List of top Engineering Mathematics Questions

Eigenvalue question: \[\begin{pmatrix} 6 & 8 \\ 4 & 2 \end{pmatrix} \quad \text{Eigenvalue options:} \quad \text{(i) 1, (ii) 2, (iii) 3, (iv) 4}\]
Given the matrix equation: \[A = \begin{pmatrix} 2 & 3 & 4 \\ 1 & 4 & 5 \\ 4 & 3 & 2 \end{pmatrix} \quad A \cdot X = B\]
Where \( A \) is the matrix, \( X \) is the unknown vector, and \( B \) is a constant vector. Solve for \( X \).
Given that \( \lambda \) is an eigenvalue of matrix \( A \) with the corresponding eigenvector \( x \), and \( x \) is also an eigenvector of \( B = A - 2I \), find the relationship between \( \lambda \) and the eigenvalue of \( B \).
Find the maximum value of the function \( f(x) = -x^3 + 2x^2 \) in the interval \( [-1, 1.5] \).
Given the random variable \( X \) which takes the values 0, 1, 2, 7, 11, and 12 with the following probabilities: \[ P(X = 0) = 0.4, \quad P(X = 1) = 0.3, \quad P(X = 2) = 0.1, \quad P(X = 7) = 0.1, \quad P(X = 11) = ? \]
Find the sum of the series: \[ 1 + \frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \cdots \]
Solve the second-order differential equation: \[ y'' + 0.8 y' + 0.16 y = 0, \quad y(0) = 3, \quad y'(0) = 4.5 \]
Solve the cubic equation: \[ x^3 - \frac{15}{2} x^2 + 18x + 20 = 0 \]
Find the order and degree of the following differential equation: \[ \frac{d^3 y}{dx^3} + \frac{d^2 y}{dx^2} + \frac{dy}{dx} + y = 0 \]
Find the next term in the sequence: 3, 9, 19, 33, _
Given the matrix: \[A = \begin{bmatrix} 2 & 3 & 4 & 5 \\ 0 & 6 & 7 & 8 \\ 0 & 0 & \alpha & \beta \\ 0 & 0 & 0 & \gamma \end{bmatrix}\]

 If rank(A) is at least 3, then what are the possible values of \( \alpha, \beta, \gamma \)?

Two fair dice are rolled, and the random variable \( X \) denotes the sum of the outcomes. What is the expected value of \( X \)?
If a complex function \( f(z) \) is analytic everywhere inside a closed contour \( C \) with anti-clockwise direction, then which of the following statements are correct?
Consider three Boolean variables \( x, y, z \). A majority function outputs 1 if the majority of its inputs are 1, otherwise, it outputs 0. Derive the Boolean expression for the majority function and simplify it using Boolean algebra.
Given the equation: \[ 3^{x^2} = 27 \times 9^x \] Find the value of: \[ \frac{2^{x^2}}{(2^x)^2} \]
If \( A \) is a \( 3 \times 3 \) matrix and determinant of \( A \) is 6, then find the value of the determinant of the matrix \((2A)^{-1}\):
For applying Simpson's \( \frac{1}{3} \) rule, the given interval must be divided into how many number of sub-intervals?
The solution of the given ordinary differential equation \( x \frac{d^2 y}{dx^2} + \frac{dy}{dx} = 0 \) is:
Which of the following formula is used to fit a polynomial for interpolation with equally spaced data?
The complete integral of the partial differential equation \( pz^2 \sin^2 x + qz^2 \cos^2 y = 1 \) is:
The value of \( m \) so that \( 2x - x^2 + m y^2 \) may be harmonic is:
If \( \nabla \phi = 2xy^2 \hat{i} + x^2z^2 \hat{j} + 3x^2y^2z^2 \hat{k} \), then \( \phi(x,y,z) \) is:
The shortest and longest distance from the point \( (1,2,-1) \) to the sphere \( x^2 + y^2 + z^2 = 24 \) is:
The value of \( \oint_C \frac{1}{z} dz \), where \( C \) is the circle \( z = e^{i\theta}, 0 \leq \theta \leq \pi \), is:
If \( A = [a_{ij}] \) is the coefficient matrix for a system of algebraic equations, then a sufficient condition for convergence of Gauss-Seidel iteration method is: