List of top Engineering Mathematics Questions

If the initial guess of the solution of \[ 1+x-x^3=0 \] is \(x_0=1\), then the \(2^{\text{nd}}\) approximate root of \[ 1+x-x^3=0 \] using Newton-Raphson method is

Let \(X\) be a discrete random variable, \(\mu\) be its mean, and \(P(X=x)\) be the probability function. The variance of \(X\) is

Let \[ f(t)= \begin{cases} \sin t, & 0\le t\le \pi,\\ 0, & t>\pi. \end{cases} \] The Laplace transform of \(f(t)\) is

In a Poisson distribution, \[ P(X=x+k)=\frac{\lambda^k}{f(x)}P(X=x), \] then \(f(x)=\)

If \[ \frac{dy}{dx}=xy+x,\; x\in\mathbb{R} \] and \(y(0)=1\), then \(y(0.2)\) with step size \(h=0.1\) using Euler's method is

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

If the Laplace transform of \(f(t)\) and \(f'(t)\) exist and \(F(s)\) is the Laplace transform of \(f(t)\), then \[ \lim_{s\to\infty}sF(s) \] is

The system of equations \[ x+4y+6z=20,\qquad x+y+z=6,\qquad x+\lambda y+6z=20 \] has

Let \[ \vec{F}=x^2yz\,\hat{i}+y^2z\,\hat{j}+zx^3\,\hat{k} \] be a vector point function. Let \(S\) be the surface of the sphere \[ x^2+y^2+z^2=a^2. \] Then \[ \iint_{S}(\nabla\times\vec{F})\cdot\vec{N}\,dS \] is equal to (\(\vec{N}\) is any unit outward normal vector to \(S\)).

Let \(A\) be a real symmetric matrix. \(\lambda_1,\lambda_2\;(\lambda_1\neq\lambda_2)\) be two eigen values of \(A\) and \(X_1,X_2\) are respectively the eigen vectors of \(A\) corresponding to \(\lambda_1\) and \(\lambda_2\), then \(X_1^TX_2=\)

If variance of \(X\) is \(4\), then the variance of \(Y=4X+2\) is

One of the normal equations for fitting a straight line \(y=a+bx\) is

Correlation coefficient is independent of

A random variable \(X\) has the probability density function \[ f(x)=Kx,\qquad 0\lt x\lt 2, \] then the ratio between \(K\) and the mean of \(X\) is

If \(A\) and \(B\) are independent random variables, then which of the following is correct?

If the observed frequencies exactly match expected frequencies, then what is \(\chi^2\) (Chi-square) value?

If \[ A= \begin{bmatrix} 2026 & 2025 & 2024\\ 2025 & 2024 & 2023\\ 2024 & 2023 & 2022 \end{bmatrix}, \] then \(\left|A^{2026}-A^{2025}\right|=\)

If the sum of the three numbers which are in A.P. is \(27\) and the product of the first and last is \(77\), then the numbers are

If \({}^nC_r={}^{\,n}C_{r-1}\) and \({}^{\,n}P_{r-1}=9\,{}^{\,r}P_r\), then \((n,r)=\)

If \(\alpha,\beta\) are the roots of \(ax^2+bx+c=0\), then \[ \left(\frac{\alpha}{\beta}-\frac{\beta}{\alpha}\right)^2 = \]

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?

Which of the following circuits is a sequential circuit?

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 propositions is logically equivalent to $p \rightarrow q$?