List of top Mathematics Questions asked in JEE Main

Let f_n = $\int\limits_0^{\pi/2}$ $\left(\displaystyle\sum_{k=1}^{n}\,sin^{k-1}x\right)\left(\displaystyle\sum_{k=1}^{n}\,(2k-1)sin^{k-1}x\right)$ cosx dx, n ∈ N. Then f₂₁ – f₂₀ is equal to____.

If y=y(x) is the solution of the differential equation $\frac{dy}{dx}+\frac{4x}{(x^2-1)}y=\frac{x+2}{(x^2-1)^{\frac{5}{2}}},x>1$ such that $y(2)=\frac{2}{9}\log_e(2+\sqrt3)\ \text{and}\ y(\sqrt2)=\alpha\log_e(\sqrt{\alpha}+\beta)+\beta-\sqrt{\gamma}∈\N,$ then αβγ is equal to

The foci of a hyperbola are (±2,0) and its eccentricity is $\frac{3}{2}$ . A tangent, perpendicular to the line 2x + 3y = 6, is drawn at a point in the first quadrant on the hyperbola. If the intercepts made by the tangent on the x- and y-axes are a and b respectively, then |6a| + |5b| is equal to_____.

The mean and standard deviation of the marks of 10 students were found to be 50 and 12 respectively. Later, it was observed that two marks 20 and 25 were wrongly read as 45 and 50 respectively. Then the correct variance is _______.

For x ∈ (–1, 1], the number of solutions of the equation sin^-1x = 2 tan^-1 x is equal to____

Let the system of linear equations
$-x + 2y - 9z = 7$,
$-x + 3y + 72 = 9$,
$-2x + y + 5z = 8$,
$-3x + y + 13z = \lambda$
has a unique solution $x = \alpha, y = \beta, z = \gamma$. Then the distance of the point $(\alpha, \beta, \gamma)$ from the plane $2x - 2y + z = \lambda$ is:

Let (a+bx+cx²)¹⁰ = $ \sum_{i=0}^{20} $ p_ixⁱ, a,b,c∈N. If p₁=20 and P₂ = 210, then 2(a+b+c) is equal to

Let A₁ and A₂ be two arithmetic means and G₁, G₂, G₃ be three geometric means of two distinct positive numbers. Then $ G_{1}^{4} + G_{2}^{4}+ G_{3}^{4} +G_{1}^{2}G_{3}^{2} $ is equal to

Let [x] denote the greatest integer function and f(x) = max{1+x+[x], 2+x, x+2[x]}, 0 ≤ x ≤2. Let m be the number of points in [0, 2], where f is not continuous and n be the number of points in (0, 2), where f is not differentiable. Then (m+n)² + 2 is equal to 2

If $\int_{0}^{1} $ 1/(5+2x-2x²)(1+e^(2-4x)) dx = 1/log_e (α+1/β) a, β>0, then a⁴- β⁴ is equal to

Let x = x(y) be the solution of the differential equation 2(y+2) log_e (y+2)dx+(x+4-2log_e(y+2))dy = 0, y >-1 with x (e⁴-2)=1. Then x(e⁹-2) is equal to

If (a, β) is the orthocenter of the triangle ABC with vertices A(3, -7), B(-1, 2), and C(4, 5), then 9α-6β+60 is equal to

The number of common tangents, to the circles $ x^2 + y^2 - 18x - 15y + 131 = 0 $ and $ x^2 + y^2 - 6x - 6y - 7 = 0 $, is

Let the foot of perpendicular of the point P(3, -2, -9) on the plane passing through the points (-1, -2, -3), (9, 3, 4), (9, -2, 1) be Q(α, β, γ). Then the distance of Q from the origin is

Let S be the set of all values of λ, for which the shortest distance between the lines x-λ/0 =y-3/4 = z+6/1 and x+λ/3 = y/-4 = z-6/0 is 13. Then 8 | $ \sum_{ λ∈S} λ| is $

Let S be the set of all (λ, μ) for which the vectors $ λ {i}ˆ-jˆ+kˆ, iˆ +2jˆ+µkˆ and 3iˆ -4jˆ +5kˆ, where λ-μ = 5, are coplanar, then $$ \sum_{(λ, μ) εs}80(λ^2, μ^2) $ is equal to

Let ABCD be a quadrilateral. If E and F are the mid points of the diagonals AC and BD respectively and $ (\vec{AB}-\vec{BC})+(\vec{AD}-\vec{DC})=k \vec{FE} $, then k is equal to

Negation of $ p \land (q \land \neg (p \land q)) $ is:}

Let A = {1, 2, 3, 4} and R be a relation on the set AxA defined by R = {((a, b), (c, d)): 2a+3b = 4c +5d}. Then the number of elements in R is

A person forgets his 4-digit ATM pin code. But he remembers that in the code all the digits are different, the greatest digit is 7 and the sum of the first two digits is equal to the sum of the last two digits. Then the maximum number of trials necessary to obtain the correct code is

If the sum of the series $\left(\frac{1}{2}-\frac{1}{3}\right) + \left(\frac{1}{2^2}-\frac{1}{2·3} + \frac{1}{3^2}\right) + \left(\frac{1}{2^2}-\frac{1}{2^2·3} + \frac{1}{2·3^2} - \frac{1}{3^3}\right) + \left(\frac{1}{2^4}-\frac{1}{2^3·3} + \frac{1}{2^2·3^2} - \frac{1}{2·3^3} + \frac{1}{3^4}\right) + ........ $
is $\frac{α}{β}$ , where α and β are co-prime, then α+3β is equal to ________

Let an ellipse with centre (1, 0) and latus rectum of length $\frac{1}{2}$ have its major axis along x-axis. If its minor axis subtends an angle 60° at the foci, then the square of the sum of the lengths of its minor and major axes is equal to

Let the plane P contain the line 2x+y-z-3=0=5x-3y+4z+9 and be parallel to the line $\frac{x+2}{2}=\frac{3-y}{-4}=\frac{z-7}{5}$. Then the distance of the point
A(8, -1, -19) from the plane P measured parallel to the line $\frac{x}{-3}=\frac{y-5}{4}=\frac{2-z}{-12}$ is equal to ___________.

If the line x = y = z intersects the line
xsinA+ysinB+zsinC-18=0=xsin2A+ysin2B+zsin2C-9,
where A, B, C are the angles of a triangle ABC, then 80$\left( sin\frac{A}{2}sin\frac{B}{2}sin\frac{C}{2} \right)$ is equal to ________.

In a group of 100 persons 75 speak English and 40 speak Hindi. Each person speaks at least one of the two languages. If the number of persons, who speak only English is a and the number of persons who speak only Hindi is b, then the eccentricity of the ellipse 25(β2 x² + α² y2) = α² β² is