List of top Engineering Mathematics Questions

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.

$L$ 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

Let $X$ follow Binomial distribution with parameters $12$ and $p$, let $q = 1 - p$. If \[ \sum_{x=0}^{12}(x - 12p)^2 \cdot {}^{12}C_x \cdot q^{12 - x} \cdot p^x = \frac{8}{3} \quad \text{and} \quad P(X>10) = \left(\frac{2}{3}\right)^K, \, (K>1), \] then $K =$

The order of the convergence of the bisection method is

If $ X $ is a continuous random variable whose probability density function is given by \[ f(x) = \begin{cases} k(4x - 2x^2), & 0<x<2 \\ 0, & \text{otherwise} \end{cases} \quad \text{then the value of } k \text{ is:} \]

If $ \mathcal{L}\{f(t)\} = \frac{1 - e^{-1/s}}{s} $, then $ \mathcal{L}\{e^{-t}f(3t)\} $ is

The table below gives values of the function $ f(x) = \frac{1}{x} $ at 5 points of $ x $.} \[ \begin{array}{|c|c|c|c|c|c|} \hline x & 1 & 1.25 & 1.5 & 1.75 & 2 \\ \hline f(x) & 1 & 0.8 & 0.6667 & 0.57143 & 0.5 \\ \hline \end{array} \] The approximate value of $ \int_1^2 \frac{1}{x} \, dx $ using Simpson’s $ \left( \frac{1}{3} \right) $rd rule is:

The solution of the differential equation $ (D^2 + 2)y = x^2 $ is

Let $ f(x) = \log x $. The number $ C $ strictly between $ e^2 $ and $ e^3 $ such that its reciprocal is equal to $ \frac{f(e^3) - f(e^2)}{e^3 - e^2} $ is

The value of the integral $ \int_C (2xy - x^2) \, dx + (x^2 + y^2) \, dy $ where $ C $ is the boundary of the region enclosed by $ y = x^2 $ and $ y^2 = x $, described in the positive sense, is

If $ P = \begin{pmatrix} 1 & 1 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 1 \end{pmatrix} $ is the modal matrix of $ A = \begin{pmatrix} 1 & 1 & 0 \\ 0 & 2 & 2 \\ 0 & 0 & 3 \end{pmatrix} $ then the sum of all the elements of $ P^{-1}AP $ is

If the system of equations $ kx + y + z = k - 1 $, $ x + ky + z = k - 1 $, and $ x + y + kz = k - 1 $ has infinite solutions, then $ k $ is

$x, y, z$ are in A.P. with common difference $d$. If the rank of the matrix \[ A = \begin{bmatrix} 4 & 5 & x \\ 5 & 6 & y \\ 6 & k & z \end{bmatrix} \] is 2, then:

If $ \lambda_1, \lambda_2, \lambda_3 $ are the eigenvalues of the matrix $ A = \begin{pmatrix} 1 & 0 & 2 \\ 0 & -3 & 1 \\ 0 & 0 & 4 \end{pmatrix} $, then the values of \[ (\lambda_1 + \lambda_2 + \lambda_3) \ \text{and} \ (\lambda_1 \cdot \lambda_2 \cdot \lambda_3) \] are respectively

The probability of getting a total of 5 at least once in three tosses of a pair of fair dice is:

If $ \dfrac{dy}{dx} = xy + y^2 $, $ y(0) = 1 $, and $ h = 0.1 $, then the value of $ y(0.1) $ using Euler’s method is:

Which of the following functions is not analytic?

The partial differential equation obtained by eliminating the constants $a$ and $b$ from \[ z = (x - a)^2 + (y - b)^2 \] is:

If it is known that $ \int_0^{\infty} \frac{e^{ix}}{x} dx = \frac{\pi i}{2}, $ then compute: $ \int_0^{\infty} \frac{\sin 5x}{x} dx = ? $