List of top Mathematics Questions asked in JEE Main

The acute angle between two lines such that the direction cosines \(l, m, n\), of each of them satisfy the equations \(l + m + n = 0\) and \(l^2 + m^2 - n^2 = 0\) is :

The number of solutions of the equation, \(\sin^{-1}x = 2\tan^{-1}x\) (in principal values) is :

The number of ways in which an examiner can assign 30 marks to 8 questions, giving not less than 2 marks to any question, is :

If a complex number \(z\) statisfies the equation \(x + \sqrt{2}|z + 1| + i = 0\), then \(|z|\) is equal to :

Given sum of the first \(n\) terms of an A.P. is \(2n + 3n^2\). Another A.P. is formed with the same first term and double of the common difference, the sum of \(n\) terms of the new A.P. is :

The sum \(\dfrac{3}{1^2} + \dfrac{5}{1^2+2^2} + \dfrac{7}{1^2+2^2+3^2} + \cdots\) upto 11-terms is :

If \(\alpha\) and \(\beta\) are roots of the equation \(x^2 + px + \frac{3p}{4} = 0\), such that \(|\alpha - \beta| = \sqrt{10}\), then \(p\) belongs to the set :

The probability of a man hitting a target is \(\frac{2}{5}\). He fires at the target \(k\) times (\(k\), a given number). Then the minimum \(k\), so that the probability of hitting the target at least once is more than \(\frac{7}{10}\), is :

Let \(\vec{a} = 2\hat{i} - \hat{j} + \hat{k}\), \(\vec{b} = \hat{i} + 2\hat{j} - \hat{k}\) and \(\vec{c} = \hat{i} + \hat{j} - 2\hat{k}\) be three vectors. A vector of the type \(\vec{b} + \lambda\vec{c}\) for some scalar \(\lambda\), whose projection on \(\vec{a}\) is of magnitude \(\sqrt{\frac{2}{3}}\) is :

The vector \((\hat{i} \times \vec{a} \cdot \vec{b})\hat{i} + (\hat{j} \times \vec{a}\vec{b})\hat{j} + (\hat{k} \times \vec{a} \cdot \vec{b})\hat{k}\) is equal to:

If \(x=\int_0^y\frac{dt}{\sqrt{1+t^2}}\), then \(\frac{d^2y}{dx^2}\) is equal to :

If the lines \(\frac{x+1}{2} = \frac{y-1}{1} = \frac{z+1}{3}\) and \(\frac{x+2}{2} = \frac{y-k}{3} = \frac{z}{4}\) are coplanar, then the value of \(k\) is :

The area bounded by the curve \(y = \ln(x)\) and the lines \(y = 0\), \(y = \ln(3)\) and \(x = 0\) is equal to:

A vector \(\vec{n}\) is inclined to \(x\)-axis at \(45^\circ\), to \(y\)-axis at \(60^\circ\) and at an acute angle to \(z\)-axis. If \(\vec{n}\) is a normal to a plane passing through the point \((\sqrt{2}, -1, 1)\) then the equation of the plane is :

The matrix \(A^2+4A-5I\), where \(I\) is identity matrix and \(A=\begin{bmatrix}1&2\\4&-3\end{bmatrix}\), equals :

The mean of a data set consisting of 20 observations is 40. If one observation 53 was wrongly recorded as 33, then the correct mean will be :

If \(a,b,c\) are sides of a scalene triangle, then the value of \(\begin{vmatrix}a&b&c\\b&c&a\\c&a&b\end{vmatrix}\) is :

Let \(A=\{1,2,3,4\}\) and \(R:A\to A\) be the relation defined by \(R=\{(1,1),(2,3),(3,4),(4,2)\}\). The correct statement is :

Let \(f(x)=\frac{x^2-x}{x^2+2x}\), \(x\ne0,-2\). Then \(\frac{d}{dx}\left[f^{-1}(x)\right]\) (wherever it is defined) is equal to :

Statement-1: The statement \(A\to(B\to A)\) is equivalent to \(A\to(A\vee B)\).
Statement-2: The statement \(\sim[(A\wedge B)\to(\sim A\vee B)]\) is a Tautology.

If each of the lines \(5x+8y=13\) and \(4x-y=3\) contains a diameter of the circle \(x^2+y^2-2(a^2-7a+11)x-2(a^2-6a+6)y+b^3+1=0\), then :

Equation of the line passing through the points of intersection of the parabola \(x^2=8y\) and the ellipse \(\frac{x^2}{3}+y^2=1\) is :

If \(a\) and \(c\) are positive real numbers and the ellipse \(\frac{x^2}{4c^2}+\frac{y^2}{c^2}=1\) has four distinct points in common with the circle \(x^2+y^2=9a^2\), then

Statement-1: The slope of the tangent at any point \(P\) on a parabola, whose axis is the axis of \(x\) and vertex is at the origin, is inversely proportional to the ordinate of the point \(P\).
Statement-2: The system of parabolas \(y^2=4ax\) satisfies a differential equation of degree 1 and order 1.

The value of \(\lim_{x\to0}\frac1x\left[\tan^{-1}\left(\frac{x+1}{2x+1}\right)-\frac\pi4\right]\) is :