List of top Mathematics Questions asked in JEE Main

A line with direction ratios 1, -1, 2 intersects the lines \(\frac{x}{2} = \frac{y}{3} = \frac{z+1}{3}\) and \(\frac{x+1}{-1} = \frac{y-2}{1} = \frac{z}{4}\) at the points P and Q, respectively. If the length of the line segment PQ is \(\alpha\), then \(225\alpha^2\) is equal to:

Suppose that two chords, drawn from the point (1, 2) on the circle \(x^2 + y^2 + x - 3y = 0\) are bisected by the y-axis. If the other ends of these chords are R and S, and the midpoint of the line segment RS is \((\alpha, \beta)\), then \(6(\alpha + \beta)\) is equal to:

Let the vertex A of a triangle ABC be (1, 2), and the mid-point of the side AB be (5, -1). If the centroid of this triangle is (3, 4) and its circumcenter is \((\alpha, \beta)\), then \(2(10\alpha + \beta)\) is equal to:

Let the line \(L_1 : x + 3 = 0\) intersect the lines \(L_2 : x - y = 0\) and \(L_3 : 3x + y = 0\) at the points A and B, respectively. Let the bisector of the obtuse angle between the lines \(L_2\) and \(L_3\) intersect the line \(L_1\) at the point C. Then \(BC^2 : AC^2\) is equal to:

Suppose that the mean and median of the non-negative numbers 21, 8, 17, \(a\), 51, 103, \(b\), 13, 67, \((a>b)\), are 40 and 21, respectively. If the mean deviation about the median is 26, then \(2a\) is equal to:

Let the smallest value of \(k \in \mathbb{N}\), for which the coefficient of \(x^3\) in \((1+x)^3 + (1+x)^4 + (1+x)^5 + \dots + (1+x)^{99} + (1 + kx)^{100}\), \(x \neq 0\), is \((43n + \frac{101}{4}) \binom{100}{3}\) for some \(n \in \mathbb{N}\), be \(p\). Then the value of \(p + n\) is:

The number of ways of forming a queue of 4 boys and 3 girls such that all the girls are not together, is:

The first term of an A.P. of 30 non-negative terms is \(\frac{10}{3}\). If the sum of this A.P. is the cube of its last term, then its common difference is:

Let \(A = \begin{bmatrix} 1 & 1 & 2 \\ -2 & 0 & 1\\ 1 & 3 & 5 \end{bmatrix}\). Then the sum of all elements of the matrix \(\operatorname{adj}(\operatorname{adj}(2(\operatorname{adj}A)^{-1}))\) is equal to:

Let \(S = \left\{ A = \begin{bmatrix} a & b \\ c & d \end{bmatrix} : a, b, c, d \in \{0, 1, 2, 3, 4\} \text{ and } A^2 - 4A + 3I = 0 \right\}\) be a set of \(2 \times 2\) matrices. Then the number of matrices in \(S\), for which the sum of the diagonal elements is equal to 4, is:

The number of functions \(f: \{1, 2, 3, 4\} \rightarrow \{a, b, c\}\), which are not onto, is:

Let \(z\) be a complex number such that \(|z + 2| = |z - 2|\) and \(\arg\left(\frac{z+3}{z-i}\right) = \frac{\pi}{4}\). Then \(|z|^2\) 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 [·] denote the greatest integer function. If the domain of the function \[ f(x) = \cos^{-1}\left(\frac{4x + 2\lfloor x \rfloor}{3}\right) \] is \([\alpha, \beta]\), then \(12(\alpha + \beta)\) is equal to:

If \[ \alpha=\int_{0}^{2\sqrt{3}} \log_2(x^2+4)\,dx + \int_{2}^{4} \sqrt{2^x-4}\,dx, \] then \(\alpha^2\) is equal to _____.

Let a circle \(C\) have its centre in the first quadrant, intersect the coordinate axes at exactly three points and cut off equal intercepts from the coordinate axes. If the length of the chord of \(C\) on the line \(x+y=1\) is \(\sqrt{14}\), then the square of the radius of \(C\) is _____.}

Let \(a,b,c \in \{1,2,3,4\}\). If the probability that \[ ax^2 + 2\sqrt{2}\,bx + c>0 \quad \text{for all } x \in \mathbb{R} \] is \( \frac{m}{n} \), where \(\gcd(m,n)=1\), then \(m+n\) is equal to _____.

If \[ \sum_{k=1}^{n} a_k = 6n^3, \] then} \[ \sum_{k=1}^{6}\left(\frac{a_{k+1}-a_k}{36}\right)^2 \] is equal to _______.

If the domain of the function} \[ f(x)=\sqrt{\log_{0.6}\left(\left|\frac{2x-5}{x^2-4}\right|\right)} \] is \((-\infty,a] \cup \{b\} \cup [c,d) \cup (e,\infty)\), then the value of \(a+b+c+d+e\) is _______.}

Let \(y=y(x)\) be the solution curve of the differential equation} \[ (1+\sin x)\frac{dy}{dx}+(y+1)\cos x=0,\qquad y(0)=0. \] If the curve passes through the point \( \left(\alpha,-\frac12\right) \), then a value of \( \alpha \) is:

Let \([\,]\) denote the greatest integer function. Then the value of} \[ \int_{0}^{3}\left(\frac{e^x+e^{-x}}{[x]!}\right)dx \] is:

If the curve \(y=f(x)\) passes through the point \((1,e)\) and satisfies the differential equation} \[ dy=y(2+\log_e x)\,dx,\quad x>0, \] then \(f(e)\) is equal to:

If \[ \lim_{x\to 2}\frac{\sin(x^3-5x^2+ax+b)}{(\sqrt{x-1}-1)\log_e(x-1)}=m, \] then \(a+b+m\) is equal to:

If \(|\vec a|=2\) and \(|\vec b|=3\), then the maximum value of \[ 3\left|\left(\vec a+2\vec b\right)\right| + 4\left|\left(3\vec a-2\vec b\right)\right| \] is: