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Question : All the points in the set S={(α+i)/(α-i):α∈R} lie on a (a) circle whose radius is √2. (b) straight line whose slope is -1. (c) circle whose radius is…

Question : Let z in C with Im (z) = 10 and it satisfies (2z-n)/(2z+n)= 2i-1 for some natural number n, then (a) n = 20 and Re(z) = - 10…

Question : what are eigen values and eigen vectors of a matrix? Find Eigen values and eigen vectors for the following matrices (a) \(A = \left(\begin{array}{cc}2 & 1 \\4 &…

Question : Find curl of r^n vec(r) Solution : We shall Find curl of r^n vec(r) We know that \[\nabla=\hat{i}\frac{\partial}{\partial x}+\hat{j}\frac{\partial}{\partialy}+\hat{k}\frac{\partial}{\partialz}\] And \[r^n\vec{r}\ =r^n\left(x\hat{i}+y\hat{j}+z\hat{k}\right)=r^nx\hat{i}+r^ny\hat{j}+r^nz\hat{k}\] Therefore curl of r^n vec(r) is…

Question : Find curl of the following Vector Field \[F\left(x,y,z\right)=\left(2xz\ ,-z^2,\ x^2\right)\] Solution : To Find curl of Vector Field \[F\left(x,y,z\right)=\left(2yz\ ,\ -z^2,\ x^2\right)\] curl of Vector Field F(x,y,z) is…

Question : Find Inverse Laplace transform of X(s)=(s-3+e^(-2s))/(s^2+4) Solution : To Find Inverse Laplace transform of X(s)=(s-3+e^(-2s))/(s^2+4) \[X\left(s\right)=\frac{s-3+e^{-2s}}{s^2+4}\] We can write function X(s) as \[X\left(s\right)=\frac{s}{s^2+4\ }-\frac{3}{s^2+4\ }+\frac{e^{-2s}}{s^2+4}\] First we shall…

Question : how do you find inverse Laplace transform of 1/(s^2+2s-3)? Solution : Given \[f(s) =\frac{1}{(s^2+2s-3)}\] It's factorization is given as \[ f(s)=\frac{1}{(s+3)(s-1)} \] \[=> f(s)=\frac{1}{4}\left(\frac{1}{(s-1)}- \frac{1}{(s+3)}\right) \] Now using…

Question : how to write c plus plus program to Sum three integers? Solution : \\ c plus plus program to Sum three integers #include <iostream> using namespace std; int…

Question : What is price elasticity of demand ? Find price elasticity of the fractional demand f(x) =(x-1)/(x+1) Solution : Price elasticity of demand: The price elasticity of demand is…

Question : Find steady states of the differential equation dy/dx =y(1-y)-a=f(y) where a is any parameter. Solution : \[\frac{dy}{dx}=y\left(1-y\right)-a=f(y) \] (1) Where a is any parameter. We shall obtain Steady…