List of top Mathematics Questions asked in JEE Main

If\[\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \sqrt{1 - \sin 2x} \, dx = \alpha + \beta \sqrt{2} + \gamma \sqrt{3},\]where \( \alpha \), \( \beta \), and \( \gamma \) are rational numbers, then \( 3\alpha + 4\beta - \gamma \) is equal to ______.

Let the area of the region \( \{(x, y): 0 \leq x \leq 3, 0 \leq y \leq \min\{x^2 + 2, 2x + 2\}\} \) be \( A \). Then \( 12A \) is equal to ______.

Let \(\alpha, \beta, \gamma\) be the foot of perpendicular from the point \((1, 2, 3)\) on the line \(\frac{x + 3}{5} = \frac{y - 1}{2} = \frac{z + 4}{3}\). Then \(19(\alpha + \beta + \gamma)\) is equal to:

If the shortest distance between the lines \(\frac{x - 4}{1} = \frac{y + 1}{2} = \frac{z}{-3} and \frac{x - \lambda}{2} = \frac{y + 1}{4} = \frac{z - 2}{-5}\) is \(\frac{6}{\sqrt{5}}\), then the sum of all possible values of \(\lambda\) is:

Let the image of the point \( (1, 0, 7) \) in the line \[ \frac{x}{1} = \frac{y - 1}{2} = \frac{z - 2}{3} \] be the point \( (\alpha, \beta, \gamma) \). Then which one of the following points lies on the line passing through \( (\alpha, \beta, \gamma) \) and making angles \( \frac{2\pi}{3} \) and \( \frac{3\pi}{4} \) with the y-axis and z-axis respectively and an acute angle with the x-axis?

The function \( f(x) = 2x + 3(x)^{\frac{2}{3}}, x \in \mathbb{R} \), has

If each term of a geometric progression \( a_1, a_2, a_3, \dots \) with \( a_1 = \frac{1}{8} \) and \( a_2 \neq a_1 \), is the arithmetic mean of the next two terms and \( S_n = a_1 + a_2 + \dots + a_n \), then \( S_{20} - S_{18} \) is equal to

A company has two plants A and B to manufacture motorcycles. 60% motorcycles are manufactured at plant A and the remaining are manufactured at plant B. 80% of the motorcycles manufactured at plant A are rated of the standard quality, while 90% of the motorcycles manufactured at plant B are rated of the standard quality. A motorcycle picked up randomly from the total production is found to be of the standard quality. If p is the probability that it was manufactured at plant B, then 126p is

The shortest distance between the lines
\[\frac{x - 3}{2} = \frac{y + 15}{-7} = \frac{z - 9}{5}\]and
\[\frac{x + 1}{2} = \frac{y - 1}{1} = \frac{z - 9}{-3}\] is:

The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. On respectively, it was found that an observation by mistake was taken 8 instead of 12. The correct standard deviation is

For \( \alpha, \beta \in \mathbb{R} \) and a natural number \( n \), let \[A_r = \begin{vmatrix} r & 1 & \frac{n^2}{2} + \alpha \\ 2r & 2 & n^2 - \beta \\3r - 2 & 3 & \frac{n(3n - 1)}{2} \end{vmatrix}.\]Then \( 2A_{10} - A_8 \) is:

Let \( A = \{ n \in [100, 700] \cap \mathbb{N} : n \text{ is neither a multiple of 3 nor a multiple of 4} \} \).
Then the number of elements in \( A \) is:

The function \( f(x) = \frac{x^2 + 2x - 15}{x^2 - 4x + 9} \), \( x \in \mathbb{R} \) is:

Let \( C \) be the circle of minimum area touching the parabola \( y = 6 - x^2 \) and the lines \( y = \sqrt{3} |x| \). Then, which one of the following points lies on the circle \( C \)?

\( \int_{0}^{\pi/4} \frac{\cos^2 x \sin^2 x}{\left( \cos^3 x + \sin^3 x \right)^2} \, dx \) is equal to:

If \( f(x) = \begin{cases} x^3 \sin\left(\frac{1}{x}\right), & x \neq 0 \\ 0, & x = 0 \end{cases} \), then:

If \( A(3, 1, -1) \), \( B\left(\frac{5}{3}, \frac{7}{3}, \frac{1}{3}\right) \), \( C(2, 2, 1) \), and \( D\left(\frac{10}{3}, \frac{2}{3}, \frac{-1}{3}\right) \) are the vertices of a quadrilateral ABCD, then its area is:

Let a ray of light passing through the point \((3, 10)\) reflects on the line \(2x + y = 6\) and the reflected ray passes through the point \((7, 2)\). If the equation of the incident ray is \(ax + by + 1 = 0\), then \(a^2 + b^2 + 3ab\) is equal to _.

If the term independent of \(x\) in the expansion of \[ \left( \sqrt{ax^2} + \frac{1}{2x^3} \right)^{10} \] is 105, then \(a^2\) is equal to:

The area of the region in the first quadrant inside the circle \(x^2 + y^2 = 8\) and outside the parabola \(y^2 = 2x\) is equal to:

An arithmetic progression is written in the following way

The sum of all the terms of the 10^th row is ______ .

If \[ \alpha = \lim_{x \to 0^+} \left( \frac{e^{\sqrt{\tan x}} - e^{\sqrt{x}}}{\sqrt{\tan x} - \sqrt{x}} \right) \] \[ \beta = \lim_{x \to 0} (1 + \sin x)^{\frac{1}{2\cot x}} \] are the roots of the quadratic equation \(ax^2 + bx - \sqrt{e} = 0\), then \(12 \log_e (a + b)\) is equal to _________.

Let $\alpha = \sum_{r=0}^n (4r^2 + 2r + 1) \binom{n}{r}$ and $\beta = \left( \sum_{r=0}^n \frac{\binom{n}{r}}{r+1} \right) + \frac{1}{n+1}$. If $140 < \frac{2\alpha}{\beta} < 281$, then the value of $n$ is _____.

Let $z$ be a complex number such that $|z + 2| = 1$ and $\text{Im}\left(\frac{z+1}{z+2}\right) = \frac{1}{5}$. Then the value of $|\text{Re}(z+2)|$ is:

If the shortest distance between the lines \[ \frac{x - \lambda}{2} = \frac{y - 4}{3} = \frac{z - 3}{4} \] and \[ \frac{x - 2}{4} = \frac{y - 4}{6} = \frac{z - 7}{8} \] is \(\frac{13}{\sqrt{29}}\), then a value of \(\lambda\) is: