Solve your IGNOU Doubts

Question:

Critically discuss the concept of Cycle of erosion of Penck.

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Question:

Discuss the different layers of Earth’s interior with the help of a neat sketch.

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Question:

‘Working Capital Module simulates the integration of working capital components into the Capital Investment (CI) process’. Give the objectives and explanation of the operation of each module that forms a part of the working capital – capital investment process. Also highlight the sequential operation of the WC module.

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Question:

Visit any Bank of your choice and study the methods of Appraisal that the Bank follows while extending Credit Facility to the Business Houses. Write a detail note on your findings.

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Question:

The company XYZ Ltd has annual sales of Rs. 50 lakhs and is currently extending 30 days’ credit to the dealers. It is considering change in credit policy and the following information is available:

The average collection period now is 30 days.

Costs: Variable Cost: 80 percent on sales

Fixed Cost: Rs. 6 lakhs per annum

Required (pre-tax) return on investment: 20 percent

Credit Policy	Average Collection Period	Annual Sales Rs
P	45 days	56,00,000
Q	60 days	60,00,000
R	75 days	62,00,000
S	90 days	63,00,000

You are required to recommend as to which of the policies given above should be adopted by XYZ Ltd. What are the assumptions you have made for coming to such decision?

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Question:

Select any two firms from the same industry and collect their Financial Statements for the years 2022-2023 & 2023-2024, and calculate their Efficiency, Liquidity and Structural Ratios. Based on these ratios give your views on the working capital management of these firms.

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Question:

Using fourth order Taylor series method with $h=0.2$ , solve Initial value problem $y' = x + cos y , \: y(0) = 0$ upto $x=1$ .

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Question:

Find approximate value of $y(1.0)$ for the initial value problem $\begin{align*} y' =x-2y, y(0)=1 \end{align*}$ using Milne-Simpson's method $y_{n+1} = y_{n-1} + \frac{h}{3}[f_{n+1} + 4f_{n} - f_{n-1}]$
with $h=0.2$ . Calculate starting value using Runge-Kutta fourth order method with the same h.

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Question:

Using standard five-point formula, solve Laplace equation $\nabla^2u=0$ in R where R is the square $0 \leq x \leq 1, 0 \leq y \leq 1$ subject to the boundary conditions $u(x,y) = x^2 - y^2$ on $x=0 , y=0, y=1$
and $3u + 2\frac{\partial u}{\partial x} = x^2 + y^2$ on $x=1$ . Assume $h=k=1/2$ .

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Question:

Find approximate value of $y(0,1)$ for initial value problem
$y'=x^3-y^3 , y(0)=1$ using multiple method

$\begin{equation} y_{n+1} = y_n + \frac{h}{3}(7f_n - 2f_{n-1} + f_{n-2}) \end{equation}$

with $h=0.2$ . Calculate the starting values using Runge-Kutta second order method with the same h.

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Question:

Solve wave equation $u_{tt}=u_{xx}$ with
$u(x,0) = 0 , u_t(x,0)=0, u(0,t)=0 , u(1,t) = 100 sin(\pi t)$ with $k=h=0.25$ , using explicit method upto 4 time levels.

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Question:

Using second order finite difference method, solve the boundary value problem $y'' + 5y' + 4y= 1$ , $y(0) = 0$ , $y(1) = 0$ , $h=1/4$

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Question:

Solve heat equation $u_{tt}=u_{xx}$ in $R(0 \leq x \leq 1, t > 0)$ with conditions $u(x,0)=0, u(0,t)=0, u(1,t)=t$ using Crank-Nicolson method with $h=0.25$ , $\lambda=1$ upto two time steps.

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Question:

Using Runge-Kutta 2nd order method with

(i) $h=0.1$ , (ii) $h=0.2$ , solve the initial value problem
$\begin{align*} y'&=y^2\sin x , y(0) =1 \end{align*}$ upto $x=0.4$ . If exact solution is $y = sec x$ , obtain the error.

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Question:

Using Fourier integral representation show that $\int_{0}^{\infty}\frac{cos(\alpha x) + \alpha sin(\alpha x)}{1 + \alpha^2} = \left\{\begin{matrix} 0 & if \: x<0\\ \pi/2 & if \: x=0 \\ \pi e^{-x} & if \: x>0 \end{matrix}\right.$

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Question:

Find the displacement $u(x,t)$ of an infinite string using Fourier transform method given that the string is initially at rest and the initial displacement is $f(x)$ , $-\infty < x < \infty$ .

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Question:

If the Fourier cosine transform of $f(x)$ is $\alpha^ne^{-a\alpha}$ , then show that

$f(x) = \frac{2}{\pi}\frac{n!cos(n+1)\theta)}{(a^2+x^2)^{\frac{n+1}{2}}}$

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Question:

If the Fourier cosine transform of $f(x)$ is $\alpha^ne^{-a\alpha}$ , then show that

$f(x) = \frac{2}{\pi}\frac{n!cos(n+1)\theta)}{(a^2+x^2)^{\frac{n+1}{2}}}$

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Question:

Solve the following IBVP using Laplace transform technique:
$u_t = u_{xx} , 0<x<1, t>0$
$u(0,t) = 1, u(1,t) = 1, t>0$
$u(x,0) = 1 + sin \pi x, 0<x<1$

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Question:

If $k_m$ and $k_n$ are distinct roots of Bessel function $J_p(kb) = 0$ with $p\geq0$ , $b>0$ then show that $\int_{0}^{b}x J_p(k_mx)J_p(k_nx)dx = \left\{\begin{matrix} 0 & if m\neq n\\ \frac{b^2}{2}[J_{p+1}(k_nb)] & if \: m = n \end{matrix}\right.$