List of top Mathematics Questions asked in JEE Main

A rod AB of length 4 units rests against a vertical wall with A on the horizontal floor. P is a point on AB such that AP : PB = 2 : 1. If the rod slides down along the wall in a vertical plane, then the point \(P(x,y)\) moves on the curve :

A line perpendicular to the line \(4x=3y\) is a tangent to the parabola \(y^2=3x+1\) at a point \(\mathrm{P}\) on it. If \(\mathrm{S}\) is the focus of the parabola, then the equation of the line \(\mathrm{SP}\) is :

Let \(f\) be a non-zero polynomial function such that \(f(3x)=f'(x)f''(x)\). Then the value of \(f(6)\) is :

Let \(\mathrm{A}(1,2)\) and \(\mathrm{B}(3,6)\) be two points on a circle of radius \(\mathrm{R}\), whose one of the diameters is along the line \(2x-y+4=0\). Then \(\mathrm{R}^2\) is equal to :

If \(\int\sqrt{\frac{\cos(x-\theta)}{\cos(x+\theta)}}\,\mathrm{d}x=\alpha\sin^{-1}\left(\frac{\sin x}{\cos\theta}\right)+\beta\log_{\mathrm e}\left|\cos x+\sqrt{\cos^{2}x-\sin^{2}\theta}\right|+\mathrm{C}\),
where C is a constant of integration and \(\frac{\pi}{6}<\theta<\frac{\pi}{4}\), then \(\alpha\sin\theta+\beta\cos\theta\) is equal to :

The sum of the series
\(\frac{1}{6}+\frac{5}{6^{2}}+\frac{19}{6^{3}}+\ldots+\frac{3^{10}-2^{10}}{3^{10}\cdot 2^{10}}\) is :

Let \(f(x)=\max\left\{x^{2},x^{3}\right\}\) for all \(x\in\mathbf{R}\). Then which of the following is NOT true ?

\(\lim_{x\to 0}\frac{1}{x^{2}}\left(\mathrm{e}^{x^{2}}-\cos\frac{x}{2}\right)\) is equal to :

If \(A=\begin{pmatrix}0&0&2\\1&0&0\\0&-1&0\end{pmatrix}\), then :

Let \(\alpha\) and \(\beta\) be the roots of the quadratic equation \(x^{2}+\sqrt{3}\,x+1=0\). Then \(\alpha^{2022}+\beta^{2022}\) is equal to :

The sum of all values of \(\lambda\), for which the system of equations
\(x+y+z=1\)
\(x+2y+4z=\lambda\)
\(x+4y+10z=\lambda^{2}\)
has infinitely many solutions, is :

The domain of the function, \(f(x)=\sqrt{\frac{\log_{0.6}|x-2|}{|x|}}\) is :

If the sum of mean and variance of a binomial distribution is 15 and the sum of their squares is 117, then the number of independent trials is equal to ________.

Let the equation of the plane passing through the points \((1,2,6),(2,5,7)\) and perpendicular to the plane \(4x-y+z=15\) be \(ax+by+cz+d=0\). If \(a, b, c, d \in \mathbf{Z}\) with \(\gcd(|a|,|b|,|c|)=1\), then \(|a+b+c+d|\) is equal to ________.

\(x^{2}+y^{2}-4x-2y-11=0\) is a circle to which tangents are drawn from the point \((4,5)\) which form a quadrilateral with a pair of radii. The area of this quadrilateral in square units is ________.

The number of real solutions in the interval \(\left[-\frac{3\pi}{2}, \frac{7\pi}{2}\right]\) of the equation \(4\sin^{2}x-8\sin x+3=0\) is ________.

Let \(A_{1}, A_{2}, A_{3}, \ldots \ldots\) be an increasing geometric progression. If \(\frac{1}{A_{4}}+\frac{1}{A_{8}}=\frac{10}{63}\) and \(A_{5} A_{7}=441\), then \(3\left(A_{2}+A_{4}\right)\) is equal to ________.

If \(x^{2}+x+1=0\), then \(-\left\{\left(x-\frac{1}{x}\right)^{2}+\left(x^{2}-\frac{1}{x^{2}}\right)^{2}+\left(x^{3}-\frac{1}{x^{3}}\right)^{2}\right\}\) is ________.

The length of the perpendicular from the point \((1,2,3)\) to the line \(\frac{-x+6}{-3}=\frac{y-7}{2}=\frac{z-7}{-2}\) is ________.

The values of \(x\), for which the vectors \(\vec{a}=\left(x^{2}-16\right) \hat{i}+4\hat{j}-\left(x^{2}-25\right) \hat{k}\) make acute angles with the (positive directions of) coordinate axes lie in :

Let \(\vec{a}, \vec{b}\) and \(\vec{c}\) be three vectors such that \(|\vec{a}|=|\vec{b}|=\frac{|\vec{c}|}{2}=1\). If \(\vec{a} \times(\vec{a} \times \vec{c})+\vec{b}=\overrightarrow{0}\), then the acute angle between \(\vec{a}\) and \(\vec{c}\) is :

Solution of the differential equation \(\left(1+y^{2}\right) \mathrm{d}x=\left(\tan^{-1}y-x\right) \mathrm{d}y\) is :
(where \(c\) is an arbitrary constant)

\(\int_{0}^{\pi} \sqrt{\frac{1+\cos 2x}{2}}\, \mathrm{d}x\) is ________.

The minimum value of \(9\tan^{2}\theta+4\cot^{2}\theta\) is ________.

If \(A=\begin{bmatrix}1&a\\0&1\end{bmatrix}\), then \(A^{k}\ (k\in\mathbf{N})\) is :