List of top Mathematics Questions asked in JEE Main

The equations of the sides AB, BC and CA of a triangle ABC are 2x + y = 0, x + py = 15a and x – y = 3, respectively. If its orthocentre is
$(2, a),−\frac{1}{2}<a<2 $
then p is equal to _______.

If$\begin{array}{l}1 + \left(2 + ^{49}C_1 + ^{49}C_2 + … ^{49}C_{49}\right) \left(^{50}C_2 + ^{50}C_4 + … ^{50}C_{50}\right) \end{array}$is equal to 2ⁿ. m, where m is odd, then n + m is equal to ______.

Let m₁, m₂ be the slopes of two adjacent sides of a square of side a such that $a^2 + 11a + 3(m_1^2 + m_2^2) = 220$. If one vertex of the square is $(10(\cos \alpha - \sin \alpha), 10(\sin \alpha + \cos \alpha))$, where $\alpha \in \left(0, \frac{\pi}{2}\right)$and the equation of one diagonal is $(\cos \alpha - \sin \alpha)x + (\sin \alpha + \cos \alpha)y = 10$, then $72(\sin^4 \alpha + \cos^4 \alpha) + a^2 - 3a + 13$ is equal to :

Let R be a relation from the set $\{1, 2, 3, ….., 60\}$ to itself such that $R = \{(a, b) : b = pq,$ where $p, q≥ 3$ are prime numbers$\}$. Then, the number of elements in R is :

If the equation of the parabola, whose vertex is at $(5, 4)$ and the directrix is $3x + y – 29 = 0$, is $x^2 + ay^2 + bxy + cx + dy + k = 0$, then $a + b + c + d + k$ is equal to

Let Q and R be two points on the line
$\frac{x+1}{2}=\frac{y+2}{3}=\frac{z−1}{2}$ at a distance $\sqrt{26}$
from the point P(4, 2, 7). Then the square of the area of the triangle PQR is _______ .

If the angle made by the tangent at the point (x₀, y₀) on the curve x = 12(t + sin t cos t),

$y=12(1+sint)^2,0<t<\frac{π}{2}, $

with the positive x-axis is π/3, then y₀ is equal to

Let A and B be two events such that

$\begin{array}{l} P\left(B/A\right)\frac{2}{5},\ P\left(A/B\right)=\frac{1}{7}\ \text{and}\ P\left(A\cap B\right)=\frac{1}{9}.\end{array} Consider \begin{array}{l} \left(S1\right)P\left(A’\cup B\right)=\frac{5}{6},\end{array}$

$\begin{array}{l} \left(S2\right)P\left(A’\cap B’\right)=\frac{1}{18}.\end{array}$Then

If the plane 2x + y – 5z = 0 is rotated about its line of intersection with the plane 3x – y + 4z – 7 = 0 by an angle of π/2, then the plane after the rotation passes through the point:

Let the tangents at the points P and Q on the ellipse

$\begin{array}{l} \frac{x^2}{2}+\frac{y^2}{4}=1\ \text{meet at the point}\ R\left(\sqrt{2},2\sqrt{2}-2\right).\end{array}$

If S is the focus of the ellipse on its negative major axis, then SP² + SQ²is equal to ________.

A line, with a slope greater than one, passes through point A(4, 3) and intersects the line x – y – 2 = 0 at the point B. If the length of the line segment AB is $\frac{\sqrt{29}}{3}$ then B also lies on the line :

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 S be the set of (α,β),π<α,β<2π,for which the complex number
$\frac{1-i\sinα}{1+2i\sinα}$ is purely imaginary and $\frac{1+i\cosβ}{1-2i\cosβ}$ is purely real,
Let $Zαβ = \sin2α+i\cos2β, (α,β) ∈ S$. Then
$\sum_{(\alpha, \beta) \in S} \left(iZ_{\alpha\beta} + \frac{1}{iZ_{\alpha\beta}}\right)$
is equal to

Let $\vec{a}, \vec{b}, \vec{c}$
be three coplanar concurrent vectors such that angles between any two of them is same. If the product of their magnitudes is 14 and
$(\vec{a} \times \vec{b}) \cdot (\vec{b} \times \vec{c}) + (\vec{b} \times \vec{c}) \cdot (\vec{c} \times \vec{a}) + (\vec{c} \times \vec{a}) \cdot (\vec{a} \times \vec{b}) = 168$, then $|\vec{a}| + |\vec{b}| + |\vec{c}|$| is equal to :

The term independent of x in the expansion of
$(1−x^2+3x^3)(\frac{5}{2}x^3−\frac{1}{5x^2})11,x≠0 $
is:

If $a = \lim_{{n \to \infty}} \sum_{{k=1}}^{n} \frac{2n}{{n^2 + k^2}}$and
$f(x) = \sqrt{\frac{1 - \cos x}{1 + \cos x}}, \quad x \in (0, 1)$ then

16 sin(20°) sin(40°) sin(80°) is equal to :

The area bounded by the curves y = |x² – 1| and y = 1 is

If $y = y ( x ), x \in\left(0, \frac{\pi}{2}\right)$ be the solution curve of the differential equation$ \left(\sin ^2 2 x\right) \frac{d y}{d x}+\left(8 \sin ^2 2 x+2 \sin 4 x\right) y$ $ =2 e^{-4 x}(2 \sin 2 x+\cos 2 x), \text { with } y\left(\frac{\pi}{4}\right)=e^{-\pi},$ then $y\left(\frac{\pi}{6}\right)$ is equal to:

If
$n(2n+1)\int_{0}^{1}(1−xn)^{2n}dx=1177\int_{0}^{1}(1−x^n)^{2n+1}dx$
,then n ∈ N is equal to ______.

Let the coefficients of the middle terms in the expansion of$\begin{array}{l} \left(\dfrac{1}{\sqrt 6}+ \beta x\right)^4, \left(1 – 3\beta x\right)^2 \text{and}\left(1 – \dfrac{\beta}{2}x\right )^6, \beta > 0,\end{array}$respectively form the first three terms of an A.P. If d is the common difference of this A.P., then $\begin{array}{l} 50-\frac{2d}{\beta^2} \end{array}$is equal to _______.

Let A, B, C be three points whose position vectors respectively are
$\vec{a} = \hat{i} + 4\hat{j} + 3\hat{k}$
$\vec{b} = 2\hat{i} + α\hat{j} + 4\hat{k}, α ∈ R$
$\vec{c} = 3\hat{i} - 2\hat{j} + 5\hat{k}$
If α is the smallest positive integer for which$\vec{a},\vec{b},\vec{c}$
are non collinear, then the length of the median, in ΔABC, through A is:

Let a vector $\vec{a}$ has a magnitude 9. Let a vector $\vec{b}$ be such that for every $(x, y) \in R \times R-\{(0,0)\}$, the vector $(x \vec{a}+y \vec{b})$ is perpendicular to the vector $(6 y \vec{a}-18 x \vec{b})$. Then the value of $|\vec{a} \times \vec{b}|$ is equal to:

Let $\vec{a} = 3\hat{i} + \hat{j}$ and $\vec{b} = \hat{i} + 2\hat{j} + \hat{k}$.
Let $\vec{c}$ be a vector satisfying $\vec{a} \times (\vec{b} \times \vec{c}) = \vec{b} + \lambda \vec{c}$
If $\vec{b}$ and $\vec{c}$ are non-parallel, then the value of $λ$ is

Let S = {E₁, E₂, ……………., E₈} be a sample space of a random experiment such that $P(E_n) = \frac{n}{36}$ for every n = 1, 2, ………, 8. Then the number of elements in the set$\{ A \subseteq S : P(A) \geq \frac{4}{5} \}$ is_________.