Mathematics Paper-II for Bihar Conservator exam

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  • Conducted By Bihar Government
  • Maximum Marks 75
  • Duration 2 Hours
  • Languages Hindi & English

Exam Details

Detail Information
Examination Mathematics Paper-II
Conducting Body Bihar Government
Paper Mathematics Paper-II
Subject Mathematics
Duration 2 Hours
Maximum Marks 75

This dataset combines OCR-repaired content from PAGE 1 and PAGE 2 of the Mathematics Paper-II for the Bihar Government Assistant Conservator of Forests competitive examination. Page 1 provides the exam header, total maximum marks (75), duration (2 hours 30 minutes), languages (Hindi and English), and general instructions. Page 2 presents repaired descriptive questions: Q1 on ring theory (ideals and principal ideal domains), Q2 on R-integrability and the fundamental theorem of calculus, and Q3 on complex analysis (Cauchy’s theorem and contour integration). The material is bilingual-friendly in parts and includes a page code 04/SBS/M-2020-10B/20. This structure supports SEO through topics like ring theory, ideals, principal ideal domains, calculus, and complex analysis, while offering a complete set of questions and topical hints for SEO-friendly FAQs, keywords, and related content.

Major Topics Covered

  • Mathematics
  • Ring Theory
  • Ideals
  • Principal Ideal Domain
  • Z (Integers)
  • Abstract Algebra
  • Algebraic Structures
  • Real Analysis
  • R-integrable
  • Calculus
  • Fundamental Theorem of Calculus
  • Cauchy's Theorem
  • Complex Analysis
  • Contour Integration
  • f(z) = 5 sin 2z
  • sin^6 z
  • Complex Integration
  • Square with vertices
  • Circle |z|=1
  • Questions with subparts

Why This Paper is Important

  • Useful for Mathematics Paper-II preparation
  • Helps understand the latest exam pattern
  • Useful for practice and self-assessment
  • Covers frequently asked General Studies topics
  • Helpful for analysing question trends

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Instructions

  • ۰ • Attempt any five questions. • Candidates are required to give their answers in their own words as far as practicable. • All questions have been printed both in Hindi and English. In case of any ambiguity in Hindi version, the English version shall be considered authentic. • Parts of the same question must be answered together and must not be interposed between answers to other questions. अनुदेश: • उपान्त के अंक पूर्णांक के द्योतक हैं। • किन्हीं पाँच प्रश्नों के उत्तर दें। • परीक्षार्थी यथासम्भव अपने शब्दों में ही उत्तर दें। • सभी प्रश्न हिन्दी और अंग्रेजी दोनों भाषा में छपे हैं।
  • यदि हिन्दी भाषा में कोई संदेह है, तो अंग्रेजी भाषा को ही प्रामाणिक माना जाएगा। • एक ही प्रश्न के विभिन्न भागों के उत्तर अनिवार्य रूप से एक-साथ ही लिखे जाएँ तथा उनके बीच में अन्य प्रश्नों के उत्तर न लिखे जाएँ।

Questions (page 2)

Q1. (a) Prove that the intersection of two ideals of a ring is again an ideal of the ring. 6 Prove that the ring (z, + , \cdot) of integers is

() (a) Prove that the intersection of two ideals of a ring is again an ideal of the ring.

() (b) Prove that the ring Z, with (+, ·), is a principal ideal domain.

  • (a) Prove that the intersection of two ideals of a ring is again an ideal of the ring. 6 Prove that the ring (z, + , \cdot) of integers is
  • (b) 9 a principal ideal domain. (क) सिद्ध कीजिये कि किसी वलय की दो गुणजावलियों का सर्वनिष्ठ भी उस वलय की गुणजावली होती है। (ख) सिद्ध कीजिये कि पूर्णांकों का वलय (z, + , \cdot) एक मुख्य गुणजावली प्रान्त है। Prove that a constant function is

Q1. (a) Prove that the intersection of two ideals of a ring is again an ideal of the ring. 6 Prove that the ring (z, + , \cdot) of integers is

(a) Prove that the intersection of two ideals of a ring is again an ideal of the ring. 6 Prove that the ring (z, + , \cdot) of integers is

(b) 9 a principal ideal domain. (क) सिद्ध कीजिये कि किसी वलय की दो गुणजावलियों का सर्वनिष्ठ भी उस वलय की गुणजावली होती है। (ख) सिद्ध कीजिये कि पूर्णांकों का वलय (z, + , \cdot) एक मुख्य गुणजावली प्रान्त है। Prove that a constant function is

  • (a) Prove that the intersection of two ideals of a ring is again an ideal of the ring. 6 Prove that the ring (z, + , \cdot) of integers is
  • (b) 9 a principal ideal domain. (क) सिद्ध कीजिये कि किसी वलय की दो गुणजावलियों का सर्वनिष्ठ भी उस वलय की गुणजावली होती है। (ख) सिद्ध कीजिये कि पूर्णांकों का वलय (z, + , \cdot) एक मुख्य गुणजावली प्रान्त है। Prove that a constant function is

Q2. (a) R-integrable. 6

(a) R-integrable. 6

(b) State and prove the fundamental theorem of integral calculus. 9 (क) सिद्ध कीजिये कि स्थिर मान फलन R-समाकलनीय है। (ख) समाकलन गणित के मूल प्रमेय का कथन कर सिद्ध कीजिये। 3. (a) If C is the square with vertices at 1 ± i, -1 ± i, then verify Cauchy's theorem for the function f(z) = 5 sin 2z, that is ∫ f(z) dz = 0 7 If C is the circle |z| = 1, then find the (b) value of integral ∫C (sin6 z \, dz)/(z - (π)/(6))^3) 04/SBS/M-2020-10B/20 2

  • (a) R-integrable. 6
  • (b) State and prove the fundamental theorem of integral calculus. 9 (क) सिद्ध कीजिये कि स्थिर मान फलन R-समाकलनीय है। (ख) समाकलन गणित के मूल प्रमेय का कथन कर सिद्ध कीजिये। 3. (a) If C is the square with vertices at 1 ± i, -1 ± i, then verify Cauchy's theorem for the function f(z) = 5 sin 2z, that is ∫ f(z) dz = 0 7 If C is the circle |z| = 1, then find the (b) value of integral ∫C (sin6 z \, dz)/(z - (π)/(6))^3) 04/SBS/M-2020-10B/20 2

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Frequently asked questions

What is the subject of the paper?

Mathematics Paper-II for the Bihar Forest Conservator competitive examination.

Which exam and position does this paper correspond to?

Assistant Conservator of Forests, Bihar Government competitive examination.

What is the total marks for the paper?

75 marks.

What is the duration of the exam?

2 hours 30 minutes (11/2 घण्टे).

Are questions available in multiple languages?

Yes. The paper is designed to be available in Hindi and English.

How many questions must a candidate attempt?

Any five questions may be attempted, as per instructions.

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