List of top Mathematics Questions asked in JEE Main

Let \(S=\left\{\begin{pmatrix}a_{11}&a_{12}\\a_{21}&a_{22}\end{pmatrix}: a_{ij}\in\{0,1,2\},\ a_{11}=a_{22}\right\}\). Then the number of non-singular matrices in the set \(S\) is :

Consider the function : \(f(x)=[x]+|1-x|,\ -1\le x\le3\) where \([x]\) is the greatest integer function. Statement 1 : \(f\) is not continuous at \(x=0,1,2\) and \(3\) Statement 2 : \(f(x)=\begin{cases}-x, & -1\le x\lt0\\ 1-x, & 0\le x\lt1\\ 1+x, & 1\le x\lt2\\ 2+x, & 2\le x\le3\end{cases}\)

If for positive integers \(r \gt 1, n \gt 2\), the coefficients of the \((3r)^{\text{th}}\) and \((r+2)^{\text{th}}\) powers of \(x\) in the expansion of \((1 + x)^{2n}\) are equal, then \(n\) is equal to:

Consider the system of equations : \(x + ay = 0,\ y + az = 0\) and \(z + ax = 0\). Then the set of all real values of 'a' for which the system has a unique solution is:

If a circle of unit radius is divided into two parts by an arc of another circle subtending an angle \(60^\circ\) on the circumference of the first circle, then the radius of the arc is:

Let \(A = \{\theta : \sin(\theta) = \tan(\theta)\}\) and \(B = \{\theta : \cos(\theta) = 1\}\) be two sets. Then:

A point on the ellipse, \(4x^2 + 9y^2 = 36\), where the normal is parallel to the line, \(4x - 2y - 5 = 0\), is :

5 - digit numbers are to be formed using \(2, 3, 5, 7, 9\) without repeating the digits. If \(p\) be the number of such numbers that exceed \(20000\) and \(q\) be the number of those that lie between \(30000\) and \(90000\), then \(p : q\) is:

The value of \(1^2 + 3^2 + 5^2 + \ldots\ldots + 25^2\) is :

Given a sequence of 4 numbers, first three of which are in G.P. and the last three are in A.P. with common difference six. If first and last terms of this sequence are equal, then the last term is :

If \(p\) and \(q\) are non-zero real numbers and \(\alpha^3 + \beta^3 = -p,\ \alpha\beta = q\), then a quadratic equation whose roots are \(\frac{\alpha^2}{\beta},\ \frac{\beta^2}{\alpha}\) is :

Let \(z\) satisfy \(|z| = 1\) and \(z = 1 - \bar{z}\). Statement 1 : \(z\) is a real number. Statement 2 : Principal argument of \(z\) is \(\frac{\pi}{3}\).

A, B, C try to hit a target simultaneously but independently. Their respective probabilities of hitting the targets are \(\frac{3}{4},\frac{1}{2},\frac{5}{8}\). The probability that the target is hit by A or B but not by C is :

If the projections of a line segment on the \(x\), \(y\) and \(z\)-axes in 3-dimensional space are 2, 3 and 6 respectively, then the length of the line segment is :

The area under the curve \(y=|\cos x-\sin x|,\ 0\le x\le\frac{\pi}{2}\), and above \(x\)-axis is :

The value of \(\displaystyle\int_{-\pi/2}^{\pi/2}\dfrac{\sin^2 x}{1+2^x}\,dx\) is :

If a curve passes through the point \(\left(2, \frac{7}{2}\right)\) and has slope \(\left(1-\frac{1}{x^2}\right)\) at any point \((x, y)\) on it, then the ordinate of the point on the curve whose abscissa is \(-2\) is :

If the curves \(\frac{x^2}{\alpha}+\frac{y^2}{4}=1\) and \(y^3=16x\) intersect at right angles, then a value of \(\alpha\) is :

Statement-1: The system of linear equations
\(x+(\sin\alpha)y+(\cos\alpha)z=0\)
\(x+(\cos\alpha)y+(\sin\alpha)z=0\)
\(x-(\sin\alpha)y-(\cos\alpha)z=0\)
has a non-trivial solution for only one value of \(\alpha\) lying in the interval \(\left(0, \frac{\pi}{2}\right)\).
Statement-2: The equation in \(\alpha\)
\(\begin{vmatrix}\cos\alpha & \sin\alpha & \cos\alpha\\ \sin\alpha & \cos\alpha & \sin\alpha\\ \cos\alpha & -\sin\alpha & -\cos\alpha\end{vmatrix}=0\)
has only one solution lying in the interval \(\left(0, \frac{\pi}{2}\right)\)

Let \(f\) be a composite function of \(x\) defined by \(f(u)=\frac{1}{u^2+u-2},\ u(x)=\frac{1}{x-1}\). Then the number of points \(x\) where \(f\) is discontinuous is :

\(S=\tan^{-1}\left(\frac{1}{n^2+n+1}\right)+\tan^{-1}\left(\frac{1}{n^2+3n+3}\right)+\ldots+\tan^{-1}\left(\frac{1}{1+(n+19)(n+20)}\right)\), then \(\tan S\) is equal to :

Let A, other than I or \(-I\), be a \(2 \times 2\) real matrix such that \(A^2=I\), I being the unit matrix. Let \(\mathrm{Tr}(A)\) be the sum of diagonal elements of A.
Statement-1: \(\mathrm{Tr}(A)=0\)
Statement-2: \(\det(A)=-1\)

If the median and the range of four numbers \(\{x, y, 2x+y, x-y\}\), where \(0 \lt y \lt x \lt 2y\), are 10 and 28 respectively, then the mean of the numbers is :

Let \(R=\{(x, y) : x, y \in N \text{ and } x^2-4xy+3y^2=0\}\), where \(N\) is the set of all natural numbers. Then the relation \(R\) is :

For integers \(m\) and \(n\), both greater than 1, consider the following three statements : \(P : m\) divides \(n\) \(Q : m\) divides \(n^2\) \(R : m\) is prime, then