List of top Mathematics Questions asked in JEE Main

If the function \(f(x)=\begin{cases}-x, & x\lt 1\\ a+\cos^{-1}(x+b), & 1\le x\le 2\end{cases}\) is differentiable at \(x=1\), then \(\frac ab\) is equal to :

If \(2\int_0^1\tan^{-1}x\,dx=\int_0^1\cot^{-1}(1-x+x^2)\,dx\), then \(\int_0^1\tan^{-1}(1-x+x^2)\,dx\) is equal to :

If \(P=\begin{bmatrix}\frac{\sqrt3}{2}&\frac12\\-\frac12&\frac{\sqrt3}{2}\end{bmatrix},\ A=\begin{bmatrix}1&1\\0&1\end{bmatrix}\) and \(Q=PAP^{T}\), then \(P^{T}Q^{2015}P\) is :

For \(x\in\mathbf{R},\ x\neq-1\), if \((1+x)^{2016}+x(1+x)^{2015}+x^2(1+x)^{2014}+\ldots+x^{2016}=\sum_{i=0}^{2016}a_i\,x^i\), then \(a_{17}\) is equal to :

The value of \(\sum_{r=1}^{15}r^2\left(\frac{{}^{15}C_r}{{}^{15}C_{r-1}}\right)\) is equal to :

Let \(x,\ y,\ z\) be positive real numbers such that \(x+y+z=12\) and \(x^3y^4z^5=(0.1)(600)^3\). Then \(x^3+y^3+z^3\) is equal to :

If the equations \(x^2+bx-1=0\) and \(x^2+x+b=0\) have a common root different from \(-1\), then \(|b|\) is equal to :

The point represented by \(2+i\) in the Argand plane moves 1 unit eastwards, then 2 units northwards and finally from there \(2\sqrt{2}\) units in the south-westwards direction. Then its new position in the Argand plane is at the point represented by :

Consider : \(f(x) = \tan^{-1}\left(\sqrt{\frac{1+\sin x}{1-\sin x}}\right),\ x \in \left(0, \frac{\pi}{2}\right)\). A normal to \(y = f(x)\) at \(x = \frac{\pi}{6}\) also passes through the point:

A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pillar is \(30^\circ\). After walking for 10 minutes from A in the same direction, at a point B, he observes that the angle of elevation of the top of the pillar is \(60^\circ\). Then the time taken (in minutes) by him, from B to reach the pillar, is :

If the line, \(\frac{x-3}{2}=\frac{y+2}{-1}=\frac{z+4}{3}\) lies in the planes, \(lx+my-z=9\), then \(l^2+m^2\) is equal to :

The distance of the point \((1,-5,9)\) from the plane \(x-y+z=5\) measured along the line \(x=y=z\) is :

Let \(P\) be the point on the parabola, \(y^2=8x\) which is at a minimum distance from the centre \(C\) of the circle, \(x^2+(y+6)^2=1\). Then the equation of the circle, passing through \(C\) and having its centre at \(P\) is:

\(\lim_{n\to\infty}\left(\frac{(n+1)(n+2)\dots3n}{n^{2n}}\right)^{\frac1n}\) is equal to:

The integral \(\int\frac{2x^{12}+5x^{9}}{(x^{5}+x^{3}+1)^{3}}\,dx\) is equal to :

The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal to half of the distance between its foci, is :

Let \(\vec a,\ \vec b\) and \(\vec c\) be three unit vectors such that \(\vec a\times(\vec b\times\vec c)=\frac{\sqrt3}{2}(\vec b+\vec c)\). If \(\vec b\) is not parallel to \(\vec c\), then the angle between \(\vec a\) and \(\vec b\) is:

If one of the diameters of the circle, given by the equation, \(x^2+y^2-4x+6y-12=0\), is a chord of a circle \(S\), whose centre is at \((-3,2)\), then the radius of \(S\) is :

If \(0\le x<2\pi\), then the number of real values of \(x\), which satisfy the equation \(\cos x+\cos 2x+\cos 3x+\cos 4x=0\) is:

If \(f(x)+2f\left(\frac1x\right)=3x,\ x\ne0\), and \(S=\{x\in\mathbf{R}: f(x)=f(-x)\}\); then \(S\) :

Let two fair six-faced dice \(A\) and \(B\) be thrown simultaneously. If \(E_1\) is the event that die \(A\) shows up four, \(E_2\) is the event that die \(B\) shows up two and \(E_3\) is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true?

A value of \(\theta\) for which \(\frac{2+3i\sin\theta}{1-2i\sin\theta}\) is purely imaginary, is :

The area (in sq. units) of the region \(\{(x,y): y^2\ge 2x\ \text{and}\ x^2+y^2\le 4x,\ x\ge0,\ y\ge0\}\) is :

If the tangent at a point $P$, with parameter $t$, on the curve $x = 4t^2 + 3, y = 8t^3 - 1, t \in R$, meets the curve again at a point $Q$, then the coordinates of $Q$ are :

A hyperbola whose transverse axis is along the major axis of the conic, $\frac{x^2}{3} + \frac{y^2}{4} = 4 $ and has vertices at the foci of this conic. If the eccentricity of the hyperbola is $\frac{3}{2}$, then which of the following points does NOT lie on it ?