List of top Mathematics Questions asked in JEE Main

If the normal at an end of a latus rectum of an ellipse passes through an extremity of the minor axis, then the eccentricity \(e\) of the ellipse satisfies :

The common difference of the A.P. \(b_1,b_2,\ldots,b_m\) is 2 more than the common difference of A.P. \(a_1,a_2,\ldots,a_n\). If \(a_{40}=-159\), \(a_{100}=-399\) and \(b_{100}=a_{70}\), then \(b_1\) is equal to :

Let \(\theta=\frac{\pi}{5}\) and \(A=\begin{bmatrix}\cos\theta & \sin\theta\\ -\sin\theta & \cos\theta\end{bmatrix}\). If \(B=A+A^4\), then det (B) :

If the constant term in the binomial expansion of \(\left(\sqrt{x}-\frac{k}{x^2}\right)^{10}\) is 405, then \(|k|\) equals :

Let \(z=x+iy\) be a non-zero complex number such that \(z^2=i|z|^2\), where \(i=\sqrt{-1}\), then z lies on the :

Let \(f:\mathbb{R}\to\mathbb{R}\) be a function defined by \(f(x)=\max\{x,x^2\}\). Let S denote the set of all points in \(\mathbb{R}\), where f is not differentiable. Then :

For all twice differentiable functions \(f:\mathbb{R}\to\mathbb{R}\), with \(f(0)=f(1)=f'(0)=0\)

Let L denote the line in the xy-plane with x and y intercepts as 3 and 1 respectively. Then the image of the point \((-1,-4)\) in this line is :

For a suitably chosen real constant a, let a function, \(f:\mathbb{R}-\{-a\}\to\mathbb{R}\) be defined by \(f(x)=\frac{a-x}{a+x}\). Further suppose that for any real number \(x\ne -a\) and \(f(x)\ne -a\), \((f\circ f)(x)=x\). Then \(f\left(-\frac12\right)\) is equal to :

The area (in sq. units) of the region enclosed by the curves \(y=x^2-1\) and \(y=1-x^2\) is equal to :

The integral
\(\int_1^2 e^x \cdot x^x\,(2+\log_e x)\,dx\)
equals :

The angle of elevation of the top of a hill from a point on the horizontal plane passing through the foot of the hill is found to be \(45^\circ\). After walking a distance of 80 meters towards the top, up a slope inclined at an angle of \(30^\circ\) to the horizontal plane, the angle of elevation of the top of the hill becomes \(75^\circ\). Then the height of the hill (in meters) is _______.

If \(\vec{a}\) and \(\vec{b}\) are unit vectors, then the greatest value of
\(\sqrt{3}\,|\vec{a}+\vec{b}|+|\vec{a}-\vec{b}|\)
is _______.

Let AD and BC be two vertical poles at A and B respectively on a horizontal ground. If AD = 8 m, BC = 11 m and AB = 10 m; then the distance (in meters) of a point M on AB from the point A such that \(MD^2+MC^2\) is minimum is _______.

The negation of the Boolean expression \(p\vee(\sim p\wedge q)\) is equivalent to :

Let \(L_1\) be a tangent to the parabola \(y^2=4(x+1)\) and \(L_2\) be a tangent to the parabola \(y^2=8(x+2)\) such that \(L_1\) and \(L_2\) intersect at right angles. Then \(L_1\) and \(L_2\) meet on the straight line :

Which of the following points lies on the locus of the foot of perpedicular drawn upon any tangent to the ellipse,
\(\frac{x^2}{4}+\frac{y^2}{2}=1\)
from any of its foci?

The shortest distance between the lines
\(\frac{x-1}{0}=\frac{y+1}{-1}=\frac{z}{1}\)
and \(x+y+z+1=0,\ 2x-y+z+3=0\) is :

Let \(f:R\to R\) be defined as
\(f(x)=\begin{cases}x^5\sin\left(\frac{1}{x}\right)+5x^2, & x\lt 0\\ 0, & x=0\\ x^5\cos\left(\frac{1}{x}\right)+\lambda x^2, & x\gt 0\end{cases}\)
The value of \(\lambda\) for which \(f''(0)\) exists, is _______.

If \(\{p\}\) denotes the fractional part of the number \(p\), then
\(\left\{\frac{3^{200}}{8}\right\}\), is equal to :

A ray of light coming from the point \((2,\,2\sqrt{3})\) is incident at an angle \(30^\circ\) on the line \(x=1\) at the point A. The ray gets reflected on the line \(x=1\) and meets x-axis at the point B. Then, the line AB passes through the point :

The general solution of the differential equation
\(\sqrt{1+x^2+y^2+x^2y^2}+xy\dfrac{dy}{dx}=0\) is :
(where C is a constant of integration)

If \(I_1=\displaystyle\int_0^1(1-x^{50})^{100}dx\) and \(I_2=\displaystyle\int_0^1(1-x^{50})^{101}dx\) such that \(I_2=\alpha I_1\) then \(\alpha\) equals to :

\(\displaystyle\lim_{x\to 1}\left(\frac{\int_{0}^{(x-1)^2} t\cos\left(t^2\right)dt}{(x-1)\sin(x-1)}\right)\)

If \(f(x+y)=f(x)f(y)\) and \(\displaystyle\sum_{x=1}^{\infty}f(x)=2\), \(x,y\in N\), where N is the set of all natural number, then the value of \(\frac{f(4)}{f(2)}\) is :