List of top Mathematics Questions asked in JEE Main

A chord is drawn through the focus of the parabola \(y^2=6x\) such that its distance from the vertex of this parabola is \(\frac{\sqrt5}{2}\), then its slope can be :

If the angle between the line \(2(x+1)=y=z+4\) and the plane \(2x-y+\sqrt{\lambda}\,z+4=0\) is \(\frac{\pi}{6}\), then the value of \(\lambda\) is :

The circumcentre of a triangle lies at the origin and its centroid is the mid point of the line segment joining the points \((a^2+1,\ a^2+1)\) and \((2a,\ -2a),\ a\neq 0\). Then for any \(a\), the orthocentre of this triangle lies on the line :

The equation of the circle described on the chord \(3x+y+5=0\) of the circle \(x^2+y^2=16\) as diameter is :

If \(\frac{dy}{dx}+y\tan x=\sin 2x\) and \(y(0)=1\), then \(y(\pi)\) is equal to :

If a line L is perpendicular to the line \(5x-y=1\), and the area of the triangle formed by the line L and the coordinate axes is \(5\), then the distance of line L from the line \(x+5y=0\) is :

The area of the region above the \(x\)-axis bounded by the curve \(y=\tan x,\ 0\le x\le \frac{\pi}{2}\) and the tangent to the curve at \(x=\frac{\pi}{4}\) is :

If m is a non-zero number and \(\displaystyle\int\frac{x^{5m-1}+2x^{4m-1}}{\left(x^{2m}+x^m+1\right)^3}\,dx=f(x)+c\), then \(f(x)\) is :

Let function F be defined as \(F(x)=\displaystyle\int_1^x\frac{e^t}{t}\,dt,\ x>0\), then the value of the integral \(\displaystyle\int_1^x\frac{e^t}{t+a}\,dt\), where \(a>0\), is :

If the volume of a spherical ball is increasing at the rate of \(4\pi\) cc/sec, then the rate of increase of its radius (in cm/sec), when the volume is \(288\pi\) cc, is :

If non-zero real numbers b and c are such that \(\min f(x)>\max g(x)\), where \(f(x)=x^2+2bx+2c^2\) and \(g(x)=-x^2-2cx+b^2\) \((x\in\mathbf{R})\); then \(\left|\frac cb\right|\) lies in the interval :

Two women and some men participated in a chess tournament in which every participant played two games with each of the other participants. If the number of games that the men played between themselves exceeds the number of games that the men played with the women by 66, then the number of men who participated in the tournament lies in the interval :

If \(\Delta_r=\begin{vmatrix} r & 2r-1 & 3r-2\\ \frac{n}{2} & n-1 & a\\ \frac12 n(n-1) & (n-1)^2 & \frac12 (n-1)(3n+4)\end{vmatrix}\), then the value of \(\displaystyle\sum_{r=1}^{n-1}\Delta_r\) :

If the function \(f(x)=\begin{cases}\dfrac{\sqrt{2+\cos x}-1}{(\pi-x)^2}, & x\ne\pi\\ k, & x=\pi\end{cases}\) is continuous at \(x=\pi\), then k equals :

Let \(f:\mathbf{R}\to\mathbf{R}\) be a function such that \(|f(x)|\le x^2\), for all \(x\in\mathbf{R}\). Then, at \(x=0\), \(f\) is :

Let A and B be any two \(3\times 3\) matrices. If A is symmetric and B is skewsymmetric, then the matrix AB \(-\) BA is :

The equation \(\sqrt{3x^2+x+5}=x-3\), where \(x\) is real, has :

Let \(f : \mathbf{R}\to\mathbf{R}\) be defined by \(f(x)=\frac{|x|-1}{|x|+1}\), then \(f\) is :

A symmetrical form of the line of intersection of the planes \(x=ay+b\) and \(z=cy+d\) is

If the distance between planes, \(4x-2y-4z+1=0\) and \(4x-2y-4z+d=0\) is 7, then \(d\) is:

The integral \(\int\frac{\sin^2x\cos^2x}{(\sin^3x+\cos^3x)^2}\,dx\) is equal to:

If \(\hat{x},\hat{y}\) and \(\hat{z}\) are three unit vectors in three-dimensional space, then the minimum value of \(|\hat{x}+\hat{y}|^2+|\hat{y}+\hat{z}|^2+|\hat{z}+\hat{x}|^2\) is:

Let \(f\) and \(g\) be two differentiable functions on \(R\) such that \(f'(x)>0\) and \(g'(x)<0\) for all \(x\in R\). Then for all \(x\):

The general solution of the differential equation, \(\sin2x\left(\frac{dy}{dx}-\sqrt{\tan x}\right)-y=0\), is:

If for a continuous function \(f(x)\), \(\int_{-\pi}^{t}(f(x)+x)\,dx=\pi^2-t^2\), for all \(t\ge-\pi\), then \(f\left(-\frac{\pi}{3}\right)\) is equal to: