List of top Engineering Mathematics Questions

For applying Simpson's \( \frac{1}{3} \) rule, the given interval must be divided into how many number of sub-intervals?
Which of the following formula is used to fit a polynomial for interpolation with equally spaced data?
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:
Given the inverse Fourier transform of \[ f(s) = \begin{cases} a - |s|, & |s| \leq a \\ 0, & |s| > a \end{cases} \] The value of \[ \int_0^\pi \left( \frac{\sin x}{x} \right)^2 dx \] is:
The Region of Convergence (ROC) of the signal \( x(n) = \delta(n - k), k>0 \) is:
The only function from the following that is analytic is:
The area between the parabolas \( y^2 = 4 - x \) and \( y^2 = x \) is given by:
The solution of the given ordinary differential equation \( x \frac{d^2 y}{dx^2} + \frac{dy}{dx} = 0 \) is:
The shortest and longest distance from the point \( (1,2,-1) \) to the sphere \( x^2 + y^2 + z^2 = 24 \) is:
Let \[ M = \begin{bmatrix} 1 & 1 & 1 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{bmatrix} \] The maximum number of linearly independent eigenvectors of \( M \) is:
If the system of equations: \[ 3x + 2y + z = 0, \quad x + 4y + z = 0, \quad 2x + y + 4z = 0 \] is given, then:
If \( A \) is a \( 3 \times 3 \) matrix and the determinant of \( A \) is 6, then find the value of the determinant of the matrix \( (2A)^{-1} \):
For a Binomial distribution with mean 4 and variance 2, the value of \( n \) 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:
The value of the integral \[ \iiint\limits_{0}^{a, b, c} e^{x+y+z} \, dz \, dy \, dx \] 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 complete integral of the partial differential equation \( pz^2 \sin^2 x + qz^2 \cos^2 y = 1 \) is:
For the matrix \[ \begin{bmatrix} 4 & 2 \\ 3 & 3 \end{bmatrix} \] , eigenvalue corresponding to the eigenvector \[ \begin{bmatrix} 2 \\ -3 \end{bmatrix} \] is ................. (in integer).
Two cards are drawn one after the other from a regular deck of 52 playing cards without replacement. The probability that the drawn cards are of different suits is
Three unbiased coins are tossed. Provided that at least two outcomes are tails, the probability of having all three outcomes as tails is
What is $\lim_{x \to 0} f(x)$, where $f(x) = x \sin \frac{1}{x}$?
The rank of the matrix $A$ given below is one. The ratio $\dfrac{\alpha}{\beta}$ is ______ (rounded off to the nearest integer). \[ A = \begin{bmatrix} 1 & 4 \\ -3 & \alpha \\ \beta & 6 \end{bmatrix} \]
Consider the real-valued function \( g(x)=\max\{(x-2)^2,\,-2x+7\}\), \(x\in(-\infty,\infty)\). The minimum value attained by \(g(x)\) is _____(rounded off to one decimal place).
Let $f(z)=j\,\dfrac{1-z}{1+z}$, where $z$ is complex and $j=\sqrt{-1}$. The inverse function $f^{-1}(z)$ maps the {real axis} to the ______.