Solve your IGNOU Doubts

Question:

A 100 m long thread carries charges uniformly distributed along its length. An electron, 10 cm away from the centre of the thread along a line perpendicular to the thread experiences an attractive force of $2.7\times 10^{-12}N.$ Calculate the total charge on the thread.

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Question:

What do you understand by electrostatic potential energy? Calculate the electrostatic potential energy for the system of charges shown below. Take

$q=5\,\mu C\,and\,a=2\,cm.$ Image ignouassignments-ignouacademy-com--p-doubts-38826

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Question:

The initial basic feasible solution of a transportation problem is given below:

Image ignouassignments-ignouacademy-com--p-doubts-31658

Check whether the given solution is optimal. If it is not, then find the optimal solution.

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Question:

Solve the following LP problem by using two-phase simplex method:

$Minimize\,z=x_1-2x_2-3x_3$

$subject\,to\,-2x_1+3x_2+3x_3=2$

$2x_1+3x_2+4x_3=1$ $x_1,x_2,x_3\geq 0$

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Question:

For the following pay-off matrix, transform the zero-sum game into an equivalent linear programming problem: Image ignouassignments-ignouacademy-com--p-solve-65686

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Question:

A businessman has to get 5 cabinets, 12 desks and 18 shelves cleaned. He has two part-time employees, Anjali and Arnav. Anjali can clean 1 cabinet, 3 desks and 3 shelves in a day, while Arnav can clean 1 cabinet, 2 desks and 3 shelves in a day. Arnav is paid Image ignouassignments-ignouacademy-com--p-doubts-57883 22 per day and Anjali is paid 25 per day. Formulate the problem of finding the number of days for which Anjali and Arnav have to be employed to get the cleaning done with minimum cost as a linear programming problem.

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Question:

Without sketching the region, check whether $P(0,0)$ is in the convex hull of the points $A(-1,-1),B(1,0)$ and $C(0,1).$ . If it is in the region, write P as convex combination of A,B and C.

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Question:

The electrostatic potential $v(x,y)$ in a rectangular region is governed by the two

dimensional Laplace equation: $\frac{\partial ^2(x,y)}{\partial x^2}+\frac{\partial ^2v(x,y)}{\partial y^2}=0$

and

$v(x,40)=110V$

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Question:

Using the principle of dominance, solve the game whose pay-off matrix is given below:

Image ignouassignments-ignouacademy-com--p-your-74183

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Question:

Test the following set for convexity. $S=\{(x,y):x+y\leq8{\mathrm{~or~}}2x+y\leq10,x\geq0,y\geq0\}.$

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Question:

Reduce the following PDE to a set of three ODEs by the method of separation of variables.

$\frac{\partial ^2u}{\partial r^2}+\frac{2}{r}\frac{\partial u}{\partial r}+\frac{1}{r^2}\frac{\partial ^2u}{\partial \Theta }+\frac{1}{r^2sin}\frac{\partial ^2u}{\partial \phi ^2}=0$

Obtain the Fourier series for the following periodic function which has a period of 2 $\pi :$

$f(x)=x^2$ for $-\pi \leq x\leq \pi$

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Question:

Using the initial basic feasible solution for the transportation problem given below, find and optimal solution for the problem.

Image ignouassignments-ignouacademy-com--p-your-98713

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Question:

Find an initial basic feasible solution for the following transportation problem using matrix-minima method. Also find the transportation cost.

Image ignouassignments-ignouacademy-com--p-your-85352

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Question:

Solve, graphically, the game whose pay-off matrix is:

Image ignouassignments-ignouacademy-com--p-ignou-61923

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Question:

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

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

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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.

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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.

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Question:

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

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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.

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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).