List of top Mathematics Questions asked in JEE Main

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 :

Let a triangle ABC be inscribed in the circle
\(x² - \sqrt2(x+y)+y² = 0\)
such that ∠BAC= π/2. If the length of side AB is √2, then the area of the ΔABC is equal to :

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

The equation of a common tangent to the parabolas y = x² and y = –(x – 2)² is

Let 
\(\vec{a}=α\hat{i}+\hat{j}−\hat{k}\ and\ \vec{b}=2\hat{i}+\hat{j}−α\hat{k},α>0\). 
If the projection of \(\vec{a}×\vec{b}\) on the vector \(−\hat{i}+2\hat{j}−2\hat{k}\) 
is 30, then α is equal to

Let f be a real valued continuous function on [0, 1] and
\(f(x) = x + \int_{0}^{1} (x - t) f(t) \,dt\)
Then, which of the following points (x, y) lies on the curve y = f(x)?

Let the solution curve y = f(x) of the differential equation
\(\frac{dy}{dx} + \frac{xy}{x^2 - 1} = + \frac{ x^4+2x}{\sqrt{1 - x^2}}, \quad x \in (-1, 1)\) pass through the origin. Then
\(\int_{-\frac{\sqrt{3}}{2}}^{\frac{\sqrt{3}}{2}} f(x) \,dx\)is

Let the hyperbola 
\(H:\frac{x^2}{a^2}−y^2=1\)
and the ellipse
 \(E:3x^2+4y^2=12\) 
be such that the length of latus rectum of H is equal to the length of latus rectum of E. If eH and eE are the eccentricities of H and E respectively, then the value of 
\(12 (e^{2}_H+e^{2}_E)\) is equal to _____ .

Let y = y(x) be the solution of the differential equation
\(x ( 1 - x² ) \frac{dy}{dx} + ( 3x²y - y - 4x³ ) = 0, x > 1\)
with y(2) = –2. Then y(3) is equal to

The area of the region
\(\left\{(x,y) : y² ≤ 8x, y ≥ \sqrt2x, x ≥ 1 \right\}\)
is