IGNOU BTMC 134 SOLVED ASSIGNMENT

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BMTC 134 (January 2025 - July 2025) - ENGLISH

ASSIGNMENT

Course Code: BMTC-134

BMTC-134/TMA/2025

Maximum Marks: 100

1. (a) Define an abelian group. Give an example of a non-abelian group. (You don't need to prove that your example is a group. You have to only prove that it is non-abelian.)

(b) Define a subgroup of a group. Check whether

is a subgroup of the the group of 2 × 3 matrices over ℂ under addition.

(c) Define a semigroup. Give an example of an infinite semigroup.

(d) State Lagrange’s theorem. What are the possible orders of subgroups of a group of order 12?

(e)and ∗ be the binary operation defined by  Compute the Cayley table focommutative? Is ∗ associative? Justify your answers.

2. (a)and 퐶 be a 2 × 3 real matrix. Which of the following operations are defined?

For those operations that are defined, what is the order of the resulting matrix?

(b)

as a product of transpositons. What is the signature of?

(c)

(d)

(i) Give, with justificaiton, a nilpotent element in R.

(ii) Give, with justification, a zero divisor in 푅 which is not nilpotent.

(iii) What is the order of U(R)?

3. (a) Let R is commutative.

(b) Define an integral domain. Give an example of an integral domain which is not a field. 

(c) Calculate the following:

(i)  

(ii)  

(d) Show that, if G is a finite group and Further, show that    Deduce the Euler-Fermat theorem   

4. (a)    Check whether R is a subring of 

? Justify your answer

(b) Find the ged of the polynomials  

(c) If H and K are normal abelian subgroups of a group, and if H∩K = {e}, show that HK is abelian. Will the result be still true if we remove the condition that H and K are normal? Justify your answer.

5. (a) Find the order of each of the elements in U(15). Is U(15) cyclic? Justify your answer.

(b) Let F be a field and let f(x) ∈ F[x] be irreducible in F[x]. Show that the ideal (f(x)) is a maximal ideal in F[x]. Use this to deduce that Q[x]/(x² + 6x³ +12) is a field.

(c) 

6. (a) Show that  is not a principal ideal in Z[x].

(b) Check whether or not  is a maximal ideal in _⁹.

(c) Let R be a ring (not necessarily commutative) and I and J be ideal of R. Show that I   J  and I + J = } are ideals of R.

7. Which of the following statements are true and which are false? Justify your answer with a short proof or a counter example.

(a) Every subgroup of S3 is normal.

(b) Every abelian group is cyclic.

(c) In a ring with unity, the sum of any two units is a unit.

(d) If a field has characteristic p, p a prime, the field is finite.

(e) If every element in group has finite order, the group is finite.

BTMC 134 (January 2025 - July 2025) - ENGLISH

BTMC 134: ENTREPRENEURSHIP AND SMALL BUSINESS

Tutor Marked Assignments

Course Code: BTMC 134

Total Marks: 100

(2025-26)

Section A

Answer the following in about 500 words each.

1. Outline the elements of entrepreneurship. Discuss the various theories of entrepreneurship.

2. What is a business plan? Discuss the different types of analysis that need to be carried out in order to determine the feasibility of a business plan.

Section B

Answer the following questions in about 250 words each.

3. State the characteristics of Creativity. Explain factors that affect Creativity.

4. Discuss the various sources of finance for a Start-up.

5. Explain the stages in contract management process.

Section C

Answer the following in about 100 words each.

6. What are the different categories of Risks?

7. Differentiate between Angel Investors and Venture Capitalist.

8. What do you understand by Family business? State the reasons of conflicts in a family business.

9. Outline the role of MSMEs in entrepreneurial development.

10. What are the different types of Innovation?

BTMC 134 (January 2025 - July 2025) - HINDI

बीटीएमसी 134: उद्यमिता और लघु व्यवसाय

शिक्षक द्वारा चिह्नित असाइनमेंट

कोर्स कोड: बीटीएमसी 134

कुल अंकः 100

(2025-26)

खंड ए

निम्नलिखित प्रश्नों के उत्तर लगभग 500 शब्दों में दें।

1. उद्यमिता के तत्वों की रूपरेखा तैयार करें। उद्यमिता के विभिन्न सिद्धांतों पर चर्चा करें।

2. व्यवसाय योजना क्या है? व्यवसाय योजना की व्यवहार्यता निर्धारित करने के लिए किए जाने वाले विभिन्न प्रकार के विश्लेषणों पर चर्चा करें।

खंड बी

निम्नलिखित प्रश्नों के उत्तर लगभग 250 शब्दों में दें।

3. रचनात्मकता की विशेषताएँ बताएँ। रचनात्मकता को प्रभावित करने वाले कारकों की व्याख्या करें।

4. स्टार्ट अप के लिए वित्त के विभिन्न स्रोतों पर चर्चा करें।

5. अनुबंध प्रबंधन प्रक्रिया के चरणों की व्याख्या करें।

खंड सी

निम्नलिखित प्रश्नों के उत्तर लगभग 100 शब्दों में दीजिए।

6. जोखिमों की विभिन्न श्रेणियाँ क्या हैं? 6

7. एंजेल निवेशकों और वेंचर कैपिटलिस्ट के बीच अंतर बताइए।

8. पारिवारिक व्यवसाय से आप क्या समझते ह? पारिवारिक व्यवसाय में संघर्ष के कारण बताइए।

9. उद्यमशीलता विकास में एमएसएमई (MSME) की भूमिका की रूपरेखा बताइए।

10. नवाचार के विभिन्न प्रकार क्या हैं?

BTMC 134 (January 2025 - July 2025) - HINDI

बीटीएमसी 134: उद्यमिता और लघु व्यवसाय

शिक्षक द्वारा चिह्नित असाइनमेंट

कोर्स कोड: बीटीएमसी 134

कुल अंकः 100

(2025-26)

खंड ए

निम्नलिखित प्रश्नों के उत्तर लगभग 500 शब्दों में दें।

1. उद्यमिता के तत्वों की रूपरेखा तैयार करें। उद्यमिता के विभिन्न सिद्धांतों पर चर्चा करें।

2. व्यवसाय योजना क्या है? व्यवसाय योजना की व्यवहार्यता निर्धारित करने के लिए किए जाने वाले

विभिन्न प्रकार के विश्लेषणों पर चर्चा करें।

खंड बी

निम्नलिखित प्रश्नों के उत्तर लगभग 250 शब्दों में दें।

3. रचनात्मकता की विशेषताएँ बताएँ। रचनात्मकता को प्रभावित करने वाले कारकों की व्याख्या करें। 10

4. स्टार्टअप के लिए वित्त के विभिन्न स्रोतों पर चर्चा करें।

5. अनुबंध प्रबंधन प्रक्रिया के चरणों की व्याख्या करें।

खंड सी

निम्नलिखित प्रश्नों के उत्तर लगभग 100 शब्दों में दीजिए।

6. जोखिमों की विभिन्न श्रेणियों क्या है?

7.एंजेल निवेशकों और वेंचर कैपिटलिस्ट के बीच अंतर बताइए। 6

8. पारिवारिक व्यवसाय से आप क्या समझते ह? पारिवारिक व्यवसाय में संघर्ष के कारण बताइए। 6

9. उद्यमशीलता विकास में एमएसएमई (MSME) की भूमिका की रूपरेखा बताइए। 6

10. नवाचार के विभिन्न प्रकार क्या है?

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Course Name	Bachelor of Arts (Vocational Studies) Tourism Management
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