List of top Engineering Mathematics Questions

Let \(A\) and \(B\) be any two \(n\times n\) matrices and \[ tr(A)=\sum_{i=1}^{n}a_{ii}, \qquad tr(B)=\sum_{i=1}^{n}b_{ii}. \] Consider the following statements:
• Statement-I : \(tr(AB)=tr(BA)\).
• Statement-II : \(tr(A+B)=tr(A)+tr(B)\).
• Statement-III : If \(tr(A)=5,\; tr(A^{2})=13\), then \[ tr(A-I)^2=6, \] where \(A_{3\times3}\) and \(I_{3\times3}\) are matrices. Choose the correct option.

What is the 2's complement representation of the decimal number -5 in 8-bit binary?

In a simple undirected graph, the sum of the degrees of all vertices is 20. How many edges are present in the graph?

Which of the following circuits is a sequential circuit?

Which of the following propositions is logically equivalent to $p \rightarrow q$?

If a graph G has 10 vertices and each vertex has degree 3, how many edges does G have?

Two graphs $G_1$ and $G_2$ are isomorphic if which of the following conditions is satisfied?

A graph is said to be Eulerian if it contains a closed trail that includes every:

For a connected planar graph with 10 vertices and 15 edges, how many faces does the graph have?

How many different 5-character passwords can be formed using the digits 0-9 and lowercase letters a-z if the first character must be a letter and repetitions are allowed?

The number of ways to distribute 10 identical apples among 4 children such that every child receives at least one apple is:

In the binomial distribution \(B(n,p)\), the variance \((\sigma^{2})\) and the mean \((\mu)\) are related by

Assertion (A): If \(X\sim N(\mu,\sigma^{2})\), then \[ P(X<\mu)=0.5. \] Reason (R): Normal distribution is symmetric about its mean.

Consider the differential equation \[ \frac{dy}{dx}=x^{2}-y,\qquad y(0)=1. \] Using the Simple Euler's Method with a step size of \(h=0.1\), the value of \(y(0.1)\) is

The solution of \[ \frac{dy}{dx}+y=f(x), \] where \[ f(x)= \begin{cases} x, & 0\le x 0, & x\ge1, \end{cases} \] with the conditions \[ y(0)=0,\qquad y(1)=e^{-1}, \] is

If \(y_{1}=x^{2}\) is a known solution of \[ x^{2}y^{\prime\prime}-3xy^{\prime}+4y=0, \] then the second independent solution \(y_{2}\) is

\[ \lim_{n\rightarrow\infty}\frac{5n^{2}+4}{7n^{2}+6n}= \]

If \[ \vec{v}=(x+y+1)\hat{i}+\hat{j}+(-x-y)\hat{k}, \] then the value of \[ \vec{v}\cdot(\nabla\times\vec{v}) \] is

Let the matrix \[ A=\begin{bmatrix} 3& 1 -1& 2 \end{bmatrix} \] and \[ I=\begin{bmatrix} 1& 0 0& 1 \end{bmatrix}, \] then \[ A^{2}-5A+7I= \]

If \[ f(x,y,z,w)=x^{2}e^{2y+3z}\cos(4w), \] then \[ \frac{\partial f}{\partial z} \] at \((2,0,-2,1)\) is

In the binomial distribution \(B(n,p)\), the variance \((\sigma^{2})\) and the mean \((\mu)\) are related by

Assertion (A): If \(X\sim N(\mu,\sigma^{2})\), then \[ P(X<\mu)=0.5. \] Reason (R): Normal distribution is symmetric about its mean.

If \(y_{1}=x^{2}\) is a known solution of \[ x^{2}y^{\prime\prime}-3xy^{\prime}+4y=0, \] then the second independent solution \(y_{2}\) is

Consider the differential equation \[ \frac{dy}{dx}=x^{2}-y,\qquad y(0)=1. \] Using the Simple Euler's Method with a step size of \(h=0.1\), the value of \(y(0.1)\) is

The solution of \[ \frac{dy}{dx}+y=f(x), \] where \[ f(x)= \begin{cases} x, & 0\le x\\ 0, & x\ge1, \end{cases} \] with the conditions \[ y(0)=0,\qquad y(1)=e^{-1}, \] is