List of top Mathematics Questions asked in JEE Main

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:

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

For $x \geq 0$, the least value of $K$, for which $4^{1+x}, 4^{1-x}, \frac{K}{2}, 16^{x}, 16^{-x}$ are three consecutive terms of an A.P. is equal to:

Let \(\vec{a}\) = 2$\hat{i}$ + 5$\hat{j}$ - $\hat{k}$, $\vec{b}$ = 2$\hat{i}$ - 2$\hat{j}$ + 2$\hat{k}$
and $\vec{c}$ be three vectors such that
($\vec{c}$ + $\hat{i}$) $\times$ ($\vec{a}$ + $\vec{b}$ + $\hat{i}$) = $\vec{a}$ $\times$ ($\vec{c}$ + $\hat{i})$ . $\vec{a}$.$\vec{c}$ = -29,)
then $\vec{c}$.(-2$\hat{i}$ + $\hat{j}$ + $\hat{k}$) is equal to :

Let the set $S = \{2, 4, 8, 16, ..., 512\}$ be partitioned into 3 sets $A, B, C$ with equal number of elements such that $A \cup B \cup C = S$ and $A \cap B = B \cap C = A \cap C = \phi$. The maximum number of such possible partitions of $S$ is equal to:

Suppose AB is a focal chord of the parabola \( y^2 = 12x \) of length \( l \) and slope \( m<\sqrt{3} \). If the distance of the chord AB from the origin is \( d \), then \( ld^2 \) is equal to _________.

If \(n-1C_r= (k^2-8)^nC_r+1\) Find \(k\).

Let A(-1, 1) and B(2, 3) be two points and P be a variable point above the line AB such that the area of $\triangle APB$ is 10. If the locus of P is $ax + by = 15$, then $5a + 2b$ is:

If the constant term in the expansion of \((1 + 2x - 3x^3) \left(\frac{3}{2}x^2 - \frac{1}{3x}\right)^9\) is \( p \), then \( 108p \) is equal to _________.

If \[1 + \frac{\sqrt{3} - \sqrt{2}}{2\sqrt{3}} + \frac{5 - 2\sqrt{6}}{18} + \frac{9\sqrt{3} - 11\sqrt{2}}{36\sqrt{3}} + \frac{49 - 20\sqrt{6}}{180} + \cdots\] up to \(\infty = 2 \left( \sqrt{\frac{b}{a}} + 1 \right) \log_e \left( \frac{a}{b} \right)\), where \(a\) and \(b\) are integers with \(\gcd(a, b) = 1\), then (11a + 18b\) is equal to _________.

Let the maximum and minimum values of \[\left( \sqrt{8x - x^2 - 12 - 4} \right)^2 + (x - 7)^2, \quad x \in \mathbb{R} \text{ be } M \text{ and } m \text{ respectively}.\] Then \( M^2 - m^2 \) is equal to _____.

Let the circle $C_{1}: x^{2}+y^{2}-2(x+y)+1=0$ and $C_{2}$ be a circle having centre at $(-1, 0)$ and radius 2. If the line of the common chord of $C_{1}$ and $C_{2}$ intersects the y-axis at the point P, then the square of the distance of P from the centre of $C_{1}$ is:

If the foot is perpendicular from (1, 2, 3) to the line \(\frac{x+1}{2} = \frac{y-2}{5} = \frac{z-1}{1}\) is \(( a, \beta, \gamma)\), then find \(a + \beta + \gamma\)

Let \( y = y(x) \) be the solution of the differential equation\[\frac{dy}{dx} + \frac{2x}{\left( 1 + x^2 \right)^2} y = x e^{\frac{1}{1+x^2}}, \quad y(0) = 0. \] Then the area enclosed by the curve \[ f(x) = y(x) e^{\frac{1}{1+x^2}} \]and the line \( y - x = 4 \) is _______.

Let $f: [-1, 2] \rightarrow \mathbb{R}$ be given by $f(x) = 2x^2 + x + [x^2] - [x]$, where $[t]$ denotes the greatest integer less than or equal to $t$. The number of points, where $f$ is not continuous, is:

Suppose \( \theta \in \left[ 0, \frac{\pi}{4} \right] \) is a solution of \( 4 \cos \theta - 3 \sin \theta = 1 \). Then \( \cos \theta \) is equal to:

The number of solutions of \[\sin^2 x + (2 + 2x - x^2) \sin x - 3(x - 1)^2 = 0, \quad \text{where } -\pi \leq x \leq \pi,\] is

If the function \(f(x) = \frac{\sin 3x + \alpha \sin x - \beta \cos 3x}{x^3},\) \(x \in \mathbb{R} \), is continuous at \( x = 0 \), then \( f(0) \) is equal to:

If the domain of the function \(f(x)\) = \(\frac{\sqrt{x^2-25}}{(4-x^2)}+ \log(x^2+2x-15)\) is \((-∞, α) ∪ (β, ∞)\), then \(α^2+β^2\) is equal to \(b\)

The number of distinct real roots of the equation \[ |x| \, |x + 2| - 5|x + 1| - 1 = 0 \] is _________.

If \(4 cos\ θ + 5 sin\ θ = 1\), then all possible values of \(tan\ θ\), is/are
Where, \(θ∈(-\frac \pi2,\frac \pi2)\)

Let the coefficient of \( x^r \) in the expansion of \((x + 3)^{n-1} + (x + 3)^{n-2} (x + 2) + (x + 3)^{n-3} (x + 2)^2 + \ldots + (x + 2)^{n-1}\)
be \( \alpha_r \). If \( \sum_{r=0}^n \alpha_r = \beta^n - \gamma^n \), \( \beta, \gamma \in \mathbb{N} \), then the value of \( \beta^2 + \gamma^2 \) equals \(\_\_\_\_\_\).

If \(f(x) =ln(\frac {1-x^2}{1+x^2})\) then value of \(225(f'(x) – f''(x))\) at \(x=\frac 12\)

Let a die rolled till 2 is obtained. The probability that 2 obtained on even numbered toss is equal to:

If \(f(x)=\begin{vmatrix} x^3 & 2x^2+1 & 1+3x \\[0.3em] 3x^2+2 & 2x & x^3+6 \\[0.3em] x^3-x & 4 & x^2-2 \end{vmatrix}\)  for all \(x∈R\), then \(2f(0) + f'(0)\) is equal to