IGNOU MEC 203 SOLVED ASSIGNMENT HINDI

MEC 203: QUANTITATIVE METHODS

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Title Name	IGNOU MEC 203 SOLVED ASSIGNMENT HINDI
Type	Soft Copy (E-Assignment) .pdf
University	IGNOU
Degree	MASTER DEGREE PROGRAMMES
Course Code	MAEC
Course Name	MASTER OF ARTS (ECONOMICS)
Subject Code	MEC 203
Subject Name	QUANTITATIVE METHODS
Year	2025 2026
Session	-
Language	English Medium
Assignment Code	MEC 203/Assignment-1/2025 2026
Product Description	Assignment of MAEC (MASTER OF ARTS (ECONOMICS)) 2025 2026. Latest MEC 203 2025-26 Solved Assignment Solutions
Last Date of IGNOU Assignment Submission	Last Date of Submission of IGNOU BEGC-131 (BAG) 2025-26 Assignment is for January 2026 Session: 30th September, 2026 (for December 2025 Term End Exam). Semester Wise January 2025 Session: 30th March, 2026 (for June 2026 Term End Exam). July 2025 Session: 30th September, 2025 (for December 2025 Term End Exam).
Format	Ready-to-Print PDF (.soft copy)

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MEC 203 2025 2026 - English

MEC 203: QUANTITATIVE METHODS
Tutor Marked Assignments

Course Code: MEC-203
Assignment Code: Asst/TMA /2025-26
Total Marks: 100

PART I

Answer the following questions. Each question carries 20 marks

1. a) Explain Taylor's theorem to polynomial expansion.
b) Using Taylor's approach, find Taylor's series expansion for the function:
f(x,y,z)=x,y,z around the point (1,1,1)

2. Given the input matrix and the final demand vector:

A = $\begin{bmatrix} 0.10 & 0.15 & 0.12 \\ 0.20 & 0 & 0.30 \\ 0.25 & 0.40 & 0.20 \end{bmatrix}$ d = $\begin{bmatrix} 100 \\ 200 \\ 300 \end{bmatrix}$

a) Explain the economic meaning of the elements 0.30,0 and 200
b) Explain the economic meaning of (if any) of the third column sum
c) Explain the economic meaning of (if any) of the third row sum
d) Write out the specific input-output matrix equation for this model
e) Find the solution output levels of the three industries using Cramer's rule.

**PART II**
**Answer the following questions. Each question carries 12 marks.**

3. a) What are isoperimetric problems?
b) Find the extremal for the functional
J(.)= $\int_{t_0}^{t_f} 2x_t^2 +24x(t).t) dt$ ,

Boundary condition x(t₀) = 0, -x(t_f) = 2
t₀=0, t_f=2

4. a) Discuss the features of chi square, t and f test?

b) x₁,x₂...x_n is a random sample from a Normal population N( $\mu$ ,1). Show that

$\bar{x} = \frac{1}{n}\sum_{i=1}^{n}x_i$ , x_i² is an unbiased estimator of $\mu^2+1$

5. Consider the following simple problem:
min. $\int_{0}^{1}\{ (x(t))^2 + (u(t))^2\}dt$
Subject to $\frac{dx}{dt} = u(t), x(0)=1$

6. Examine the following functions for maxima and minima:
a) $z = -x^2 + xy - y^2 + x + 5y$
b) $y = x^3 - 2x^2 + x - 6$

7. Write short notes on following:
e) Euler-Lagrange equation
f) Central Limit theorem
g) Hamiltonian function
h) Cramer -Rao inequality

MEC 203 2025 2026 - Hindi

एमईसी-203: परिमाणात्मक विधियाँ

शिक्षक मूल्यांकित सत्रीय कार्य (टीएमए)

पाठ्यक्रम कोङः एमईसी 203

सत्रीय कार्य कोड: एएसटी/टीएमए/2025-26 कुल अंक : 100

नोट: सभी प्रश्नों के उत्तर दें।

खंड - क

प्रत्येक प्रश्न का उत्तर लगभग 700 शब्दों में देना है। इस खंड का प्रत्येक प्रश्न 20 अंक का है। परिमाणात्मक प्रश्नों पर शब्द सीमा लागू नहीं होती।

1(क) बहुपदी सन्नियन के प्रतिटेलर के प्रमेय की व्याख्या करें।

(ख) टेलर के दृष्टिकोण का उपयोग करते हुए टेलर श्रृंखला में बिंदु (1,1,1) के गिर्द फलन f(x,y,z)=x,y,z का विस्तार ज्ञात करें।

2 इनपुट मैट्रिक्स और अंतिम मांग वेक्टर को देखते हुएः

$$ A = \begin{bmatrix} 0.10 & 0.15 & 0.12 \\ 0.20 & 0 & 0.30 \\ 0.25 & 0.40 & 0.20 \end{bmatrix} \quad d = \begin{bmatrix} 100 \\ 200 \\ 300 \end{bmatrix}$ $

(क) 0.30,0 और 200 के अवयवों का आर्थिक अर्थ समझाइए

(ख) तीसरे स्तंभ योग के (यदि कोई हो) का आर्थिक अर्थ समझाइए

(ग) तीसरी पंक्तिके योग (यदि कोई हो) का आर्थिक अर्थ समझाइए

(घ) इस मॉडल के लिए विशिष्ट इनपुट-आउटपुट मैट्रिक्स समीकरण लिखें

(ड़) क्रमर के नियम का उपयोग करके तीन उद्योगों के समाधान उत्पादन स्तर का पता लगाएं।

खंड ख

प्रत्येक प्रश्न का उत्तर लगभग 500 शब्दों में देना है। इस खंड का प्रत्येक प्रश्न 12 अंक का है। परिमाणात्मक प्रश्नों पर शब्द सीमा लागू नहीं होती।

3. (क) आइसोपेरिमेट्रिक समस्याएँ क्या हैं?

Sure, here's the text exactly as it appears in the image:

$J(.) = \int_{t_0}^{t_f} 2x'_t{}^2 + 24x(t).t) dt,$
सीमाशर्त: $x(t_0) = 0, -x(t_f) = 2$
$t_0=0, t_f=2$

Sure, here's the text from the image:

4 (क) काई-वर्ग परीक्षण, t और f परीक्षण की विशेषताओं पर चर्चा करें?

(ख) x1, x2...xn एक सामान्य जनसंख्या; N(μ,l) से एक यादृच्छिक नमूना है। दिखाएँ कि
$\bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i^2$ ,

μ² + 1 का एक निष्पक्ष अनुमान है

5 निम्नलिखित सरल समस्या पर विचार करें :

$\min \{g_0(u)\} = \int_0^1 \{(x(t))^2 + (u(t))^2\} dt$

Subject to $\frac{dx}{dt} = u(t), x(0) = 1$

6 नीचे दिए गए फलनों की भूयिष्ठ को अथवा अल्पिष्ठ को हेतु जांच कीजिए:

(क) $z = -x^2 + xy - y^2 + x + 5y$

(ख) $y = x^3 - 2x^2 + x - 6$

7 निम्नलिखित पर संक्षिप्त टिप्पणीयाँ लिखिएः

(क) यूलर-लाग्रेंज समीकरण

(ख) केंद्रीय सीमा प्रमेय

(ग) हैमिल्टोनियन फलन

(घ) क्रमर-राव असमानता

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