List of top Engineering Mathematics Questions

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 $.

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.

If $u = \sin^{-1}\left(\frac{x}{y}\right) + \tan^{-1}\left(\frac{y}{x}\right)$, then the value of $ x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y} $ is:

If $ A = \begin{bmatrix} 6 & -2 & 2 \\ -2 & 3 & -1 \\ 2 & -1 & 3 \end{bmatrix} $, then eigen value and its corresponding eigen vector

Let E and F be the events of a sample space S of an experiment, if $ P(S/F) = P(F/F) $, then $ P(S/F) $ is equal to:

A constant force $\vec{F} = (4\hat{i} + \hat{j} - 3\hat{k}) \, \text{N} $ moves a particle from $ A: (1, 2, 3) \, \text{m} \text{to} B: (5, 4, 1) \, \text{m}. $
Find the work done by the force (in joules). Answer as an integer.

Using Trapezoidal rule with one interval, find the approximate value of $\displaystyle \int_{1}^{2}\frac{dx}{1+x^{2}}$ (rounded off to 2 decimal places).

Given $y=e^{px}\sin(qx)$, where $p,q\neq 0$ are real, find the value of \[ \frac{d^{2}y}{dx^{2}}-2p\frac{dy}{dx}+(p^{2}+q^{2})y. \]

Consider \[ f(x) = \begin{cases} x^2, & x < 0, \\[6pt] x, & x \ge 0. \end{cases} \] Which statements are correct?

Consider the matrix \[A = \begin{bmatrix} 5 & -4 \\ k & -1 \end{bmatrix},\]
where $k$ is a constant. If $\det(A) = 3$, then the ratio of the largest eigenvalue of $A$ to $k$ is ___________ (rounded off to 1 decimal place).

The following system of linear equations \[ 7x-3y+z=0,\quad 3x-y+z=0,\quad x-y-z=0 \] has:

The acceleration of a body travelling in a straight line is $a=-C_1-C_2v^2$ where $v$ is the velocity and $C_1,C_2 > 0$. Starting with an initial positive velocity $v_0$, the distance travelled before coming to rest for the first time is:

Evaluate the limit $$ \lim_{x \to \infty} \frac{\sin x}{x} $$

$L$ is a lower triangular matrix with all Principal diagonal elements equal to 1 and $U$ is an upper triangular matrix such that \[ LU = \begin{bmatrix} 1 & 3 & 0 \\ 3 & 7 & 1 \\ 2 & 8 & 3 \end{bmatrix}, \] then the Trace of $L$ + Trace of $U$ =

For the matrix \[ \begin{bmatrix} 2 & 1 & 1 \\ 0 & 2 & 1 \\ 1 & 0 & 1 \end{bmatrix}, \] an Eigen vector among the following vectors is

In a communication network, 98% of messages are transmitted correctly with no error. If the random variable X denotes the number of messages transmitted with error, then the probability that at most two messages are transmitted with error out of 1000 messages sent, is

Two numbers are drawn simultaneously from the set of integers from 1 to 12. If it is known that the sum of drawn two numbers is odd, then the probability that only one of the two numbers is a prime number, is

If $ A = \begin{pmatrix} 2024 & 2021 \\ 2023 & 2022 \end{pmatrix} $, then the value of \[ \left| A^{2024} - A^{2023} \right| \] is