List of top Mathematics Questions asked in JEE Main

Area bounded by y = -2|x| and y = x|x| is:

If |a| = 2, |b| = 3 and a = b × 2, then minimum value of \(|\hat{c} - a|^2\) is:

Consider the equation ax² + bx + c = 0 . Find probability if a, b, c ∈ A where A = {1,2,3, ... , 8} that the equation has equal roots.

Consider a equation  P(x)= ax² + bx + c =0. If a,b,c ∈ A, were A = {1, 2, 3, 4, 5, 6} . Then the probability that P(x) has real and distinct roots?

If S = {2, 4, 8, 16, ..., 512}. If S is broken in 3 equal subsets A, B and C such that A∩B = B∩C = C∩A = φ and A∪B∪C = S then maximum number of ways to break is

\(\left( \frac{3^{\frac{1}{5}}}{x}+\frac{2x}{5^\frac{1}{3}} \right)^{12}\)Find which term is constant.

Let image of point(8,5,7) with respect to line \(\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-2}{5}\) is (α,β,γ). Then, α+β+γ is equal to______.

A line L is perpendicular to y = 2x + 10 such that it touches the parabola y² = 4(x – g). Then the distance between point of contact and origin is equal to

A ray of light coming from (3, 1) incident on 2x + y = 6 and deflected ray passing through (7, 2). If equation of incident ray is ax + by + 1 = 0, then a² + b² + 3ab =

If the complex number (1 + 2i cosθ) / (1 - 3i cosθ) is purely imaginary, then find the number of values of θ in the interval [-2π, 2π].

If \(\frac{1}{(1+d)(1+2d)}+\frac{1}{(1+2d)(1+3d)}+...+\frac{1}{(1+9d)(1+10d)}=1,\) then the value of 50d is____. (d > 0)

A ray of light passing through (1, 2) after reflecting on x-axis at point Q passes through R(3, 4). If S(h, k) is such that PQRS is a parallelogram, then find the value of hk².

For 8^2x - 16.8^x + 48 = 0, the sum of values of x is equal to:

Let,\(f(\theta)=\frac{sin^4\theta+3cos^2\theta}{sin^4\theta+cos^2\theta},\)then range of f(θ) ∈ [a, b]. The sum of infinite G.P., where first term is 64 and common ratio is a/b is equal to:

A=\(\begin{bmatrix}   2 & -1 \\   1 & 1  \end{bmatrix}\)if sum of diagonal elements of A¹³ is 3ⁿ then n equal to:

A tower stands at the center of a circular park. $A$ and $B$ are two points on the boundary of the park such that $AB=a$ subtends an angle ${60}^{\circ }$ of at the foot of the tower and the angle of elevation of the top of the tower from $A$ or $B$ is ${30}^{\circ }$. The height of the tower is

If the angle $\theta$ between the line $\frac{x+1}{1}=\frac{y-1}{2}=\frac{z-2}{2}$ and the plane $2x-y+\sqrt{\lambda z}+4=0$ is such that $\sin \theta =\frac{1}{3},$ then value of $\lambda$ is

The general solution of $\cot \theta +\tan \theta =2$

Two adjacent sides of a parallelogram ABCD are given by  $\overrightarrow{AB}=2\hat{i}+10\hat{j}+11\hat{k} and \overrightarrow{AD}=-\hat{i}+2\hat{j}+2\hat{k}$.The side AD is rotated by an acute angel $\alpha$ in the plane of the parallelogram so that AD becomes AD'. If AD' makes a right angle with the side AB, then the cosine of the angle $\alpha$ is given by;

From an airplane flying, vertically above a horizontal road, the angles of depression of two consecutive stones on the same side of the airplane are observed to be 30° and 60° respectively. The height at which the airplane is flying in km is :

Let a, b, c be such that b $(a+c)\ne 0.$ If $\left|\begin{array}{ccc}a& a+1& a-1\\ -b& b+1& b-1\\ c& c-1& c+1\end{array}\right|+\left|\begin{array}{ccc}a+1& b+1& c-1\\ a-1& b-1& c+1\\ (-1{)}^{n+2}a& (-1{)}^{n+1}b& (-1{)}^{n}c\end{array}\right|=0$Then the value of $n$ is?

The rank of $\left[\begin{array}{lll}4& 0& 0\\ 0& 3& 0\\ 0& 0& 5\end{array}\right]$ is equal to

If ⁿ⁺¹C_r+1: ⁿC_r: ^n-1C_r-1 = 55: 35: 21 then the value of n + r is _____.

Find the domain for function $$f(x)=[\sin x]\cos \left(\frac{\pi }{[x-1]}\right)$$