List of top Mathematics Questions asked in JEE Main

Let b₁b₂b₃b₄ be a 4-element permutation with b_i{1, 2, 3,…..,100} for 1≤i≤4 and b_i ≠b_j for i≠ j, such that either b₁, b₂, b₃ are consecutive integers or b₂, b₃, b₄ are consecutive integers. Then the number of such permutations b₁b₂b₃b₄ is equal to _______ .

Let Q be the foot of perpendicular drawn from the point P(1, 2, 3) to the plane x + 2y + z = 14. If R is a point on the plane such that ∠PRQ = 60°, then the area of ΔPQR is equal to :

The area of the region bounded by y² = 8x and y² = 16(3 – x) is equal to

The total number of three-digit numbers, with one digit repeated exactly two times, is ______.

Let A = {n∈N : H.C.F. (n, 45) = 1} and
Let B = {2k :k∈ {1, 2, …,100}}. Then the sum of all the elements of \(A∩B\) is ___________

Let R₁ = {(a, b) ∈ N × N : |a – b| ≤ 13} and R₂ = {(a, b) ∈ N × N : |a – b| ≠ 13}. Then on N:

If A =\(\sum_{n=1}^{\infty}\)\(\frac{1}{( 3 + (-1)^n)^n}\) and B = \(\sum_{n=1}^{\infty}\)\(\frac{(-1)^n}{( 3 + (-1)^n)^n}\) ,
then A/B is equal to :

Let the eccentricity of the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) be \(\frac{5}{4}\). If the equation of the normal at the point \((\frac{8}{√5}, \frac{12}{5})\) on the hyperbola is 8√5 x + β y = λ, then λ – β is equal to ____.

If the lines
\(\stackrel{→}{r}= ( \hat{i} - \hat{j} + \hat{k} ) + λ (\hat{3j} - \hat{k} )= ( \hat{i} - \hat{j} + \hat{k} ) + λ (\hat{3j} - \hat{k} )\)
and
\(\stackrel{→}{r} = ( \alpha \hat{i} - \hat{j} ) + μ( \hat{2j} - \hat{3k} )\)
are co-planer , then the distance of the plane containing these two lines from the point \(( α , 0 , 0 )\) is :

\(\lim_{{x \to 0}} \limits\) \(\frac{cos(sin x) - cos x }{x^4}\) is equal to :

If the sum of the co-efficients of all the positive even powers of x in the binomial expansion of \((2x^3+\frac{3}{x})^{10} \) is 5¹⁰ – β·3⁹, the β is equal to ____.

Let \(\vec a=a_1\hat i+a_2\hat j+a_3\hat k\), \(a_i>0,\ i=1, 2, 3\) be a vector which makes equal angles with the coordinate axes OX, OY and OZ. Also, let the projection of \(\vec a\) on the vector \(3\hat i+4\hat j\) be 7. Let \(\vec b\) be a vector obtained by rotating \(\vec a\) with 90°. If \(\vec a,\vec b\) and x-axis are co-planar, then projection of a vector \(\vec b\) on \(3\hat i+4\hat j\) is equal to :

If the mean deviation about the mean of the numbers 1, 2, 3, …. n, where n is odd, is \(\frac{5(n + 1)}{n}\), then n is equal to ______.

Let a circle C touch the lines L₁ : 4x – 3y +K₁ = 0 and L₂ : 4x – 3y + K₂ = 0, K₁, K₂∈R. If a line passing through the centre of the circle C intersects L₁ at (–1, 2) and L₂ at (3, –6), then the equation of the circle C is :

Let f(x) = min {1, 1 + x sin x}, 0 ≤ x ≤ 2π. If m is the number of points, where f is not differentiable, and n is the number of points, where f is not continuous, then the ordered pair (m, n) is equal to

Let l₁ be the line in xy-plane with x and y intercepts ⅛ and \(\frac{1}{4√2} \) respectively and l₂ be the line in zx-plane with x and z intercepts -⅛ and \(−\frac{1}{6√3}\) respectively. If d is the shortest distance between the line l₁ and l₂, then d^–2 is equal to ______.

The value of \(\int\limits_0^π \frac {e^{cos⁡\ x} sin⁡x}{(1+cos^2⁡x)(e^{cos⁡\ x}+e^{−cos⁡\ x})}dx\) is equal to :

If \(y = m_1x + c_1 \)and \(y = m_2x + c_2\), \(m_1≠m_2\) are two common tangents of circle \(x_2 + y_2 = 2\) and parabola \(y^2 = x\), then the value of \(8|m_1m_2|\) is equal to :

If m is the slope of a common tangent to the curves
\(\frac{x²}{16} + \frac{y²} {9} = 1\)
and x² + y² = 12, then 12m² is equal to:

Let
ƒ : R → R
be defined as f(x) = x -1 and
g : R - { 1, -1 } → R
be defined as
g(x) = \(\frac{x²}{x² - 1}\)
Then the function fog is :

\(lim(x→\frac{x}{2}) tan^2x((2sin^2x+3sinx+4)^{\frac{1}{2}}-(sin^2x+6sinx+2)^{\frac{1}{2}}\) is equal to.

Let d be the distance between the foot of perpendiculars of the point P(1, 2, –1) and Q(2, –1, 3) on the plane –x + y + z = 1. Then d²is equal to ____.

If the system of equations αx + y + z = 5, x + 2y + 3z = 4, x + 3y +5z = β has infinitely many solutions, then the ordered pair (α, β) is equal to:

Let
A=\(\begin{bmatrix} 2 & -1 \\ 0 & 2 \end{bmatrix}\)
If B = I – ⁵C₁(adjA) + ⁵C₂(adjA)² – …. – ⁵C₅(adjA)⁵, then the sum of all elements of the matrix B is

The function \(f(x)=xe^{x(1-x)}\),x∈R is