UPSC Math Paper II 2024 - Descriptive Questions (Q1) and Concepts

Central Government Jobs Administrative / Civil Services 2024

  • Year 2024
  • Conducted By Union Public Service Commission (UPSC)
  • Questions 8
  • Maximum Marks 250
  • Duration Three Hours प्रश्न-पत्र सम्बन्धी विशेष अनुदेश कपया प्रश्नों के उत्तर देने से पूर्व निम्नलिखित प्रत्येक अनुदेश को ध्यानपूर्वक पढ़ें : इसमें आठ प्रश्न हैं जो दो खण्डों में विभाजित हैं तथा हिन्दी और अंग्रेज़ी दोनों में छपे हुए हैं । परीक्षार्थी को कुल
  • Languages Hindi & English

Exam Details

Detail Information
Examination UPSC Civil Services (Main) Examination
Year 2024
Conducting Body Union Public Service Commission (UPSC)
Paper Mathematics Paper - II
Subject Mathematics
Duration Three Hours प्रश्न-पत्र सम्बन्धी विशेष अनुदेश कपया प्रश्नों के उत्तर देने से पूर्व निम्नलिखित प्रत्येक अनुदेश को ध्यानपूर्वक पढ़ें : इसमें आठ प्रश्न हैं जो दो खण्डों में विभाजित हैं तथा हिन्दी और अंग्रेज़ी दोनों में छपे हुए हैं । परीक्षार्थी को कुल
Maximum Marks 250
Number of Questions 8
Question Type Descriptive + conceptual

This JSON aggregates UPSC Civil Services Main Examination Mathematics Paper II (2024). It includes exam overview, page-2 repaired objective questions (Q1 with sub-parts on group theory, complex analysis, integration convergence, and analytic function construction), plus SEO metadata: titles, descriptions, keywords, and structured data guidance. Page-1 context provides the exam structure: eight questions in two sections; candidates must answer five, with Q1 and Q5 compulsory. Paper code PHKM-B-MTH; duration three hours; maximum marks 250; languages Hindi & English.

Major Topics Covered

  • UPSC Civil Services Main Examination
  • Mathematics
  • Mathematics Paper II
  • Group Theory
  • Finite Groups
  • Subgroups
  • Complex Analysis
  • Analytic Functions
  • Laplacian
  • Cauchy-Riemann Equations
  • Harmonic Functions
  • Convergence of Integrals
  • Definite Integrals
  • Analytic Construction of f(z)
  • Laplace Equation
  • Phi and Psi functions
  • CR Equations
  • QCA Booklet
  • Paper Code PHKM-B-MTH
  • Bilingual Question Papers

Why This Paper is Important

  • Useful for UPSC Civil Services (Main) Examination preparation
  • Helps understand the latest exam pattern
  • Useful for practice and self-assessment
  • Covers frequently asked General Studies topics
  • Helpful for analysing question trends

Related Resources

Instructions

  • पुस्तिका के मुख-पृष्ठ पर निर्दिष्ट स्थान पर किया जाना चाहिए ।
  • प्राधिकृत माध्यम के अतिरिक्त अन्य किसी माध्यम में लिखे गए उत्तर पर कोई अंक नहीं मिलेंगे ।
  • यदि आवश्यक हो, तो उपयुक्त आँकड़ों का चयन कीजिए तथा उनको निर्दिष्ट कीजिए ।
  • जब तक उल्लिखित न हो, संकेत तथा शब्दावली प्रचलित मानक अर्थों में प्रयुक्त हैं ।
  • प्रश्नों के उत्तरों की गणना क्रमानुसार की जाएगी ।
  • यदि काटा नहीं हो, तो प्रश्न के उत्तर की गणना की जाएगी चाहे वह उत्तर अंशतः दिया गया हो ।
  • प्रश्न-सह-उत्तर (क्यू.सी.ए.) पुस्तिका में खाली छोड़ा हुआ पुष्ठ या उसके अंश को स्पष्ट रूप से काटा जाना चाहिए ।

  • There are EIGHT questions divided in TWO SECTIONS and printed both in HINDI and in ENGLISH.
  • Candidate has to attempt FIVE questions in all.
  • Questions no. 1 and 5 are compulsory and out of the remaining, any THREE are to be attempted choosing at least ONE question from each section.
  • The number of marks carried by a question / part is indicated against it.
  • Answers must be written in the medium authorized in the Admission Certificate which must be stated clearly on the cover of this Question-cum-Answer (QCA) Booklet in the space provided.
  • No marks will be given for answers written in a medium other than the authorized one.
  • Assume suitable data, if considered necessary, and indicate the same clearly.
  • Unless and otherwise indicated, symbols and notations carry their usual standard meanings.
  • Attempts of questions shall be counted in sequential order.
  • Unless struck off, attempt of a question shall be counted even if attempted partly.
  • Any page or portion of the page left blank in the Question-cum-Answer (QCA) Booklet must be clearly struck off.

Questions (page 2)

Q1. Q1. (a) संख्याएँ हैं । दर्शाइए कि G का कोटि m का अधिक-से-अधिक एक उपसमूह है । Let G be a finite group of order mn, where m and n are prime numbers with m > n. Show that G has at most one subgroup of order m.

Q2.

(b) If w = f(z), z का एक विश्लेषिक फलन है, तब दर्शाइए कि (∂^2/∂x2 + ∂^2/∂y2) log |f'(z)| = 0.

Q3.

(c) ∫ log x / sqrt(2-x) dx के अभिसरण का परीक्षण कीजिए। Test the convergence of ∫_0^2 log x / sqrt(2-x) dx.

Q4.

(d) यदि x तथा y के फलन φ और ψ लाप्लास समीकरण को सन्तुष्ट करते हैं, तो दर्शाइए कि f(z) = p + iq, i = √-1 एक विश्लेषिक फलन है, जहाँ p = ∂φ/∂y - ∂ψ/∂x और q = ∂φ/∂x + ∂ψ/∂y.

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Frequently asked questions

What is the maximum marks for Mathematics Paper II?

250 marks.

How many questions must a candidate answer?

Five questions in total.

Which questions are compulsory?

Questions 1 and 5 are compulsory.

From how many sections do you choose the questions?

Two sections.

In which languages is the question paper printed?

Hindi and English.

Where should the answers be written?

In the medium authorized in the Admission Certificate, clearly mentioned on the QCA booklet cover.

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