List of top Mathematics Questions asked in JEE Main

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 d2 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

Let the line
\(\frac{x - 3}{7} = \frac{y - 2}{-1} = \frac{z - 3}{-4}\)
intersect the plane containing the lines
\(\frac{x - 4}{1} = \frac{y + 1}{-2} = \frac{z}{1}\) and \(4ax-y+5z-7a = 0 = 2x-5y-z-3, a∈R\)
at the point P(α, β, γ). Then the value of α + β + γ equals _____.

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

If y = y(x) is the solution of the differential equation

\(2x^2\frac{dy}{dx}-2xy+3y^2=0\) such that \(y(e)=\frac{e}{3},\)

then y(1) 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 ________.

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

The mean and variance of 10 observation were calculated as 15 and 15 respectively by a student who took by mistake 25 instead of 15 for one observation. Then, the correct standard deviation is ________.
 The area of the region given by A={(x,y); \(x^2\)≤y≤min{x+2,4−3x}} is
If the area of the region \(\{(x, y) : x^{2/3} + y^{2/3} \leq 1, x + y \geq 0, y \geq 0\}\) is A, then \(\frac{(256 A)}{\pi} \)is equal to_______.

Let
\(f(x) = 2x^2 - x - 1\ and\ S = \{ n \in \mathbb{Z} : |f(n)| \leq 800 \}\)
Then, the value of ∑n∈S f(n) is equal to ________.

Let H:  \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1, a > 0, b > 0,\) be a hyperbola such that the sum of lengths of the transverse and the conjugate axes is \(4(2\sqrt 2 + \sqrt {14}).\) If the eccentricity H is \(\frac{\sqrt {11}}{2}\), then the value of \(a^2 + b^2 \) is equal to ______.
Let A be a 3 × 3 invertible matrix. If |adj (24A)| = |adj (3 adj (2A))|, then |A|2 is equal to :

Let 
\(\stackrel{→}{a} = \hat{i} + \hat{j} + \hat{2k}, \stackrel{→}{b} = \hat{2i} - \hat{3j} + \hat{k}\)
and 
\(\stackrel{→}{c}= \hat{i} - \hat{j} + \hat{k}\)
be three given vectors.
Let \(\stackrel{→}{v}\) be a vector in the plane of \(\stackrel{→}{a}\) and \(\stackrel{→}{b}\) whose projection on \(\stackrel{→}{c}\) is \(\frac{2}{\sqrt3}\).
If \(\stackrel{→}{v}.\hat{j}\) = 7 , then \(\stackrel{→}{v}.(\hat{i}+\hat{k})\) is equal to :

If the two lines 
\(l1:\frac{(x−2)}{3}=\frac{(y+1)}{−2},z=2 \)
and
\( l2:\frac{(x−1)}{1}=\frac{(2y+3)}{α}=\frac{(z+5)}{2} \)
are perpendicular, then an angle between the lines l2 and 
\(l3:\frac{(1−x)}{3}=\frac{(2y−1)}{−4}=\frac{z}{4} \)
is

Let the image of the point P(1, 2, 3) in the line 
\(L:\frac{x−6}{3}=\frac{y−1}{2}=\frac{z−2}{3} \)
be Q. Let R (α, β, γ) be a point that divides internally the line segment PQ in the ratio 1 : 3. Then the value of 22(α + β + γ) is equal to ________.

Numbers are to be formed between 1000 and 3000, which are divisible by 4, using the digits 1, 2, 3, 4, 5 and 6 without repetition of digits. Then the total number of such numbers is ______________.

A vector \(\vec{a}\)
is parallel to the line of intersection of the plane determined by the vectors
\(\hat{i},\hat{i}+\hat{j} \)and the plane determined by the vectors 
\(\hat{i}−\hat{j},\hat{i}+\hat{k}\). The obtuse angle between 
\(\vec{a}\) and the vector \(\vec{b}=\hat{i}−2\hat{j}+2\hat{k}\)
is