List of top Mathematics Questions asked in JEE Main

Let [t] denote the greatest integer \(\le\) t. If for some \(\lambda \in \mathbb{R} - \{1, 0\}\),
\(\lim_{x \to 0}\left|\frac{1 - x + |x|}{\lambda - x + [x]}\right| = L\), then L is equal to :
The value of (\(2\cdot{}^{1}P_0 - 3\cdot{}^{2}P_1 + 4\cdot{}^{3}P_2 \ldots\) up to 51th term) + (\(1! - 2! + 3! - \ldots\) up to 51th term) is equal to :
The lines
\(\vec{r} = (\hat{i} - \hat{j}) + l(2\hat{i} + \hat{k})\)
and
\(\vec{r} = (2\hat{i} - \hat{j}) + m(\hat{i} + \hat{j} + \hat{k})\)
The solution curve of the differential equation, \((1 + e^{-x})(1 + y^2)\frac{dy}{dx} = y^2\), which passes through the point \((0, 1)\), is :
A hyperbola having the transverse axis of length \(\sqrt{2}\) has the same foci as that of the ellipse \(3x^2 + 4y^2 = 12\), then this hyperbola does not pass through which of the following points?
\(2\pi - \left(\sin^{-1}\frac{4}{5} + \sin^{-1}\frac{5}{13} + \sin^{-1}\frac{16}{65}\right)\) is equal to :
If \(y^2 + \log_e(\cos^2 x) = y\), \(x \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\), then :
If \(\Delta = \begin{vmatrix} x - 2 & 2x - 3 & 3x - 4 \\ 2x - 3 & 3x - 4 & 4x - 5 \\ 3x - 5 & 5x - 8 & 10x - 17 \end{vmatrix} = Ax^3 + Bx^2 + Cx + D\), then \(B + C\) is equal to :
If the number of integral terms in the expansion of \((3^{1/2} + 5^{1/8})^n\) is exactly 33, then the least value of \(n\) is :
If \(\alpha\) and \(\beta\) are the roots of the equation \(x^2 + px + 2 = 0\) and \(\frac{1}{\alpha}\) and \(\frac{1}{\beta}\) are the roots of the equation \(2x^2 + 2qx + 1 = 0\), then \(\left(\alpha - \frac{1}{\alpha}\right)\left(\beta - \frac{1}{\beta}\right)\left(\alpha + \frac{1}{\beta}\right)\left(\beta + \frac{1}{\alpha}\right)\) is equal to :
Let P be a point on the parabola, \(y^2 = 12x\) and N be the foot of the perpendicular drawn from P on the axis of the parabola. A line is now drawn through the mid-point M of PN, parallel to its axis which meets the parabola at Q. If the y-intercept of the line NQ is \(\frac{4}{3}\), then :
Consider the two sets :
\(A = \{m \in \mathbb{R} : \text{both the roots of } x^2 - (m + 1)x + m + 4 = 0 \text{ are real}\}\)
and \(B = [-3, 5)\).
Which of the following is not true?
\(\int_{-\pi}^{\pi} \left| \pi - |x| \right| dx\) is equal to :
The function, \(f(x) = (3x - 7)x^{2/3}\), \(x \in \mathbb{R}\), is increasing for all \(x\) lying in :
For the frequency distribution :
Variate (x) : \(x_1\) \(x_2\) \(x_3\) .... \(x_{15}\)
Frequency (f) : \(f_1\) \(f_2\) \(f_3\) ...... \(f_{15}\)
where \(0 \lt x_1 \lt x_2 \lt x_3 \lt ... \lt x_{15} = 10\) and \(\sum_{i=1}^{15} f_i \gt 0\), the standard deviation cannot be :
The area (in sq. units) of the region \(\{(x, y) : 0 \le y \le x^2 + 1,\ 0 \le y \le x + 1,\ \frac{1}{2} \le x \le 2\}\) is :
For a positive integer \(n\),
\(\left(1+\frac{1}{x}\right)^{n}\) is expanded
in increasing powers of \(x\). If three consecutive
coefficients in this expansion are in the ratio,
\(2 : 5 : 12\), then \(n\) is equal to _______.
If the variance of the terms in an increasing A.P.,
\(b_1, b_2, b_3, \ldots, b_{11}\) is 90, then the common difference of this A.P. is _______.
Let the position vectors of points \(A\) and \(B\) be \(\hat{i}+\hat{j}+\hat{k}\) and \(2\hat{i}+\hat{j}+3\hat{k}\), respectively. A point \(P\) divides the line segment \(AB\) internally in the ratio \(\lambda : 1\) (\(\lambda \gt 0\)). If \(O\) is the origin and
\(\overrightarrow{OB}\cdot\overrightarrow{OP}-3\left|\overrightarrow{OA}\times\overrightarrow{OP}\right|^{2}=6\), then \(\lambda\) is equal to _______.
If \(y=\displaystyle\sum_{k=1}^{6} k\cos^{-1}\left\{\frac{3}{5}\cos kx-\frac{4}{5}\sin kx\right\}\), then \(\frac{dy}{dx}\) at \(x=0\) is _______.
The equation of the normal to the curve
\(y = (1+x)^{2y} + \cos^{2}(\sin^{-1}x)\) at \(x = 0\) is :
Let \([t]\) denote the greatest integer less than or equal to \(t\). Then the value of
\(\displaystyle\int_{1}^{2}\left|2x-[3x]\right|dx\) is _______.
Let a, b, c \(\in \mathbb{R}\) be all non-zero and satisfy \(a^3+b^3+c^3=2\). If the matrix \(A=\begin{pmatrix} a & b & c \\ b & c & a \\ c & a & b \end{pmatrix}\) satisfies \(A^TA = I\), then a value of abc can be :
Let \(n > 2\) be an integer. Suppose that there are n Metro stations in a city located along a circular path. Each pair of stations is connected by a straight track only. Further, each pair of nearest stations is connected by blue line, whereas all remaining pairs of stations are connected by red line. If the number of red lines is 99 times the number of blue lines, then the value of n is :
\(\lim\limits_{x\to0}\left(\tan\left(\frac{\pi}{4}+x\right)\right)^{\frac1x}\) is equal to :