List of top Mathematics Questions asked in JEE Main

Suppose A is any \(3 \times 3\) non-singular matrix and \((A - 3I)(A - 5I) = O\) where \(I = I_3\) and \(O = O_3\). If \(\alpha A + \beta A^{-1} = 4I\), then \(\alpha + \beta\) is equal to :

Let \(f(x) = \begin{cases} (x-1)^{\frac{1}{2-x}}, & x > 1,\ x \neq 2 \\ k, & x = 2 \end{cases}\)
The value of k for which f is continuous at \(x = 2\) is :

If \(\beta\) is one of the angles between the normals to the ellipse, \(x^2 + 3y^2 = 9\) at the points \((3\cos\theta, \sqrt3\sin\theta)\) and \((-3\sin\theta, \sqrt3\cos\theta)\); \(\theta \in \left(0, \frac{\pi}{2}\right)\); then \(\frac{2\cot\beta}{\sin2\theta}\) is equal to :

An angle between the plane, \(x + y + z = 5\) and the line of intersection of the planes, \(3x + 4y + z - 1 = 0\) and \(5x + 8y + 2z + 14 = 0\), is :

If \(n\) is the degree of the polynomial,
\(\left[\frac{2}{\sqrt{5x^3+1}-\sqrt{5x^3-1}}\right]^8 + \left[\frac{2}{\sqrt{5x^3+1}+\sqrt{5x^3-1}}\right]^8\)
and \(m\) is the coefficient of \(x^n\) in it, then the ordered pair \((n, m)\) is equal to :

If \((p \wedge \sim q) \wedge (p \wedge r) \rightarrow\ \sim p \vee q\) is false, then the truth values of \(p, q\) and \(r\) are, respectively :

\(n\)-digit numbers are formed using only three digits 2, 5 and 7. The smallest value of \(n\) for which 900 such distinct numbers can be formed, is :

A circle passes through the points \((2, 3)\) and \((4, 5)\). If its centre lies on the line, \(y - 4x + 3 = 0\), then its radius is equal to :

Consider the following two binary relations on the set \(A = \{a, b, c\}\) :
\(R_1 = \{(c, a), (b, b), (a, c), (c, c), (b, c), (a, a)\}\) and
\(R_2 = \{(a, b), (b, a), (c, c), (c, a), (a, a), (b, b), (a, c)\}\).
Then :

Let \(A\) be a matrix such that \(A\cdot\begin{bmatrix}1&2\\0&3\end{bmatrix}\) is a scalar matrix and \(|3A|=108\). Then \(A^2\) equals :

A box 'A' contains 2 white, 3 red and 2 black balls. Another box 'B' contains 4 white, 2 red and 3 black balls. If two balls are drawn at random, without replacement, from a randomly selected box and one ball turns out to be white while the other ball turns out to be red, then the probability that both balls are drawn from box 'B' is :

The mean of set of 30 observations is 75. If each observation is multiplied by a non-zero number \(\lambda\) and then each of them is decreased by 25, their mean remains the same. Then \(\lambda\) is equal to :

If \(x_1,x_2,\ldots,x_n\) and \(\frac{1}{h_1},\frac{1}{h_2},\ldots,\frac{1}{h_n}\) are two A.P.s such that \(x_3=h_2=8\) and \(x_8=h_7=20\), then \(x_5\cdot h_{10}\) equals :

Let \(y=y(x)\) be the solution of the differential equation \(\frac{dy}{dx}+2y=f(x)\), where \(f(x)=\begin{cases}1, & x\in[0,1]\\ 0, & \text{otherwise}\end{cases}\) If \(y(0)=0\), then \(y\left(\frac32\right)\) is :

If \(x^2 + y^2 + \sin y = 4\), then the value of \(\frac{d^2y}{dx^2}\) at the point \((-2, 0)\) is :

If \(f\left(\frac{x-4}{x+2}\right)=2x+1\), \((x\in\mathbf{R}-\{1,-2\})\), then \(\int f(x)\,dx\) is equal to :
(where C is a constant of integration)

Let S be the set of all real values of k for which the system of linear equations
\(x+y+z=2\)
\(2x+y-z=3\)
\(3x+2y+kz=4\)
has a unique solution. Then S is :

If \(\vec{a},\vec{b}\), and \(\vec{c}\) are unit vectors such that \(\vec{a}+2\vec{b}+2\vec{c}=\vec{0}\), then \(|\vec{a}\times\vec{c}|\) is equal to :

If \(\lambda\in\mathbf{R}\) is such that the sum of the cubes of the roots of the equation, \(x^2+(2-\lambda)x+(10-\lambda)=0\) is minimum, then the magnitude of the difference of the roots of this equation is :

The area (in sq. units) of the region \(\{x\in\mathbf{R}: x\ge0,\ y\ge0,\ y\ge x-2\ \text{and}\ y\le\sqrt{x}\}\), is :

If \(f(x)=\begin{vmatrix}\cos x & x & 1\\ 2\sin x & x^2 & 2x\\ \tan x & x & 1\end{vmatrix}\), then \(\lim_{x\to0}\frac{f'(x)}{x}\)

In a triangle ABC, coordinates of A are \((1, 2)\) and the equations of the medians through B and C are respectively, \(x + y = 5\) and \(x = 4\). Then area of \(\Delta\) ABC (in sq. units) is :

If a right circular cone, having maximum volume, is inscribed in a sphere of radius 3 cm, then the curved surface area (in cm²) of this cone is :

Let \(S = \{(\lambda, \mu) \in \mathbf{R}\times\mathbf{R} : f(t) = (|\lambda|e^{|t|} - \mu)\cdot\sin(2|t|),\ t\in\mathbf{R},\) is a differentiable function\(\}\). Then S is a subset of :

The value of the integral \(\int_{-\pi/2}^{\pi/2} \sin^4 x\left(1+\log\left(\frac{2+\sin x}{2-\sin x}\right)\right)dx\) is :