List of top Mathematics Questions asked in JEE Main

Let in a $\triangle ABC$, given that $A \equiv (1, 2)$, mid-point of $AB$ is $(-5, -1)$ and centroid is $(3, 4)$ then circumcentre is $(\alpha, \beta)$, then the value of $21(\alpha + \beta)$ is :

If $Z$ be a complex number such that $|Z + 2| = |Z - 2|$ and $\text{arg} \left( \frac{Z - 3}{Z + 1} \right) = \frac{\pi}{4}$, then the value of $|Z|^2$ is

If $\int_{-2}^2 ([\sin x] + |x \sin x|) dx = 2 \sin 2 - 4 \cos 2 - \beta$, then the value of $|\beta|$ where $[\cdot]$ is GIF is

If coefficient of $x^3$ in $(1+x)^3 + (1+x)^4 + \dots + (1+x)^{99} + (1+kx)^{100}$ is $\binom{100}{3} \left( \frac{101}{4} - 43n \right)$, then the value of $(k^3 + 43n)$ is

The domain of $f(x) = \cos^{-1} \left( \frac{4x + 2[x]}{3} \right)$ (where $[x]$ denotes greatest integer function) is

If $f(x)$ is a non-constant polynomial satisfying $f(x) = f'(x)f''(x)$ and $f(0) = 0$. Then the value of $\int_0^2 f(x) dx + f'(2) + f''(2)$ is :

A circle $x^2 + y^2 + x - 3y = 0$ passes through $P(1, 2)$. If 2 chords (PS \& PR) drawn from P are bisected by $y$-axis, then mid point of RS is $(\alpha, \beta)$, find $6(\alpha + \beta)$

Consider the differential equation $\frac{dy}{dx} = (x^2 + x + 1)(y^2 - y + 1)$. If $y(0) = \frac{1}{2}$, then the value of $2(y(1)) - 1$ is

If Latus rectum of parabola $y^2 = 4kx$ and ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ coincide then the value of $e^2 + 2\sqrt{2}$ is, where $e$ is eccentricity of ellipse

Find number of ways of arranging 4 Boys \& 3 Girls such that all girls are not together :

If \( L_1 : x - y = 0 \), \( L_2 : y = -3x \), \( L_3 \) is the obtuse angle bisector of \( L_1 \) and \( L_2 \), and \( L_4 : x + 3 = 0 \). Let \( A \) be the point of intersection of \( L_4 \) and \( L_1 \), \( B \) be the point of intersection of \( L_4 \) and \( L_2 \), and \( C \) be the point of intersection of \( L_4 \) and \( L_3 \). Then the value of \( \dfrac{(BC)^2}{(AC)^2} \) is:

A bag contains 4 red balls, 6 yellow balls and 5 blue balls. In how many ways we can select 8 balls such that we get at least two balls of each colour?

The value of the sum of r / (4 + r⁴) for r = 1 to 10 is:

The coefficient of x² in the binomial expansion of (2x² + 1/x)¹⁰ is:

Let A1, A2, A3, ..., A49 be 49 arithmetic means between 49 and 149. Then the mean of A1, A25, A47 and A49 is:

Let \( A = \{2, 3\ \) and \( B = \{5, 6\} \). Then, the number of relations from \( A \times B \) to \( A \times B \) are:

If \[ (2\alpha+1,\; \alpha^2-3\alpha,\; \frac{\alpha-1}{2}) \] is the image of the point \[ (\alpha,\; 2\alpha,\; 1) \] in the line \[ \frac{x-2}{3}=\frac{y-1}{2}=\frac{z}{1}, \] then find the possible values of \(\alpha\).

Let \(x_1, x_2, x_3, \ldots, x_n\) be ‘\(n\)’ observations such that \( \sum_{i=1}^{n-1} x_i = 48 \) and \( \sum_{i=1}^{n-1} x_i^2 = 496 \). If mean and variance of the distribution are 8 and 16 respectively then value of \(n\) is:

The sum of value \( \sum_{n=1}^{10} \frac{528}{n(n+1)(n+2)} \) is equal to:

The value of \( \int_{0}^{\infty} \frac{\ln x}{x^2 + 4} \, dx \) is equal to:

Consider a set \( A = \{1, 2, 3, 5, 6\ \). The number of one-one functions \( f: A \to A \) such that \( f(1) \geq 3 \), \( f(3) \leq 4 \), and \( f(2) + f(3) = 5 \) is equal to:}