List of top Mathematics Questions asked in JEE Main

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 :

Negation of the Boolean statement (p ∨ q) ⇒ ((~ r) ∨ p) is equivalent to

Let n ≥ 5 be an integer. If 9n – 8n – 1 = 64α and 6n – 5n – 1 = 25β, then α – β is equal to

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 ___________.

In an isosceles triangle ABC, the vertex A is \((6, 1)\) and the equation of the base BC is \(2x + y = 4\). Let the point B lie on the line \(x + 3y = 7\). If \((α, β)\) is the centroid of ΔABC, then \(15(α + β)\) is equal to :

Let the eccentricity of an ellipse \(\frac {x^2}{a^2}+\frac {y^2}{b^2}=1\), \(a>b\), be \(\frac 14\). If this ellipse passes through the point \((−4\sqrt {\frac 25},3)\), then \(a^2 + b^2\) 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 

Let y = y(x), x > 1, be the solution of the differential equation
\((x-1)\frac{dy}{dx} + 2xy = \frac{1}{x-1}\)with \(y(2) = \frac{1+e^4}{2e^4}\). If \(y(3) = \frac{e^α + 1}{βe^α}\) , 
then the value of α + β is equal to ____.

Let 3, 6, 9, 12, … upto 78 terms and 5, 9, 13, 17, … upto 59 terms be two series. Then, the sum of terms common to both the series is equal to _____.

The number of solutions of the equation sin x = cos2 x in the interval (0, 10) is _____.

Let f and g be twice differentiable even functions on (–2, 2) such that
\(ƒ(\frac{1}{4})=0, ƒ(\frac{1}{2})=0, ƒ(1) =1\) and \(g(\frac{3}{4}) = 0 , g(1)=2\)
.Then, the minimum number of solutions of f(x)g′′(x) + f′(x)g′(x) = 0 in (–2, 2) is equal to_____.

Let the coefficients of x–1 and x–3 in the expansion of
\((2x^{\frac{1}{5}} - \frac{1}{x^{\frac{1}{5}}} )^{15} , x > 0\)be m and n respectively. If r is a positive integer such that
\(mn² = ^{15}C_r.2^r\)
then the value of r is equal to ______.

The total number of four digit numbers such that each of first three digits is divisible by the last digit, is equal to _______.

Let
\(M = \begin{bmatrix}   0 & -\alpha \\   \alpha & 0 \\ \end{bmatrix}\)
where α is a non-zero real number an
\(N =   \sum\limits_{k=1}^{49} M^{2k}. \) If \((I - M^2)N = -2I\)
then the positive integral value of α is ____ .