List of top Mathematics Questions asked in JEE Main

The locus of mid-points of the line segments joining \( (-3, -5) \) and the points on the ellipse \( \frac{x^2}{4} + \frac{y^2}{9} = 1 \) is :

Let \( A \) be the set of all points \( (\alpha, \beta) \) such that the area of triangle formed by the points \( (5, 6), (3, 2) \) and \( (\alpha, \beta) \) is 12 square units. Then the least possible length of a line segment joining the origin to a point in \( A \), is :

If \( \alpha = \lim_{x \to \pi/4} \frac{\tan^3 x - \tan x}{\cos(x + \frac{\pi}{4})} \) and \( \beta = \lim_{x \to 0} (\cos x)^{\cot x} \) are the roots of the equation, \( ax^2 + bx - 4 = 0 \), then the ordered pair \( (a, b) \) is :

Let \( f : \mathbb{N} \to \mathbb{N} \) be a function such that \( f(m + n) = f(m) + f(n) \) for every \( m, n \in \mathbb{N} \). If \( f(6) = 18 \), then \( f(2) \cdot f(3) \) is equal to :

An angle of intersection of the curves, \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \) and \( x^2 + y^2 = ab, a>b \), is :

Let \( a_1, a_2, a_3, \dots \) be an A.P. If \( \frac{a_1 + a_2 + \dots + a_{10}}{a_1 + a_2 + \dots + a_p} = \frac{100}{p^2}, p \neq 10 \), then \( \frac{a_{11}}{a_{10}} \) is equal to :

If \( \alpha + \beta + \gamma = 2\pi \), then the system of equations
\( x + (\cos \gamma)y + (\cos \beta)z = 0 \)
\( (\cos \gamma)x + y + (\cos \alpha)z = 0 \)
\( (\cos \beta)x + (\cos \alpha)y + z = 0 \)
has :

The sum of the roots of the equation, \( x + 1 - 2\log_2(3 + 2^x) + 2\log_4(10 - 2^{-x}) = 0 \), is :

If \( z \) is a complex number such that \( \frac{z - i}{z - 1} \) is purely imaginary, then the minimum value of \( |z - (3 + 3i)| \) is :

The mean of 10 numbers \(7 \times 8, 10 \times 10, 13 \times 12, 16 \times 14, \dots\) is ___________

The number of six letter words (with or without meaning), formed using all the letters of the word 'VOWELS', so that all the consonants never come together, is ___________

The square of the distance of the point of intersection of the line \(\frac{x-1}{2} = \frac{y-2}{3} = \frac{z+1}{6}\) and the plane \(2x - y + z = 6\) from the point \((-1, -1, 2)\) is _____________

If the variable line \(3x + 4y = \alpha\) lies between the two circles \((x-1)^2 + (y-1)^2 = 1\) and \((x-9)^2 + (y-1)^2 = 4\), without intercepting a chord on either circle, then the sum of all the integral values of \(\alpha\) is _____________

If \(x \phi(x) = \int_{5}^{x} (3t^2 - 2\phi'(t))dt\), \(x>-2\), and \(\phi(0)=4\), then \(\phi(2)\) is ___________

Let \([t]\) denote the greatest integer \(\leq t\). Then the value of \(8 \cdot \int_{-1/2}^{1} ([2x] + |x|) \, dx\) is _________

A point \(z\) moves in the complex plane such that \(\arg\left(\frac{z-2}{z+2}\right) = \frac{\pi}{4}\), then the minimum value of \(|z - 9\sqrt{2} - 2i|^2\) is equal to _________

If \(\left(\frac{3^6}{4^4}\right)k\) is the term independent of \(x\) in the binomial expansion of \(\left(\frac{x}{4} - \frac{12}{x^2}\right)^{12}\), then \(k\) is equal to ___________

Let \(*, \square \in \{\wedge, \vee\}\) be such that the Boolean expression \((p * \sim q) \implies (p \square q)\) is a tautology. Then :

Let \(f\) be a non-negative function in \([0, 1]\) and twice differentiable in \((0, 1)\). If \(\int_0^x \sqrt{1 - (f'(t))^2} \, dt = \int_0^x f(t) \, dt\), \(0 \leq x \leq 1\) and \(f(0) = 0\), then \(\lim_{x \to 0} \frac{1}{x^2} \int_0^x f(t) \, dt\) :

The integral \(\int \frac{1}{\sqrt[4]{(x - 1)^3 (x + 2)^5}} \, dx\) is equal to :
(where C is a constant of integration)

The function \(f(x) = |x^2 - 2x - 3| \cdot e^{|9x^2 - 12x + 4|}\) is not differentiable at exactly :

If the function

is continuous at \(x = 0\), then \(\frac{1}{a} + \frac{1}{b} + \frac{4}{k}\) is equal to :}