List of top Mathematics Questions

The corner points of the feasible region in graphical representation of a L.P.P. are \( (2, 72), (15, 20) \) and \( (40, 15) \). If \( Z = 1x + 9y \) be the objective function, then:
If \( \begin{bmatrix} 7 & 0 \\ 0 & 7 \end{bmatrix} \) is a scalar matrix, then \( x^y \) is equal to:

In a Linear Programming Problem (LPP), the objective function $Z = 2x + 5y$ is to be maximized under the following constraints:

\[ x + y \leq 4, \quad 3x + 3y \geq 18, \quad x, y \geq 0. \] Study the graph and select the correct option.

If A and B are two square matrices of the same order, then (A + B)(A - B) is equal to:
If $f : \mathbb{N} \rightarrow \mathbb{W}$ is defined as \[ f(n) = \begin{cases} \frac{n}{2}, & \text{if } n \text{ is even} \\ 0, & \text{if } n \text{ is odd} \end{cases} \] then $f$ is :
Find the angle at which the given lines are inclined to each other: \[ l_1: \frac{x - 5}{2} = \frac{y + 3}{1} = \frac{z - 1}{-3} \] \[ l_2: \frac{x}{3} = \frac{y - 1}{2} = \frac{z + 5}{-1} \]
If \[ A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & -2 \end{bmatrix}, \] then \( |A| \) is:
For positive integers \( n \), if \( 4 a_n = \frac{n^2 + 5n + 6}{4} \) and \[ S_n = \sum_{k=1}^{n} \left( \frac{1}{a_k} \right), \text{ then the value of } 507 S_{2025} \text{ is:} \]
If a matrix A is both symmetric and skew-symmetric, then A is:
If the matrix \[ \begin{bmatrix} 1 & 12 & 4y \\ 6x & 5 & 2x \\ 8x & 4 & 6 \end{bmatrix} \]
is a symmetric matrix, then the value of \( 2x + y \) is:
Let P be a skew-symmetric matrix of order 3. If \( \det(P) = \alpha \), then \( (2025)^\alpha \) is
The integrating factor of the differential equation \[ \frac{dy}{dx} + y \tan x - \sec x = 0 \quad \text{is:} \]
If \( p \) and \( q \) are respectively the order and degree of the differential equation \( \frac{d}{dx} \left( \frac{dy}{dx} \right)^3 = 0 \), then \( (p - q) \) is:
The order and degree of the differential equation \[ \left( \frac{d^2y}{dx^2} \right)^2 + \left( \frac{dy}{dx} \right)^2 = x \sin \left( \frac{dy}{dx} \right) \] are :
The sum of the order and degree of the differential equation \[ \left( 1 + \left( \frac{dy}{dx} \right)^2 \right) \frac{d^2y}{dx^2} = \left( \frac{dy}{dx} \right)^3 \] is:
The integrating factor of the differential equation \( \frac{dx}{dy} = \frac{x \log x}{2 \log x - y} \) is:
The order and degree of the differential function \[ \left[ 1 + \left( \frac{dy}{dx} \right)^2 \right]^5 = \frac{d^2y}{dx^2} \]
The solution for the differential equation $\log \left( \frac{dy}{dx} \right) = 3x + 4y$ is:
The order and degree of the following differential equation are, respectively: \[ \frac{d^4y}{dx^4} + 2 \frac{d^2y}{dx^2} + y^2 = 0. \]
If \( m' \) and \( n' \) are the degree and order respectively of the differential equation \( 1 + \left( \frac{dy}{dx} \right)^3 = \frac{d^2 y{dx^2} \), then the value of \( (m + n) \) is: }
The order and degree of the differential equation \[ \left[ \left( \frac{d^2 y}{dx^2} \right)^2 - 1 \right]^2 = \frac{dy}{dx} \text{ are, respectively:} \]
The order and degree of the differential equation \[ \frac{d^2y}{dx^2} + 4 \left(\frac{dy}{dx}\right) = x \log \left(\frac{d^2y}{dx^2}\right) \text{ are respectively:} \]
If the rate of change of volume of a sphere is twice the rate of change of its radius, then the surface area of the sphere is:
The general solution of the differential equation \( \frac{dy}{dx} = 2x \cdot e^{x^2 + y} \) is:
Four friends Abhay, Bina, Chhaya, and Devesh were asked to simplify \( 4 AB + 3(AB + BA) - 4 BA \), where \( A \) and \( B \) are both matrices of order \( 2 \times 2 \). It is known that \( A \neq B \) and \( A^{-1} \neq B \). Their answers are given as: