List of top Engineering Mathematics Questions

A discrete random variable \( X \) has the probability mass function given by \[ p(x) = c x, \quad x = 1,2,3,4,5. \] The value of the constant \( c \) is:
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 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 value of \( \oint_C \frac{1}{z} dz \), where \( C \) is the circle \( z = e^{i\theta}, 0 \leq \theta \leq \pi \), is:
The complete integral of the partial differential equation \( pz^2 \sin^2 x + qz^2 \cos^2 y = 1 \) is:
Let $w^4 = 16j$. Which of the following cannot be a value of $w$?
The value of the contour integral, $\displaystyle \oint_{C}\left(\frac{z+2}{z^{2}+2z+2}\right)dz$, where the contour $C$ is $\left\{ z:\; \left| z+1-\tfrac{3}{2}j \right| = 1 \right\}$, taken in the counter clockwise direction, is
Let \(\mathbf{v}_1=\begin{bmatrix}1 \\ 2 \\ 0\end{bmatrix}\) and \(\mathbf{v}_2=\begin{bmatrix}2 \\ 1 \\ 3\end{bmatrix}\) be two vectors. The value of the coefficient \(\alpha\) in the expression \(\mathbf{v}_1=\alpha \mathbf{v}_2+\mathbf{e}\), which minimizes the length of the error vector \(\mathbf{e}\), is
Let the sets of eigenvalues and eigenvectors of a matrix $B$ be $\{\lambda_k \mid 1 \le k \le n\}$ and $\{\mathbf{v}_k \mid 1 \le k \le n\}$, respectively. For any invertible matrix $P$, the sets of eigenvalues and eigenvectors of the matrix $A$, where $B=P^{-1}AP$, respectively, are
Let $\mathbf{x}$ be an $n \times 1$ real column vector with length $l=\sqrt{\mathbf{x}^T\mathbf{x}}$. The trace of the matrix $P=\mathbf{x}\mathbf{x}^T$ is _____________
The state equation of a second order system is $\dot{x}(t)=Ax(t)$, with $x(0)$ as the initial condition. Suppose $\lambda_1$ and $\lambda_2$ are two distinct eigenvalues of $A$ and $v_1$ and $v_2$ are the corresponding eigenvectors. For constants $\alpha_1$ and $\alpha_2$, the solution $x(t)$ of the state equation is _____________