UPSC Civil Services Main Examination 2019 — I Question Paper PDF Download

Name: UPSC Civil Services Main Examination 2019 — I Question Paper PDF Download
Creator: UPSC
Keywords: UPSC Civil Services Main Examination, UPSC Civil Services Main Examination 2019, I question paper, UPSC question paper, previous year question paper

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Year 2019
Conducted By UPSC
Maximum Marks 250
Duration Three Hours Question Paper Specific Instructions (please Read Each Of The Following Instructions Carefully Before Attempting Questions) 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.

Exam Details

Detail	Information
Examination	UPSC Civil Services Main Examination
Year	2019
Conducting Body	UPSC
Paper	Mathematics Paper - I
Subject	I
Duration	Three Hours Question Paper Specific Instructions (please Read Each Of The Following Instructions Carefully Before Attempting Questions) 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.
Maximum Marks	250

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Major Topics Covered

UPSC Civil Services Main Examination
Mathematics Paper - I
UPSC
2019 question paper
previous year paper
PDF download

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Useful for UPSC Civil Services Main Examination preparation
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Instructions

इसमें आठ प्रश्न हैं जो दो खण्डों में विभाजित हैं तथा हिन्दी एवं अंग्रेजी दोनों में छपे हैं।
उम्मीदवार 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 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 (क्यू० सी० ए०) 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.

Questions (page 2)

Formatted from page 2 OCR. Download the PDF for the full paper.

-A / SECTION-A 101 (:

1.

(a) Prove that माना कि f: $\left[0, \frac{\pi}{2}\right] \rightarrow \mathbb{R}$ एक संतत फलन है, जैसा कि $f(x) = \frac{\cos^2 x}{4x^2 - \pi^2}, \quad 0 \le x < \frac{\pi}{2}$ f(π)/(2))का मान ज्ञात कीजिए। Let $f: \left[0, \frac{\pi}{2}\right] \to \mathbb{R}$ be a continuous function such that $f(x) = \frac{\cos^2 x}{4x^2 - \pi^2}, \quad 0 \le x < \frac{\pi}{2}$ Find the value of f(π)/(2)). [8 Marks]

(b) माना कि $f: D ( ⊆ \mathbb{R}^2)$ → $\mathbb{R}$ एक फलन है और (a, b) ∈ D. अगर f(x, y) बिंदु (a, b) पर संतत है, तो दर्शाइए कि फलन f(x, b) और f(a, y) क्रमशः x = a और y = b पर संतत हैं। Let $f: D(\subseteq \mathbb{R}^2) \to \mathbb{R}$ be a function and (a, b) ∈ D. If f(x, y) is continuous at (a, b), then show that the functions f(x, b) and f(a, y) are continuous at x = a and at y = b respectively. [10 Marks]

(c) माना कि $T: \mathbb{R}^2 \to \mathbb{R}^2$ एक रैखिक प्रतिचित्र है, जैसा कि T(2, 1) = (5, 7) एवं T(1, 2) = (3, 3). अगर |c| A मानक आधारों e₁,\,e₂ के सापेक्ष T के संगत आव्यूह है, तो A की कोटि ज्ञात कीजिए। Let $T: \mathbb{R}^2 \to \mathbb{R}^2$ be a linear map such that T(2, 1) = (5, 7) and T(1, 2) = (3, 3). If A is the matrix corresponding to T with respect to the standard bases e₁, e₂, then find Rank [10 Marks]

Paper Code: SDF-U-MTH/10

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