UPSC Civil Services Mains 2021 Mathematics Paper-I PDF

Central Government Jobs Other Jobs 2021

  • Year 2021
  • Conducted By UPSC
  • Questions 8
  • Maximum Marks 250
  • Duration Three Hours
  • Languages English & Hindi

Exam Details

Detail Information
Examination UPSC Civil Services Main Exam
Year 2021
Conducting Body UPSC
Paper Mathematics Paper-I
Subject Mathematics
Duration Three Hours
Maximum Marks 250
Number of Questions 8
Question Type Descriptive / Subjective

This is the Mathematics Paper-I from the UPSC Civil Services Main Examination held in 2021. The paper is designed to test advanced mathematical knowledge and problem-solving skills. It consists of 8 questions divided into two sections, with candidates required to answer five questions in total, including compulsory questions from each section. The exam is conducted by the UPSC and allows three hours to complete, with a maximum of 250 marks. This paper is crucial for candidates aiming for a career in the Indian Civil Services.

Major Topics Covered

  • Linear Algebra
  • Calculus
  • Differential Equations
  • Geometry

Why This Paper is Important

  • Useful for UPSC Civil Services Main Exam 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

  • UPSC Civil Services Main Exam 2020 Mathematics Paper-I
  • UPSC Civil Services Main Exam 2021 Mathematics Paper-II
  • UPSC Civil Services Preliminary Exam 2021 General Studies Paper-I
  • UPSC Civil Services Main Exam 2021 Mathematics Paper-I Answer Key
  • UPSC Civil Services Main Exam Mathematics Syllabus
  • UPSC Civil Services Exam Syllabus
  • UPSC Civil Services Main Exam Pattern
  • UPSC Civil Services Exam Pattern

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 पुस्तिका में खाली छोड़ा हुआ पृष्ठ 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.
  • Question Nos. 1 and 5 are compulsory and out of the remaining, 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 ANDER HALL 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.
  • Wild String Assume suitable data, if considered necessary, and indicate the same clearly.
  • LBHH 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 Salthan question shall be counted even if attempted partly.
  • Any page or portion of the page left blank PHILLE in the Question-cum-Answer Booklet must be clearly struck off. \mathbb{R} (Hita)

Questions (page 2)

Q1.

(a) यदि A = eginbmatrix 1 & -1 & 1 \ 2 & -1 & 0 \ 1 & 0 & 0 endbmatrix है, तो A-1 को ज्ञात किए बिना दर्शाइए कि A2 = A-1If A = eginbmatrix 1 & -1 & 1 \ 2 & -1 & 0 \ 1 & 0 & 0 endbmatrix, then show that A2 = A-1 (without finding A-1).

(b) क्रमित आधार B = (0, 1, 1), (1, 0, 1), (1, 1, 0) के सापेक्ष V3(R) पर परिभाषित रैखिक संकारक: T(a, b, c) = (a + b, a - b, 2c) से संबन्धित आव्यूह ज्ञात कीजिए। Find the matrix associated with the linear operator on V3(R) defined by T(a, b, c) = (a + b, a - b, 2c) with respect to the ordered basis B = (0, 1, 1), (1, 0, 1), (1, 1, 0).

(c) दिया गया है: Delta(x) = eginvmatrix f(x + lpha) & f(x + 2lpha) & f(x + 3lpha) \ f(lpha) & f(2lpha) & f(3lpha) \ f'(lpha) & f'(2lpha) & f'(3lpha) endvmatrix जहाँ f एक वास्तविक-मान अवकलनीय फलन है तथा lpha एक अचर है। limx o 0racDelta(x)x को ज्ञात कीजिए। Given: Delta(x) = eginvmatrix f(x + lpha) & f(x + 2lpha) & f(x + 3lpha) \ f(lpha) & f(2lpha) & f(3lpha) \ f'(lpha) & f'(2lpha) & f'(3lpha) endvmatrix where f is a real valued differentiable function and lpha is a constant. Find limx o 0 racDelta(x)x.

(d) दर्शाइए कि ex cos x = 1 के किन्हीं दो मूलों के बीच में ex sin x - 1 = 0 का कम से कम एक मूल विद्यमान है। Show that between any two roots of ex cos x = 1, there exists at least one root of ex sin x - 1 = 0.

(e) उस बेलन का समीकरण ज्ञात कीजिए जिसके जनक, रेखा : racx2 = racy-2 = racz3 के समान्तर हैं तथा जिसका निर्देशांक-वक्र x2 + 2y2 = 1, z = 0 है । Find the equation of the cylinder whose generators are parallel to the line : racx2 = racy-2 = racz3 and whose director curve is x2 + 2y2 = 1, z = 0.

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Frequently asked questions

What is the name of the exam?

The exam is the UPSC Civil Services Main Examination.

Which paper is this question paper for?

This is for Mathematics Paper-I.

What is the conducting body?

The Union Public Service Commission (UPSC).

What is the maximum marks for this paper?

The maximum marks are 250.

What is the time allowed to complete the paper?

The time allowed is three hours.

How many questions are there in total?

There are 8 questions in total.

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