List of top Mathematics Questions asked in JEE Main

If for $x \epsilon \left(0, \frac{1}{4}\right) ,$ the derivative of $ \tan^{-1} \left(\frac{6x \sqrt{x}}{1-9x^{3}}\right) $ is $\sqrt{x} . g(x)$, then $g(x)$ equals :

Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in $s m$) of the flower-bed, is :

Let $l_n = \int \tan^{n} x \, dx , (n > 1) . l_4 + l_6 = a \, \, \tan^5 \, x + bx^5 + C$, where $C$ is a constant of integration, then the ordered pair $(a, b)$ is equal to :

The integral $\int\limits^{\frac{3\, \pi}{4}}_{\frac{\pi}{4}} \frac{dx}{ 1 + \cos \, x}$ is equal to :

The area (in s units) of the region $\{ (x , y) : x \geq 0 , x + y \leq 3, x^2 \leq 4 y$ and $y \leq 1 + \sqrt{x} \}$ is

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

If $(27)^{999}$ is divided by $7$, then the remainder is :

If, for a positive integer n, the quadratic equation, $x(x+1)+(x+1)(x+2)+....+(x + \overline{ n - 1}) (x+ n)=10n$ has two consecutive integral solutions, then $n$ is equal to :

If two different numbers are taken from the set $\{0,1,2,3, \ldots \ldots, 10\}$then the probability that their sum as well as absolute difference are both multiple of $4$, is :

Let a vertical tower $AB$ have its end $A$ on the level ground. Let $C$ be the mid-point of $AB$ and $P$ be a point on the ground such that $AP = 2AB$. If $\angle BPC = \beta $, then tan $\beta$ is equal to :

Let $S_{n} = \frac{1}{1^{3}} + \frac{1+2}{1^{3} + 2^{3}} + \frac{1+2+3}{1^{3} + 2^{3} + 3^{3}} + ...... + \frac{1+2+...+n}{1^{3} + 2^{3} +.... +n^{3}} . $ . If $100 \, S_n = n , $ then $n$ is equal to :

Let $z \in C$, the set of complex numbers. Then the equation, $2 | z + 3i| - | z - i| = 0 $ represents :

The value of $\tan^{-1} \left[\frac{\sqrt{1+x^{2}} + \sqrt{1-x^{2}}}{\sqrt{1+x^{2}} - \sqrt{1-x^{2}}}\right] , \left|x\right| < \frac{1}{2}, x \ne0, $ is equal to :

Let $\omega$ be a complex number such that $2 \omega + 1 = z$ where $z = \sqrt{-3}$ ,If $\begin{vmatrix}1&1&1\\ 1&-\omega^{2} - 1 &\omega^{2}\\ 1&\omega^{2}& \omega^{7}\end{vmatrix} = 3 k , $ then $k$ is equal to :

The integral $\int \sqrt{ 1 + 2 \cot \, x (cosec \, x + \cot \, x) } dx \, \left( 0 < x < \frac{\pi}{2} \right)$ is equal to : (where $C$ is a constant of integration)

The value of $(^{21}C_{1} - ^{10}C_{1}) + (^{21}C_{2} - ^{10}C_{2}) + (^{21}C_{3} - ^{10}C_{3}) +(^{21}C_{4} - ^{10}C_{4}) +....+(^{21}C_{10} - ^{10}C_{10})$ is :

The contrapositive of the following statement, "If the side of a square doubles, then its area increases four times", is :

The angle of elevation of the top of a vertical tower from a point A, due east of it is \(45^\circ\). The angle of elevation of the top of the same tower from a point B, due south of A is \(30^\circ\). If the distance between A and B is \(54\sqrt2\) m, then the height of the tower (in metres), is :

If \(A\gt0,\ B\gt0\) and \(A+B=\frac{\pi}{6}\), then the minimum value of \(\tan A+\tan B\) is :

Let ABC be a triangle whose circumcentre is at P. If the position vectors of A, B, C and P are \(\vec{a},\ \vec{b},\ \vec{c}\) and \(\frac{\vec{a}+\vec{b}+\vec{c}}{4}\) respectively, then the position vector of the orthocentre of this triangle, is :

A straight line through origin O meets the lines \(3y=10-4x\) and \(8x+6y+5=0\) at points A and B respectively. Then O divides the segment AB in the ratio :

The number of distinct real values of \(\lambda\) for which the lines \(\frac{x-1}{1}=\frac{y-2}{2}=\frac{z+3}{\lambda^2}\) and \(\frac{x-3}{1}=\frac{y-2}{\lambda^2}=\frac{z-1}{2}\) are coplanar is :

A ray of light is incident along a line which meets another line, \(7x-y+1=0\), at the point \((0,1)\). The ray is then reflected from this point along the line, \(y+2x=1\). Then the equation of the line of incidence of the ray of light is :

Let \(f(x)=\sin^4x+\cos^4x\). Then \(f\) is an increasing function in the interval :

The solution of the differential equation \(\frac{dy}{dx}+\frac{y}{2}\sec x=\frac{\tan x}{2y}\), where \(0\le x\lt\frac{\pi}{2}\), and \(y(0)=1\), is given by :