List of top Mathematics Questions asked in JEE Main

Negation of the statement \((p \lor r) \implies (q \lor r)\) is :

The number of elements in the set \[ \left\{ A = \begin{pmatrix} a & b \\ 0 & d \end{pmatrix} : a, b, d \in \{-1, 0, 1\} \text{ and } (I - A)^3 = I - A^3 \right\}, \] where \( I \) is the \( 2 \times 2 \) identity matrix, is _________.

The number of 4-digit numbers which are neither multiple of 7 nor multiple of 3 is _________.

If the coefficient of \( a^7b^8 \) in the expansion of \( (a + 2b + 4ab)^{10} \) is \( K \cdot 2^{16} \), then K is equal to _________.

If \( S = \frac{7}{5} + \frac{9}{5^2} + \frac{13}{5^3} + \frac{19}{5^4} + ... \), then 160 S is equal to _________.

Let \( f(x) \) be a cubic polynomial with \( f(1) = -10 \), \( f(-1) = 6 \), and has a local minima at \( x = 1 \), and \( f'(x) \) has a local minima at \( x = -1 \). Then \( f(3) \) is equal to _________.

If \( \int \frac{\sin x}{\sin^3 x + \cos^3 x} dx = \alpha \log_e |1 + \tan x| + \beta \log_e |1 - \tan x + \tan^2 x| + \gamma \tan^{-1} \left( \frac{2 \tan x - 1}{\sqrt{3}} \right) + C \), when C is a constant of integration, then the value of \( 18(\alpha + \beta + \gamma^2) \) is _________.

If the line \( y = mx \) bisects the area enclosed by the lines \( x = 0, y = 0, x = \frac{3}{2} \) and the curve \( y = 1 + 4x - x^2 \), then 12 m is equal to _________.

Let B be the centre of the circle \( x^2 + y^2 - 2x + 4y + 1 = 0 \). Let the tangents at two points P and Q on the circle intersect at the point \( A(3, 1) \). Then \( 8 \cdot \frac{\text{area } \Delta APQ}{\text{area } \Delta BPQ} \) is equal to _________.

A tangent line L is drawn at the point \( (2, -4) \) on the parabola \( y^2 = 8x \). If the line L is also tangent to the circle \( x^2 + y^2 = a \), then 'a' is equal to _________.

Suppose the line $\frac{x - 2}{\alpha} = \frac{y - 2}{-5} = \frac{z + 2}{2}$ lies on the plane $x + 3y - 2z + \beta = 0$. Then $(\alpha + \beta)$ is equal to _________.

If $\vec{P} \times \vec{Q} = \vec{Q} \times \vec{P}$, the angle between $\vec{P}$ and $\vec{Q}$ is $\theta$ (0°<$\theta$<360°). The value of '$\theta$' will be ________°.

If for the matrix, A = \( A = \begin{bmatrix} 1 & -\alpha \\ \alpha & \beta \end{bmatrix} \), and \( A A^T = I_2 \), then the value of \( \alpha^4 + \beta^4 \) is :

Let A be a 3$\times$3 matrix with det(A)=4. Let R$_i$ denote the i$^{th}$ row of A. If a matrix B is obtained by performing the operation R$_2$ $\rightarrow$ 2R$_2$+5R$_3$ on 2A, then det(B) is equal to:

The following system of linear equations
2x + 3y + 2z = 9
3x + 2y + 2z = 9
x - y + 4z = 8

If I$_n$ = $\int_{\pi/4}^{\pi/2} \cot^n x \,dx$, then :

A function f(x) is given by f(x) = $\frac{5^x}{5^x + 5}$, then the sum of the series $f(\frac{1}{20}) + f(\frac{2}{20}) + \dots + f(\frac{39}{20})$ is equal to:

Let $\alpha$ and $\beta$ be the roots of $x^2 - 6x - 2 = 0$. If $a_n = \alpha^n - \beta^n$ for $n \ge 1$, then the value of $\frac{a_{10} - 2a_8}{3a_9}$ is:

The minimum value of f(x) = $a^{a^x} + a^{1-a^x}$, where a, x $\in$ R and a>0, is equal to :

The integral $\int \frac{e^{3\log_e{2x}} + 5e^{2\log_e{2x}}}{e^{4\log_e{x}} + 5e^{3\log_e{x}} - 7e^{2\log_e{x}}} \,dx$, x>0, is equal to: (where c is a constant of integration)

If $\alpha, \beta \in R$ are such that 1$-$2i (here $i^2$=$-$1) is a root of z$^2$+$\alpha$z+$\beta$=0, then ($\alpha-\beta$) is equal to:

If the curve $x^2+2y^2 = 2$ intersects the line $x+y=1$ at two points P and Q, then the angle subtended by the line segment PQ at the origin is :

The shortest distance between the line $x-y=1$ and the curve $x^2 = 2y$ is:

A hyperbola passes through the foci of the ellipse $\frac{x^2}{25} + \frac{y^2}{16} = 1$ and its transverse and conjugate axes coincide with major and minor axes of the ellipse, respectively. If the product of their eccentricities is one, then the equation of the hyperbola is: