List of top Mathematics Questions asked in JEE Main

Consider two G.Ps. \(2, 2^2, 2^3, ….\) and \(4, 4^2, 4^3, …\) of \(60\) and n terms respectively. If the geometric mean of all the \(60 + n\) terms is \((2)^{\frac {225}{8}}\) then \(\sum_{k=1}^{n}k(n−k)\) 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 sum of the infinite series
\(1 + \frac{5}{6} + \frac{12}{6^2} + \frac{22}{6^3} + \frac{35}{6^4} +\frac{51}{6^5} + \frac{70}{6^6}+…..\)
is equal to

Let f : R → R be a function defined by:
\(ƒ(x) = (x-3)^{n_1} (x-5)^{n_2} , n_1, n_2 ∈ N\)
Then, which of the following is NOT true?

Let f be a real valued continuous function on [0, 1] and
\(f(x) = x + \int_{0}^{1} (x - t) f(t) \,dt\)
Then, which of the following points (x, y) lies on the curve y = f(x)?

If
\(\int_{0}^{2} (\sqrt{2x} - \sqrt{2x - x^2}) \,dx = \int_{0}^{1} \left(1 - \sqrt{1 - y^2} - \frac{y^2}{2}\right) \,dy + \int_{1}^{2} (2 - \frac{y^2}{2}) \,dy + I\)
then I equal is

Let P : y2 = 4ax, a > 0 be a parabola with focus S. Let the tangents to the parabola P make an angle of π/4 with the line y = 3x + 5 touch the parabola P at A and B. Then the value of a for which A, B and S are collinear is

Let a triangle ABC be inscribed in the circle
\(x² - \sqrt2(x+y)+y² = 0\)
such that ∠BAC= π/2. If the length of side AB is √2, then the area of the ΔABC is equal to :

The distance of the origin from the centroid of the triangle whose two sides have the equations
x – 2y + 1 = 0 and 2x – y – 1 = 0 and whose orthocenter is (7/3, 7/3) is :
The probability that a relation R from {x, y} to {x, y} is both symmetric and transitive, is equal to
The number of values of a ∈ N such that the variance of 3, 7, 12, a, 43 – a is a natural number is :
From the base of a pole of height 20 meter, the angle of elevation of the top of a tower is 60°. The pole subtends an angle 30° at the top of the tower. Then the height of the tower is :

Let ƒ :R→R be a function defined by 
\(f(x) = \frac{2e^{2x}}{e^{2x} + e^x}\)
Then \(f\left(\frac{1}{100}\right) + f\left(\frac{2}{100}\right) + f\left(\frac{3}{100}\right) + \ldots + f\left(\frac{99}{100}\right)\)
 is equal to ________.

If the sum of all the roots of the equation \(e^{2x} - 11e^x - 45e^{-x} + \frac{81}{2} = 0\)
 is logeP, then p is equal to _____.

The positive value of the determinant of the matrix A, whose 
\(\text{Adj}(\text{Adj}(A)) = \begin{bmatrix} 14 & 28 & -14 \\ -14 & 14 & 28 \\ 28 & -14 & 14 \end{bmatrix}\)
 is ___.

The number of ways, 16 identical cubes, of which 11 are blue and rest are red, can be placed in a row so that between any two red cubes there should be at least 2 blue cubes, is _________.

If the coefficient of x10 in the binomial expansion of 
\(\left(\frac{\sqrt{x}}{5^{\frac{1}{4}}} + \frac{\sqrt{5}}{x^{\frac{1}{3}}}\right)^{60}\)
is 5k.l, where l, k∈N and l is co-prime to 5, then k is equal to ___________.

If two straight lines whose direction cosines are given by the relations \(l + m – n = 0\), \(3l^2 + m^2 + cnl = 0\) are parallel, then the positive value of \(c\) is :
Let \(\vec a=\hat i+\hat j−\hat k\) and \(\vec c=2\hat i−3\hat j+2\hat k\). Then the number of vectors \(\vec b\) such that \(\vec b×\vec c=\vec a\) and \(|\vec b|∈{1,2,…,10}\) is :

Let 
\(A1 = {(x,y):|x| <= y^2,|x|+2y≤8} \)
and 
\(A2 = {(x,y) : |x| +|y|≤k}. \)
If 27(Area A1) = 5(Area A2), then k is equal to :

If the sum of the first ten terms of the series
 \(\frac{1}{5} + \frac{2}{65} + \frac{3}{325} + \frac{4}{1025} + \frac{5}{2501}\)+… is \(\frac{m}{n}\), 
where m and n are co-prime numbers, then m + n is equal to __________.

A rectangle R with end points of one of its sides as (1, 2) and (3, 6) is inscribed in a circle. If the equation of a diameter of the circle is 2x – y + 4 = 0, then the area of R is ________.
A circle of radius 2 unit passes through the vertex and the focus of the parabola y2 = 2x and touches the parabola \(y=\left (x−\frac{1}{4}\right)^2+α,\) where \(α > 0\). Then \((4α – 8)^2\) is equal to ___________.
Let the mirror image of the point (a, b, c) with respect to the plane 3x – 4y + 12z + 19 = 0 be (a – 6, β, γ). If a + b + c = 5, then 7β – 9γ is equal to __________.

Let
\(\vec{a}=\hat{i} - 2\hat{j} + 3\hat{k}, \vec{b}=\hat{i} - \hat{j} + \hat{k} \) and \(\vec{c}\)
be a vector such that
\(\vec{a} + (\vec{b}×\vec{c}) = \vec{0}\) and \(\vec{b}.\vec{c} = 5.\)
Then the value of 3(\(\vec{c}.\vec{a}\)) is equal to