List of top Mathematics Questions asked in JEE Main

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 ________.

Let the solution curve of the differential equation \(x\frac{dy}{dx}-y=\sqrt{y^2+16x^2},\)  y(1) = 3 be y = y(x). Then y(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 :

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 ________.

Consider a cuboid of sides 2x, 4x and 5x and a closed hemisphere of radius r. If the sum of their surface areas is a constant k, then the ratio x : r, for which the sum of their volumes is maximum, is
Let α and β be the roots of the equation x2 + (2i – 1) = 0. Then, the value of |α2 + β2| is equal to

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

If  \(b_n= ∫_0^{\frac{π}{2}} \frac{cos^2nx}{sinx }dx, n∈N,\) Then

Let ƒ R ⇒ R be a function defined by

Let ƒ : R ⇒ R be a function defined by

where [t] is the greatest integer less than or equal to t. Let m be the number of points where ƒ is not differentiable and 

Then the ordered pair (m, I) is equal to :

Let \([t]\) denote the greatest integer less than or equal to \(t\). Then, the value of the integral \(∫_0^1 [ -8x^2 + 6x - 1] dx\) is equal to 
The boolean expression (~(p ∧q)) ∨q is equivalent 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 ________.

The sum of all the elements of the set {α ∈ {1, 2, …, 100} : HCF(α, 24) = 1} is

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 ___.

Let \(x, y > 0\). If \(x^3y^2 = 2^{15}\), then the least value of \(3x + 2y\) is

The number of q∈ (0, 4π) for which the system of linear equations
3(sin 3θ) x – y + z = 2
3(cos 2θ) x + 4y + 3z = 3
6x + 7y + 7z = 9
has no solution, is

Let \(f :R→R\) and \(g : R→R\) be two functions defined by \(f(x) = log_e(x^2 + 1) – e^{–x} + 1\) and \(g(x)=\frac {1−2e^{2x}}{e^x}\). Then, for which of the following range of α, the inequality \(f(g((\frac {α−1)^2}{3}))>f(g(α−\frac 53))\) holds?
A horizontal park is in the shape of a triangle OAB with AB = 16. A vertical lamp post OP is erected at the point O such that\( \begin{array}{l}\angle PAO = \angle PBO = 15^\circ ~\text{and}~ \angle PCO = 45^\circ,\end{array}\)where C is the midpoint of AB. Then (OP)2 is equal to
Let A1, A2, A3, … be an increasing geometric progression of positive real numbers. If A1A3A5A7 = \(\frac {1}{1296}\) and A2 + A4 = \(\frac {7}{36}\) then, the value of A6 + A8 + A10 is equal to

Let 

\(a→=α\^{i}+3\^{j}−\^{k},  \overrightarrow{b}=3\^{i}−β\^{j}+4\^{k} and  \overrightarrow{c}=\^{i}+2\^{j}−2\^{k }\)

where α,β∈R, be three vectors. If the projection of 

\(\overrightarrow{a} on \overrightarrow{c} is \frac{10}{3} and \overrightarrow{b}×\overrightarrow{c}=−6\^{i}+10\^{j}+7\^{k}, \)

then the value of α+β is equal to

The area (in sq. units) of the region enclosed between the parabola y2 = 2x and the line x + y = 4 is _______.
Let \(X\) be a random variable having binomial distribution \(B(7, p)\). If \(P(X = 3) = 5P(X = 4)\), then the sum of the mean and the variance of \(X\) is:

The remainder on dividing 1 + 3 + 32 + 33 + … + 32021 by 50 ____ is

The number of values of a ∈ N such that the variance of 3, 7, 12, a, 43 – a is a natural number is :
Let the area of the triangle with vertices \(A(1, α), B(α, 0)\) and \(C(0, α)\) be \(4\) sq. units. If the points \((α, –α), (–α, α)\) and \((α^2, β)\) are collinear, then \(β\) is equal to