UPSC Civil Services Exam 2016 Mathematics Paper I PDF

Central Government Jobs Other Jobs 2016

  • Year 2016
  • Conducted By UPSC
  • Questions 8
  • Maximum Marks 250
  • Duration Three Hours
  • Languages English & Hindi

Exam Details

Detail Information
Examination UPSC Civil Services Exam
Year 2016
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 Exam held in 2016. The paper was conducted by UPSC and allowed candidates three hours to complete, with a maximum of 250 marks. It consists of eight descriptive questions divided into two sections, requiring candidates to answer five questions in total, including compulsory questions 1 and 5. This paper is crucial for aspirants aiming to assess their understanding of advanced mathematical concepts relevant to the civil services.

Major Topics Covered

  • Linear Equations
  • Matrix Inverse
  • Vector Spaces
  • Linear Algebra

Why This Paper is Important

  • Useful for UPSC Civil Services 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 Exam 2015 Mathematics Paper I
  • UPSC Civil Services Exam 2017 Mathematics Paper I
  • UPSC Civil Services Exam 2016 General Studies Paper I
  • UPSC Civil Services Exam 2016 Mathematics Paper I Answer Key
  • UPSC Civil Services Exam Mathematics Syllabus
  • UPSC CSE Paper I Syllabus
  • UPSC Civil Services Exam Pattern
  • CSE Paper I Exam Structure

Instructions

  • इसमें आठ प्रश्न हैं जो दो खण्डों में विभाजित हैं तथा हिन्दी और अंग्रेज़ी दोनों में छपे हैं।
  • परीक्षार्थी को कुल पाँच प्रश्नों के उत्तर देने हैं।
  • प्रश्न संख्या 1 और 5 अनिवार्य हैं तथा बाकी प्रश्नों में से प्रत्येक खण्ड से कम-से-कम एक प्रश्न चुनकर किन्हीं तीन प्रश्नों के उत्तर दीजिए।
  • प्रत्येक प्रश्न/भाग के अंक उसके सामने दिए गए हैं।
  • प्रश्नों के उत्तर उसी माध्यम में लिखे जाने चाहिए जिसका उल्लेख आपके प्रवेश-पत्र में किया गया है, और इस माध्यम का स्पष्ट उल्लेख प्रश्न-सह-उत्तर (क्यू॰ सी॰ ए॰) पुस्तिका के मुखपृष्ठ पर अंकित निर्दिष्ट स्थान पर किया जाना चाहिए।
  • उल्लिखित 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 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 Booklet must be clearly struck off. 711-ESC-4-711TF / 54 1

Questions (page 2)

Section A

Q1.

(a) (i) यदि A = eginbmatrix 1 & 2 & 1 \ 1 & 3 & 2 \ 1 & 0 & 1 endbmatrix है, तो प्रारम्भिक पंक्ति संक्रिया (elementary row operation) के प्रयोग से A-1निकालिये। Using elementary row operations, find the inverse of A = eginbmatrix 1 & 2 & 1 \ 1 & 3 & 2 \ 1 & 0 & 1 endbmatrix.

(a) (ii) यदि A = eginbmatrix 1 & 1 & 3 \ 5 & 2 & 6 \ -2 & -1 & -3 endbmatrix है, तो A14+ 3A - 2I का मान निकालिये। If A = eginbmatrix 1 & 1 & 3 \ 5 & 2 & 6 \ -2 & -1 & -3 endbmatrix, then find A14 + 3A - 2I.

(b) (i) प्रारम्भिक पंक्ति संक्रिया (elementary row operation) के प्रयोग से वह शर्त निकालिये, जिससे प्रथम-घातीय समीकरणों (linear equations) x - 2y + z = a, 2x + 7y - 3z = b, 3x + 5y - 2z = c का एक हल हो। Using elementary row operations, find the condition that the linear equations x-2y + z = a, 2x + 7y - 3z = b, 3x + 5y - 2z = c have a solution.

(b) (ii) यदि W1 = (x, y, z) | x + y - z = 0, W2 = (x, y, z) | 3x + y - 2z = 0, W3 = (x, y, z) | x - 7y + 3z = 0 तो dim (W1 cap W2 cap W3) तथा dim (W1 + W2) का मान निकालिये। If W1 = (x, y, z) | x + y - z = 0, W2 = (x, y, z) | 3x + y - 2z = 0, W3 = (x, y, z) | x - 7y + 3z = 0 then find dim(W1 cap W2 cap W3) and dim(W1 + W2).

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Frequently asked questions

What is the name of the exam?

The exam is the UPSC Civil Services Exam.

What year is this question paper from?

This question paper is from the year 2016.

Who conducts the Civil Services Exam?

The Civil Services Exam is conducted by the UPSC (Union Public Service Commission).

What is the subject of this paper?

This paper is Mathematics Paper - I.

What is the time duration for this paper?

The time allowed for this paper is Three Hours.

What are the maximum marks for this paper?

The maximum marks for this paper are 250.

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