List of top Mathematics Questions asked in JEE Main

The constant term in the expansion of $\left(2 x+\frac{1}{x^7}+3 x^2\right)^5$ is_____

A rectangle is drawn by lines x=0, x=2, y=0 and y=5. Points A and B lie on coordinate axes. If line AB divides the area of rectangle in 4:1, then the locus of mid-point of AB is?

The mean of the coefficients of \( x^n, x^{n+1}, \dots, x^r \) in the binomial expansion of \( (2 + x)^r \) is:

If \( a \) and \( b \) are the roots of the equation \( x^2 - 7x - 1 = 0 \), then the value of \( a^2 + b^2 + a^3 + b^3 is equal to:}

Let a line \( l \) pass through the origin and be perpendicular to the lines \[ l_1: \vec{r}_1 = i + j + 7k + \lambda(i + 2j + 3k), \quad \lambda \in \mathbb{R} \] \[ l_2: \vec{r}_2 = -i + j + 2k + \mu(i + 2j + k), \quad \mu \in \mathbb{R} \] If \( P \) is the point of intersection of \( l_1 \) and \( l_2 \), and \( Q (a, b, \gamma) \) is the foot of perpendicular from P on \( l \), then \( (a + b + \gamma) \) is equal to:

In an examination, 5 students have been allotted their seats as per their roll numbers. The number of ways, in which none of the students sit on the allotted seat, is:

The number of ordered triplets of the truth values of \( p, q, r \) and such that the truth value of the statement \[ (p \lor q) \land (p \lor r) \implies (q \lor r) \text{ is True, is equal to:} \]

Let \( A = \begin{bmatrix} 0 & 1 & 2 \\ 1 & 0 & 3 \\ 1 & 0 & 0 \end{bmatrix} \), where \( a, c \in \mathbb{R} \). If \( A^n = A \) and the positive value of \( a \) belongs to the interval \( (n-1, n] \), where \( n \in \mathbb{N} \), then \( n \) is equal to:

The number of integral terms in the expansion of \left( 3^{\frac{1}{2}} + 5^{\frac{1}{4}} \right)^{680} \text{ is equal to:}

Let \( S = 109 + \frac{108}{5} + \frac{107}{5^2} + \frac{106}{5^3} + \cdots \). Then the value of \( (16S - (25)^{3}) \) is equal to:

Let \( H_n : \frac{x^2}{1 + n} + \frac{y^2}{3 + n} = 1, n \in \mathbb{N} \). Let \( k \) be the smallest even value of \( n \) such that the eccentricity of \( H_n \) is a rational number. If \( l \) is the length of the latus rectum of \( H_k \), then 21 \( l \) is equal to:

For \( m, n>0 \), let \( \alpha(m,n) = \int_{0}^{1} (1 + 3t)^{n} \, dt \). If \( \alpha(10,6) = \int_{0}^{1} (1 + 3t)^{6} \, dt \) and \( \alpha(11,5) = p(14)^{5} \), then \( p \) is equal to:

Let (\alpha, \beta, \gamma) \text{ be the image of the point } P(3, 3, 5) \text{ in the plane } 2x + y - 3z = 6. \text{ Then } \alpha + \beta + \gamma \text{ is equal to:}

If equation of the plane that contains the point \((-2,3,5)\) and is perpendicular to each of the planes \( 2x + 4y + 5z = 8 \) and \( 3x - 2y + 3z = 5 \), is \( \alpha x + \beta y + \gamma z = 97 \), then \( \alpha + \beta + \gamma \) is:

Consider ellipse \( E_k : \frac{x^2}{k} + \frac{y^2}{k} = 1 \), for \( k = 1, 2, \dots, 20 \). Let \( C_k \) be the circle which touches the four chords joining the end points (one on the minor axis and another on the major axis) of the ellipse \( E_k \). If \( r_k \) is the radius of the circle \( C_k \), then the value of \( \sum_{k=1}^{20} r_k^2 \) is:

\( Let f(x) = | x^2 - x | + |x|, \text{ where } x \in \mathbb{R} \text{ and } | t | \text{ denotes the greatest integer less than or equal to } t. \text{ Then, } f \text{ is:} \)

Let \( \mathbf{a} \) be a non-zero vector parallel to the line of intersection of the two planes described by \( i + j + k \) and \( -i - j - k \). If \( \theta \) is the angle between the vector \( \mathbf{a} \) and the vector \( \mathbf{b} = -2i - 2j + 2k \), and \( \left| \mathbf{a} \right| = 6 \), then ordered pair \( (\mathbf{a} \cdot \mathbf{b}) \) is equal to:

Area of the region \((x, y) : x^2 + (y - 2)^2 \leq 4, \, x^2 \geq 2y\) is:

For any vector \( \mathbf{a} = a_1 \hat{i} + a_2 \hat{j} + a_3 \hat{k} \), with \( 10 | \mathbf{a} |<1 \), \( i = 1, 2, 3 \), consider the following statements:

The number of triplets \( (x, y, z) \), where \( x, y, z \) are distinct non-negative integers satisfying \( x + y + z = 15 \), is:

Let sets A and B have 5 elements each. Let mean of the elements in sets A and B be 5 and 8 respectively and the variance of the elements in sets A and B be 12 and 20 respectively. A new set C of 10 elements is formed by subtracting 3 from each element of A and adding 2 to each element of B. Then the sum of the mean and variance of the elements of C is:

The value of the integral \[ \int_{\log_2}^{-\log_2} e^x \left( \log \left( e^x + \sqrt{1 + e^{2x}} \right) \right) dx \] is equal to:

The number of integral solutions of \( \log_2 \left( \frac{x - 7}{2x - 3} \right) \geq 0 \) is:

Let \( f: [2, 4] \to \mathbb{R} \) be a differentiable function such that \( (x \log x) f'(x) + (\log x) f(x) \geq 1 \), \( x \in [2, 4] \) with \( f(2) = \frac{1}{2} \) and \( f(4) = \frac{1}{4} \). Consider the following two statements:
\( (A) \quad f(x) \geq 1 \quad \text{for all} \quad x \in [2, 4] \)
\( (B) \quad f(x) \leq \frac{1}{8} \quad \text{for all} \quad x \in [2, 4] \) Then,

The number of elements in the set \(S = \{ \theta \in [0, 2\pi] : 3 \cos^4 \theta - 5 \cos^2 \theta - 2 \sin^2 \theta + 2 = 0 \}\) is: