous edges are represented by \( , + \) and \( + 2 + 3 \) is equal to: \\ \\
Let line L pass through the point \( (0, 1, 2) \), intersect the line \( {2 = {3 = {4 \), and be parallel to the plane \( 2x + y - 3z = 4 \). Find the distance of the point \( P(1, -9, 2) \) from line L. \\
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: \\ \\
If the domain of \(f(x)=\sin^{-1}(\frac{x-1}{2x+3})\) is R – (α, β] then find the value of 12αβ.
Let \(S=x: x∈R\) and $\left(\sqrt{3}+\sqrt{2})^{x^2-4}+(\sqrt{3}-\sqrt{2})^{x^2-4}=10\right\}$Then $n(S)$ is equal to
Let the solution curve $y=y(x)$ of the differential equation $\frac{d y}{d x}-\frac{3 x^5 \tan ^{-1}\left(x^3\right)}{\left(1+x^6\right)^{3 / 2}} y=2 x \exp \left\{\frac{x^3-\tan ^{-1} x^3}{\sqrt{\left(1+x^6\right)}}\right\}$ pass through the origin Then $y(1)$ is equal to :
R = (a, b) : a + 5b = 42 and a, b ∈ N has m elements and \(\sum\limits_{n=1}^{m}(1+i^{n!})\) = x + iy (where i = √-1). Find x + y + m.