List of top Mathematics Questions asked in JEE Main

Let a line \(y = mx\) \((m \gt 0)\) intersect the parabola, \(y^2 = x\) at a point P, other than the origin. Let the tangent to it at P meet the x-axis at the point Q. If area \((\Delta OPQ) = 4\) sq. units, then m is equal to __________.

The sum, \(\sum_{n=1}^{7} \frac{n(n+1)(2n+1)}{4}\) is equal to ________.

If \(\frac{\sqrt{2}\sin\alpha}{\sqrt{1 + \cos 2\alpha}} = \frac{1}{7}\) and \(\sqrt{\frac{1 - \cos 2\beta}{2}} = \frac{1}{\sqrt{10}}\), \(\alpha, \beta \in \left(0, \frac{\pi}{2}\right)\), then \(\tan(\alpha + 2\beta)\) is equal to _____.

The mirror image of the point \((1,2,3)\) in a plane is \(\left(-\dfrac73,-\dfrac43,-\dfrac13\right)\). Which of the following points lies on this plane ?

The length of the perpendicular from the origin, on the normal to the curve, \(x^2+2xy-3y^2=0\) at the point \((2,2)\) is

The area (in sq. units) of the region \(\{(x,y)\in\mathbb{R}^2: x^2\le y\le3-2x\}\), is :

The differential equation of the family of curves, \(x^2=4b(y+b)\), \(b\in\mathbb{R}\), is :

Let S be the set of all functions \(f:[0,1]\to\mathbb{R}\), which are continuous on \([0,1]\) and differentiable on \((0,1)\). Then for every \(f\) in S, there exists a \(c\in(0,1)\), depending on \(f\), such that

Let \(f:(1,3)\to\mathbb{R}\) be a function defined by \(f(x)=\dfrac{x[x]}{1+x^2}\), where \([x]\) denotes the greatest integer \(\le x\). Then the range of \(f\) is

If \(I=\displaystyle\int_1^2\dfrac{dx}{\sqrt{2x^3-9x^2+12x+4}}\), then :

\(\displaystyle\lim_{x\to0}\dfrac{\int_0^x t\sin(10t)\,dt}{x}\) is equal to

If the \(10^{\text{th}}\) term of an A.P. is \(\dfrac{1}{20}\) and its \(20^{\text{th}}\) term is \(\dfrac{1}{10}\), then the sum of its first 200 terms is

Let \(\alpha=\dfrac{-1+i\sqrt3}{2}\). If \(a=(1+\alpha)\displaystyle\sum_{k=0}^{100}\alpha^{2k}\) and \(b=\displaystyle\sum_{k=0}^{100}\alpha^{3k}\), then \(a\) and \(b\) are the roots of the quadratic equation :

Let S be the set of all real roots of the equation, \(3^x(3^x-1)+2=|3^x-1|+|3^x-2|\). Then S :

If \(A=\begin{pmatrix}2&2\\9&4\end{pmatrix}\) and \(I=\begin{pmatrix}1&0\\0&1\end{pmatrix}\), then \(10A^{-1}\) is equal to :

An urn contains 5 red marbles, 4 black marbles and 3 white marbles. Then the number of ways in which 4 marbles can be drawn so that at the most three of them are red is ___________.

The sum \(\displaystyle\sum_{k=1}^{20} (1 + 2 + 3 + \ldots + k)\) is :

Let the normal at a point P on the curve \(y^2 - 3x^2 + y + 10 = 0\) intersect the y-axis at \(\left(0, \frac{3}{2}\right)\). If m is the slope of the tangent at P to the curve, then \(|m|\) is equal to

The number of all \(3 \times 3\) matrices A, with entries from the set \(\{-1, 0, 1\}\) such that the sum of the diagonal elements of \(AA^T\) is 3, is

The least positive value of 'a' for which the equation \(2x^2 + (a - 10)x + \frac{33}{2} = 2a\) has real roots is

If \(c\) is a point at which Rolle's theorem holds for the function,
\(f(x)=\log_e\left(\frac{x^2+\alpha}{7x}\right)\)
in the interval \([3,4]\), where \(\alpha\in R\), then \(f''(c)\) is equal to

If the equation, \(x^2+bx+45=0\) (\(b\in R\)) has conjugate complex roots and they satisfy \(|z+1|=2\sqrt{10}\), then :

Let the line \(y=mx\) and the ellipse \(2x^2+y^2=1\) intersect at a ponit \(P\) in the first quadrant. If the normal to this ellipse at \(P\) meets the co-ordinate axes at
\(\left(-\frac{1}{3\sqrt2},0\right)\) and \((0,\beta)\), then \(\beta\) is equal to :

The mean and the standard deviation (s.d.) of 10 observations are 20 and 2 resepectively. Each of these 10 observations is multiplied by \(p\) and then reduced by \(q\), where \(p\ne0\) and \(q\ne0\). If the new mean and new s.d. become half of their original values, then \(q\) is equal to

Let \(f(x) = (\sin(\tan^{-1}x)+\sin(\cot^{-1}x))^2-1\), \(|x|>1\).
If \(\frac{dy}{dx}=\frac12\frac{d}{dx}\left(\sin^{-1}(f(x))\right)\) and \(y(\sqrt3)=\frac{\pi}{6}\), then \(y(-\sqrt3)\) is equal to :