List of top Mathematics Questions asked in JEE Main

Consider an A.P. $a_1,a_2,\ldots,a_n$ with $a_1>0$, $a_2-a_1=-\dfrac{3}{4}$ and $a_n=\dfrac{a_1}{4}$. If \[ \sum_{i=1}^{n} a_i=\frac{525}{2}, \] then find $\sum_{i=1}^{17} a_i$.

The number of critical points of the function} \[ f(x)= \begin{cases} \dfrac{|\sin x|}{x}, & x\neq0\\ 1, & x=0 \end{cases} \] in the interval \((-2\pi,2\pi)\) is equal to:

If the coefficient of \( x \) in the expansion of \[ (ax^2 + bx + c)(1 - 2x)^{26} \] is \(-56\) and the coefficients of \( x^2 \) and \( x^3 \) are both zero, then \( a + b + c \) is equal to

If \[ \lim_{x\to 0} \frac{e^{(a-1)x}+2\cos bx+(c-2)e^{-x}} {x\cos x-\log_e(1+x)} =2, \] then \(a^2+b^2+c^2\) is equal to

If the set of all solutions of \(|x^2 + x - 9| = |x| + |x^2 - 9|\) is \([\alpha, \beta] \cup [\gamma, \infty)\), then \((\alpha^2 + \beta^2 + \gamma^2)\) is equal to:

Let $\alpha, \beta$ be the roots of the equation $x^2 - x + p = 0$ and $\gamma, \delta$ be the roots of the equation $x^2 - 4x + q = 0$; $p, q \in \mathbb{Z}$. If $\alpha, \beta, \gamma, \delta$ are in G.P., then $|p+q|$ equals :

Let \( A = \{1, 2, 3, 4, 5\} \) and \( B = \{a, b, c\} \). Then the number of functions which are not onto are:

The number of distinct real solutions of the equation \[ x|x + 4| + 3|x + 2| + 10 = 0 \] is

Let \(x\) and \(y\) be real numbers such that} \[ 50\left(\frac{2x}{1+3i} - \frac{y}{1-2i}\right) = 31 + 17i, \qquad i = \sqrt{-1}. \] Then the value of \(10(x-3y)\) is:

Let \( R=\{(x,y)\in \mathbb{N}\times\mathbb{N}:\log_e(x+y)\le2\} \). Then the minimum number of elements required to be added in \(R\) to make it a transitive relation is ________.

Two players A and B play a series of games of badminton. The player who wins 5 games first, wins the series. Assuming that no game ends in a draw, the number of ways in which player A wins the series is _________.

Let \( f(x) = \begin{cases} x^3 + 8 & x < 0 \\ x^2 - 4 & x \ge 0 \end{cases} \) and \( g(x) = \begin{cases} (x-8)^{1/3} & x < 0 \\ (x+4)^{1/2} & x \ge 0 \end{cases} \) then find number of points of discontinuity of \( g(f(x)) \).

Let \(O\) be the vertex of the parabola \(y^2 = 4x\). Let \(P\) and \(Q\) be two points on parabola such that chords \(OP\) and \(OQ\) are perpendicular to each other. If the locus of mid-point of segment \(PQ\) is a conic \(C\), then latus rectum of \(C\) is

Let \(P(3\cos\alpha, 2\sin\alpha), \alpha \neq 0\), be a point on the ellipse \(\frac{x^2}{9} + \frac{y^2}{4} = 1\). \(Q\) be a point on the circle \(x^2 + y^2 - 14x - 14y + 82 = 0\) and \(R\) be a point on the line \(x + y = 5\) such that the centroid of the triangle \(PQR\) is \(\left( 2 + \cos\alpha, 3 + \frac{2}{3}\sin\alpha \right)\). Then the sum of the ordinates of all possible points \(R\) is:

Let \( \alpha, \beta \in \mathbb{R} \) be such that the system of linear equations} \[ x + 2y + z = 5 \] \[ 2x + y + \alpha z = 5 \] \[ 8x + 4y + \beta z = 18 \] has no solution. Then \( \frac{\beta}{\alpha} \) is equal to:

If \( 26 \left( \dfrac{2^3 \cdot \binom{12}{2}}{3} + \dfrac{2^5 \cdot \binom{12}{4}}{5} + \dots + \dfrac{2^{13} \cdot \binom{12}{12}}{13} \right) = 3^{13 - \alpha} \), then find the value of \( \alpha \).

If \(\int_0^{\pi/4} \left[ \cot(x - \frac{\pi}{3}) - \cot(x + \frac{\pi}{3}) + 1 \right] dx = \alpha \log(\sqrt{3} - 1)\) then \(9\alpha\) is

The mean & variance of \(x_1, x_2, x_3, x_4\) is 1 and 13 respectively and the mean and variance of \(y_1, y_2, \dots, y_6\) be 2 and 1 respectively, the variance of \(x_1, x_2, \dots, x_4, y_1, y_2, \dots, y_6\) will be

The number of values of \(z \in \mathbb{C}\) satisfying \(|z-4-8i| = \sqrt{10}\) and \(|z-3-5i| + |z-5-11i| = 4\sqrt{5}\) is

Locus of the mid-point of chord of circle \(x^2 + y^2 - 6x - 8y - 11 = 0\), subtending a right angle at the center is

Let \( \frac{x^2}{f(a^2 + 2a + 7)} + \frac{y^2}{f(3a + 14)} = 1 \) represent an ellipse. The major axis of the given ellipse is the y-axis and \( f \) is a decreasing function. If the range of \( a \) is \( R - [\alpha, \beta] \), then \( \alpha + \beta \) is:

A person has 3 different bags & 4 different books. The number of ways in which he can put these books in the bags so that no bag is empty, is