List of top Mathematics Questions asked in JEE Main

If the following system of linear equations
\( 2x + y + z = 5 \)
\( x - y + z = 3 \)
\( x + y + az = b \)
has no solution, then :
The sum of 10 terms of the series \( \frac{3}{1^2 \times 2^2} + \frac{5}{2^2 \times 3^2} + \frac{7}{3^2 \times 4^2} + \dots \) is :

If the function 

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

The function \(f(x) = |x^2 - 2x - 3| \cdot e^{|9x^2 - 12x + 4|}\) is not differentiable at exactly :
The integral \(\int \frac{1}{\sqrt[4]{(x - 1)^3 (x + 2)^5}} \, dx\) is equal to :
(where C is a constant of integration)
If \(\frac{dy}{dx} = \frac{2^{x+y} - 2^x}{2^y}\), \(y(0) = 1\), then \(y(1)\) is equal to :
If \(p\) and \(q\) are the lengths of the perpendiculars from the origin on the lines, \(x \csc \alpha - y \sec \alpha = k \cot 2\alpha\) and \(x \sin \alpha + y \cos \alpha = k \sin 2\alpha\) respectively, then \(k^2\) is equal to :
The length of the latus rectum of a parabola, whose vertex and focus are on the positive \(x\)-axis at a distance \(R\) and \(S\) (\(S>R\)) respectively from the origin, is :
The line \(12x \cos \theta + 5y \sin \theta = 60\) is tangent to which of the following curves ?
Let the equation of the plane, that passes through the point \((1, 4, -3)\) and contains the line of intersection of the planes \(3x - 2y + 4z - 7 = 0\) and \(x + 5y - 2z + 9 = 0\), be \(\alpha x + \beta y + \gamma z + 3 = 0\), then \(\alpha + \beta + \gamma\) is equal to :
A vertical pole fixed to the horizontal ground is divided in the ratio \(3 : 7\) by a mark on it with lower part shorter than the upper part. If the two parts subtend equal angles at a point on the ground \(18\text{ m}\) away from the base of the pole, then the height of the pole (in meters) is :

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 ___________
 

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 'R' is the least value of 'a' such that the function \(f(x) = x^2 + ax + 1\) is increasing on \([1, 2]\) and 'S' is the greatest value of 'a' such that the function \(f(x) = x^2 + ax + 1\) is decreasing on \([1, 2]\), then the value of \(|R-S|\) is \dots\dots.

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

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

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 _____________
 

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 mean of 10 numbers \(7 \times 8, 10 \times 10, 13 \times 12, 16 \times 14, \dots\) 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 :
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 sum of the roots of the equation, \( x + 1 - 2\log_2(3 + 2^x) + 2\log_4(10 - 2^{-x}) = 0 \), 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 \( \alpha = \lim_{x \to \pi/4} \frac{\tan^3 x - \tan x}{\cos(x + \frac{\pi}{4})} \) 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 :