List of top Engineering Mathematics Questions

If the characteristic polynomial of the matrix \( A_{3\times3} \) is given by \( f(\lambda) = \lambda^3 - 10\lambda^2 + 27\lambda - 18 \), then trace of A and determinant of A respectively are
If the equations $x^2+2x+K=0$ and $x^2+Kx+2=0$ have one root in common, then the product of the other two roots is?
If $b_{yx}$ and $b_{xy}$ are regression coefficients and they are equal, then?
If $$ A = \begin{pmatrix} 3 & -2 \\ 4 & -2 \end{pmatrix} $$ satisfies the matrix equation $$ A^2 - K A + 2I = 0, $$ then the value of $ K $ is:
Given $$ x = 4y + 5, \quad y = Kx + 4, $$ the lines of regression of $ x $ on $ y $ and $ y $ on $ x $ respectively. What is the value of $ K $, if the value of correlation coefficient $ r = 0.5 $?
If $ X $ is a Poisson variate such that $ P(X=1) = \frac{3}{10} $ and $ P(X=2) = \frac{1}{5} $, then the mean of the distribution is:
The general solution of the differential equation $$ (D^2 - 5D + 6) y = e^{3x} $$ is:
The particular integral of $$ (x^2 D^2 + 4 x D + 2) y = x^2 $$ is:
The Newton-Raphson iteration $$ x_{n+1} = \frac{1}{3} \left( 2 x_n + \frac{N}{x_n^2} \right) $$ is used to compute
Compute the Jacobian $ \frac{\partial(x,y)}{\partial(u,v)} $ of the transformation: $$ x = \frac{u+v}{1 - uv}, \quad y = \tan^{-1} u + \tan^{-1} v $$
The value of $$ \int_0^1 x^4 (1 - x)^2 \, dx $$ is:
The unit normal vector to the level surface $$ x^2 y + 2 x z = 4 $$ at the point $ (2, -2, 3) $ is:
If $$ A = \frac{1}{2} \begin{pmatrix} -1 & 1 & 1 & 1 \\ 1 & -1 & 1 & 1 \\ 1 & 1 & -1 & 1 \\ 1 & 1 & 1 & -1 \end{pmatrix}, $$ then the inverse of $ AA^T $ is:
If the linear transformation \( X = BY \) transforms \( X^\top AX \) to \( Y^\top PY \), then \( P = \):
Let \( A = \begin{bmatrix} 1 & 1 & 3 \\ 1 & 5 & 1 \\ 3 & 1 & 1 \end{bmatrix} \), \( P = \begin{bmatrix} -1 & 1 & 1 \\ 0 & -1 & 2 \\ 1 & 1 & 1 \end{bmatrix} \). Then \( \det(P^{-1} A P - 2I) \) is equal to:

Let $f(x) = \begin{cases} h(x), & 0<x<C \\-h(-x), & -C<x<0 \end{cases}$ and $f(x+2C)=f(x) \; \forall x \in \mathbb{R}$. If the Fourier series of $f(x) = \sum_{n=0}^\infty \left(a_n \cos\frac{n\pi x}{C} + b_n \sin\frac{n\pi x}{C}\right)$ then $\sum_{n=0}^\infty a_n b_n =$

If the characteristic equation of a $3 \times 3$ square matrix A is $ax^3+bx^2+cx+d=0$, $(a \neq 0)$ then the Trace of A + det A =
If $\lambda_1$ and $\lambda_2$ are two distinct eigen values of a symmetric matrix, $X_1$ and $X_2$ are the eigen vectors corresponding to $\lambda_1, \lambda_2$ respectively, then
When the IVP \( \frac{dy}{dx} = y + x,\; y(0) = 1 \) is solved by Rung–Kutta fourth order method to find \( y(0.2) \), the approximate value of \( y(0.2) \) by taking step size \( h = 0.2 \) is:
The real part of an analytic function \( f(z) = u + iv \), where \( v(x, y) = \left( \frac{e^{-y} - e^y}{2} \right) \sin x \), is:
If the probability density function of a continuous random variable \( X \) is \( f(x) \), \( -\infty<x<\infty \), and if the median of \( X \) is \( M \), then:
A card is drawn from a pack of cards successively 5 times by replacing the card drawn in the pack of cards. What is the mean of the number of red cards drawn?
If \( \mathcal{L}(f(t)) = F(s) \), then \( \mathcal{L}((\cosh 2t)f(t)) \) is:
The substitution which reduces the differential equation \( t^2 \frac{d^2y}{dt^2} + 5t \frac{dy}{dt} + 7y = 0 \) to \( \frac{d^2y}{dx^2} + 4 \frac{dy}{dx} + 7y = 0 \) is:
If \( E \) is the region bounded by a closed curve \( C \) in the \( xy \)-plane, then \( \iint_E dx\,dy = \)