List of top Mathematics Questions asked in JEE Main

Let \(f : R \to R\) be differentiable at \(c \in R\) and \(f(c) = 0\). If \(g(x) = |f(x)|\), then at \(x = c\), \(g\) is :

If for some \(x \in R\), the frequency distribution of the marks obtained by 20 students in a test is :

Marks	2	3	5	7
Frequency	\((x+1)^2\)	\(2x - 5\)	\(x^2 - 3x\)	\(x\)

then the mean of the marks is

If \(a_1, a_2, a_3, \ldots, a_n\) are in A.P. and \(a_1 + a_4 + a_7 + \ldots + a_{16} = 114\), then \(a_1 + a_6 + a_{11} + a_{16}\) is equal to :

If \(a > 0\) and \(z = \dfrac{(1+i)^2}{a - i}\), has magnitude \(\sqrt{\frac{2}{5}}\), then \(\bar{z}\) is equal to :

If the length of the perpendicular from the point \((\beta, 0, \beta)\) \((\beta \ne 0)\) to the line, \(\frac{x}{1} = \frac{y-1}{0} = \frac{z+1}{-1}\) is \(\sqrt{\frac{3}{2}}\), then \(\beta\) is equal to :

If \(f(x) = \begin{cases} \dfrac{\sin(p+1)x + \sin x}{x}, & x < 0 \\ q, & x = 0 \\ \dfrac{\sqrt{x + x^2} - \sqrt{x}}{x^{3/2}}, & x > 0 \end{cases}\) is continuous at \(x = 0\), then the ordered pair \((p, q)\) is equal to

The value of \(\displaystyle\int_0^{2\pi} \left[\sin 2x\,(1 + \cos 3x)\right] dx\), where \([t]\) denotes the greatest integer function is :

If a directrix of a hyperbola centred at the origin and passing through the point \((4, -2\sqrt{3})\) is \(5x = 4\sqrt{5}\) and its eccentricity is \(e\), then :

If \(\alpha\) and \(\beta\) are the roots of the quadratic equation, \(x^2 + x\sin\theta - 2\sin\theta = 0\), \(\theta \in \left(0, \frac{\pi}{2}\right)\), then \(\dfrac{\alpha^{12} + \beta^{12}}{\left(\alpha^{-12} + \beta^{-12}\right)\cdot(\alpha - \beta)^{24}}\) is equal to :

If \(\displaystyle\lim_{x \to 1} \frac{x^4 - 1}{x - 1} = \lim_{x \to k} \frac{x^3 - k^3}{x^2 - k^2}\), then \(k\) is :

Let P be the plane, which contains the line of intersection of the planes, \(x+y+z-6=0\) and \(2x+3y+z+5=0\) and it is perpendicular to the xy-plane. Then the distance of the point \((0,0,256)\) from P is equal to :

Two poles standing on a horizontal ground are of heights \(5\) m and \(10\) m respectively. The line joining their tops makes an angle of \(15^\circ\) with ground. Then the distance (in m) between the poles, is :-

The common tangent to the circles \(x^2+y^2=4\) and \(x^2+y^2+6x+8y-24=0\) also passes through the point :

If the system of equations 2x + 3y - z = 0, x + ky - 2z = 0 and 2x - y + z = 0 has a non-trival solution (x, y, z), then \(\frac{x}{y} + \frac{y}{z} + \frac{z}{x} + k\) is equal to :-

The sum of the series \(1+2\times 3+3\times 5+4\times 7+\ldots\) upto 11th term is :-

If the two lines x + (a - 1) y = 1 and 2x + a²y = 1 \((a \in R - \{0, 1\})\) are perpendicular, then the distance of their point of intersection from the origin is :

If the tangent to the parabola \(y^2=x\) at a point \((\alpha,\beta)\), \((\beta\gt 0)\) is also a tangent to the ellipse, \(x^2+2y^2=1\), then \(\alpha\) is equal to :

The value of the integral \(\int_0^1 x\cot^{-1}(1-x^2+x^4)\,dx\) is :-

Let z \(\in\) C be such that |z| \(\lt\) 1. If \(\omega = \frac{5 + 3z}{5(1 - z)}\), then :

The total number of matrices \(A = \begin{pmatrix} 0 & 2y & 1 \\ 2x & y & -1 \\ 2x & -y & 1 \end{pmatrix}\) \((x, y \in R,\ x \ne y)\) for which \(A^{T}A = 3I_3\) is :-

\(\int e^{\sec x}\left(\sec x\tan x\, f(x) + \sec x\tan x + \sec^2 x\right)dx = e^{\sec x} f(x) + C\) then a possible choice of f(x) is :-

A rectangle is inscribed in a circle with a diameter lying along the line 3y = x + 7. If the two adjacent vertices of the rectangle are (-8, 5) and (6, 5), then the area of the rectangle (in sq. units) is :

The domain of the definition of the function \(f(x) = \frac{1}{4 - x^2} + \log_{10}(x^3 - x)\) is

If \(f(x) = [x] - \left[\frac{x}{4}\right],\ x \in \mathbb{R}\), where [x] denotes the greatest integer function, then

The area (in sq. units) of the region \(A = \left\{(x, y) : \frac{y^2}{2} \le x \le y + 4\right\}\) is :-