Solve your IGNOU Doubts

Question:

b) Obtain all the first and second order partial derivatives of the function:

$f(x,y)=x^2sin\,y+y^2 cosx$

See Answer →

Question:

i) Formulate the dual of the following problem:

$Minimize\,\,z=9x_1+12x_2+15x_3$

$s.t.\,\,2x_1+2x_2+x_3\geq 10$

$2x_1+3x_2+x_3\geq 12$

$x_1+x_2+5x_3\geq 14$

$x_1,x_2,x_3\geq 0$

ii) Check whether $(2,2,2)$ is a feasible solution to the primal and $\left ( \frac{1}{3},3,\frac{7}{3} \right )$ is a feasible solution to the dual.

iii) Use duality to check whether $(2,2,2)$ is an optimal solution to the primal.

See Answer →

Question:

a) Show that the function $i) u(x,t)=A(x+ct)^3$ is a solution of the one-dimensional wave equation.

ii) $i) u(x,t)=e^{-\pi t}$ sin $x$ is a solution of the one-dimensional heat equation.

See Answer →

Question:

Use the Frobenius method to obtain one solution of the following ODE: $4xy''+2y'+y=0$

See Answer →

Question:

A chain hangs over a nail with 2.0 m on one side and 6.0 m on the other side. If the force of friction is equal to the weight of 1.0 m of the chain, calculate the time required for the chain to slide off the nail.

See Answer →

Question:

2. An emf of 100 V is applied to a series RC circuit in which the resistance is 200 ohms

and the capacitance is $10^{-1}$ farads. Determine the charge q(t) on the capacitor if q(0) = 0. Also determine the current i(t).

See Answer →

Question:

a) Solve the following ordinary differential equations:

i) $\frac{dy}{dx}+4xy=x$

ii) $\frac{d^2y}{dx^2}+4\frac{dy}{dx}-12=cos2x$

b) Solve the initial value problem:

$\frac{d^2x}{dt^2}-6\frac{dx}{dt}+9x=0,\,x(0)=-1$

See Answer →

Question:

Use the principle of dominance to reduce the size of the following game. Hence solve the game.

$\begin{bmatrix} 3 & 0 & 4\\ 1 &4 & 2\\ 2 & 2 & 6 \end{bmatrix}.$

See Answer →

Question:

Show that the set of vectors

$a_1=\begin{bmatrix} 1\\2 \\0 \end{bmatrix} ,a_2=\begin{bmatrix} 2\\0 \\2 \end{bmatrix},a_3=\begin{bmatrix} 0\\2 \\3 \end{bmatrix}.$

from a basis for $E^3.$

See Answer →

Question:

Solve by simplex method the following linear programming problem: $Max\,z=2x+y+2z$

$s.t$

$3x-y+2z\leq 12$

$-2x+4y\leq 9$

$-x+3y+8z\leq 15$

$x,y,z\geq 0.$

See Answer →

Question:

The following table is obtained in the intermediate stage while solving an LPP by the simplex method. Image ignouassignments-ignouacademy-com--p-doubts-21246

Discuss whether an optimal solution will exist or not.

See Answer →

Question:

Find the maximum and minimax values of the following matrix game.

Image ignouassignments-ignouacademy-com--p-solve-85027

Does the matrix have a saddle point. Justify your answer.

See Answer →

Question:

Given all the portfolios of n securities what criterion would an investor use to select a good portfolio?

See Answer →

Question:

Explain the method of delineating the efficient frontier of a feasible region.

See Answer →

Question:

For a given set of securities, all their portfolios lie on or within the boundary of the region shown in Fig.1.

Image ignouassignments-ignouacademy-com--p-your-70062

In the feasible region, find a portfolio which has maximum return. Also, find a portfolio in this region which has minimum risk.

See Answer →

Question:

Consider the epidemic model governed by the following equation

${\frac{\mathrm{d}\mathbf{x}}{\mathrm{dt}}}=-\mathbf{\beta }\mathbf{x}\,\left(\mathbf{n}+1-\mathbf{x}\right)$

with initial condition x = n at t = 0 . Here )t(x is the number of susceptibles at time ,t β is the contact rate. The population is assumed to be closed and homogeneously mixing. Let the contact rate be 0.002 and the number of susceptibles be 5000 initially
i) Find the density of the population when the rate of appearance of new cases is maximum.
ii) Find the time (in weeks) at which the rate of appearance of new cases is maximum.
iii) Obtain the maximum rate of appearance of new cases.

See Answer →

Question:

Compare the phase diagrams of the systems:
i) $\dot{x}=y,\dot{y}=-x$
ii) $\dot{x}=xy,\dot{y}=-x^2$

by locating the equilibrium points and sketching the phase paths.

See Answer →

Question:

Suppose that the previous forecast was 2090 and the actual value of the variable of interest for the period was 1985 and the oldest value of interest was 1955. Using the moving average technique based upon the most recent four observations find new forecast for the next period.

See Answer →

Question:

Apply dominance to find the optimum strategies of A and B from the pay-off matrix given below Image ignouassignments-ignouacademy-com--p-ignou-81501

See Answer →

Question:

Consider the cubic total cost function ${\bf C}=0.06{\bf q}^{3}-0.8{\bf q}^{2}+13{\bf q}+10$