What type of questions are asked in this paper?

The questions are objective type, with each question having five options.

Is there any negative marking for wrong answers?

Yes, 1/3 part of the mark(s) of each question will be deducted for each wrong answer.

What should a candidate do if they don't want to attempt a question?

If a candidate does not want to attempt a question, they should darken the fifth (5) option on the OMR Answer Sheet.

What is the penalty for not darkening any circle for a question?

If none of the five circles is darkened, one third (1/3) part of the marks of the question shall be deducted.

What is the penalty for darkening more than 10% of questions with no option selected?

If a candidate does not mark any option for more than 10% of the questions, they will be disqualified.

What happens if there is an ambiguity or mistake in the question?

If there is any ambiguity or mistake, the English version of the question will be treated as standard.

Are electronic gadgets allowed in the examination hall?

No, mobile phones or any other electronic gadgets are strictly prohibited in the examination hall.

What action will be taken if a candidate is caught copying or with unauthorized material?

If a candidate is found copying or with unauthorized material, FIR will be lodged, and they may be debarred from future examinations.

What is the paper code for Mathematics Paper I?

The paper code for Mathematics Paper I is 61.

RPSC Asst. Prof. Math Paper I 2023 Question Paper PDF

Name: RPSC Asst. Prof. Math Paper I 2023 Question Paper PDF
Creator: RPSC
Keywords: RPSC Asst. Prof. Mathematics Paper I 2023, College Education Exam Mathematics Question Paper, RPSC Mathematics Paper I PDF, Asst. Prof. Exam 2023 Mathematics, Rajasthan PSC Mathematics Paper, Mathematics Paper I 2023, Objective Mathematics Questions, RPSC Exam Paper, College Professor Recruitment, Mathematics Syllabus, RPSC Previous Year Paper, Mathematics Exam Paper, 2023 Mathematics Paper, Asst. Prof. Mathematics, Librarian Exam Paper

Rajasthan Government Jobs Professor 2023

Year 2023
Conducted By RPSC
Questions 150
Maximum Marks 75
Duration 03 Hours
Languages Hindi & English

Exam Details

Detail	Information
Examination	Assistant Professor, Librarian and PTI (College Education) Exam 2023
Year	2023
Conducting Body	RPSC
Paper	Mathematics - Paper I
Subject	Mathematics
Duration	03 Hours
Maximum Marks	75
Number of Questions	150
Question Type	Objective (MCQ)

This document contains the official question paper for the Assistant Professor, Librarian, and PTI (College Education) Examination 2023, conducted by RPSC. Specifically, it features Paper I for the Mathematics subject. The exam was held in 2023, allowing 3 hours and 10 minutes for candidates to answer 150 objective questions, with a maximum score of 75 marks. This paper is crucial for aspirants preparing for recruitment in college education roles in Rajasthan, providing valuable insights into the exam pattern and difficulty level. Candidates can use this paper to assess their preparation and identify areas for improvement.

Major Topics Covered

Mathematics
Calculus
Differential Equations
Linear Algebra
Conics
SHM

Why This Paper is Important

Useful for ASST. PROF., LIBRARIAN AND PTI (COLLEGE 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

RPSC Asst. Prof. Mathematics Paper II 2023
RPSC Asst. Prof. General Studies 2023
RPSC Librarian Exam Paper 2023
RPSC PTI Exam Paper 2023
RPSC Asst. Prof. Mathematics Paper I 2023 Answer Key
RPSC Asst. Prof. Mathematics Syllabus
College Education Exam Syllabus Rajasthan
RPSC Asst. Prof. Exam Pattern

Instructions

ъ सभी प्रश्नों के अंक समान है। All questions carry equal marks, 2.
प्रत्येक प्रश्न का मात्र एक ही उत्तर दीजिये।
एक से अधिक उत्तर देने Only one answer is to be given for each question. If more than one answers
are marked, it would be treated as wrong answer. की दशा में प्रश्न के उत्तर को गलत माना जाएगा। The OMR Answer Sheet is inside this Question Booklet. When you are
OMR उत्तर-पत्रक इस प्रश्न पुस्तिका के अन्दर रखा है।
जब आपको प्रश्न directed to open the Question Booklet, take out the Answer Sheet and fill पुरितका खोलने को कहा जाए, तो ततर-पत्रक निकाल कर ध्यान से केवल नीले in the particulars carefully with BLUE BALL POINT PEN only. बॉल प्वॉइंट पेन से विवरण भरे। Please correctly fill your Roll Number in OMR Answer Sheet. Candidate कृपया अपना रोल नम्बर ओ.एम.आर. उत्तर-पत्रक पर साताशानीपूर्वक सही भरें।
will themselves be responsible for filling wrong Roll Number. गलत रोल नम्बर भरने पर परीक्षार्थी स्वयं उत्तरदायी होगा।
1/3 part of the mark(s) of each question will be deducted for each प्रत्येक गलत उत्तर के लिए प्रश्न अंक का 1/3 माग काटा जायेगा। गलत उत्तर
wrong answer. A wrong answer means an incorrect answer or more than से तालयें अशुद्ध उत्तर अथवा किसी भी प्रश्न के एक से अधिक उत्तर से हैं। one answers for any question. प्रत्येक प्रश्न के पांच विकल्प दिये गये हैं, जिन्हें क्रमशः 1, 2, 3, 4, 5 अंकित
Each question has five options marked as 1, 2, 3, 4,
You have to darken only one circle (bubble) indicating the correct answer on the किया गया है।
अभ्यर्धी को सही उत्तर निर्दिष्ट करते हुए उनमें से केवल एक Answer Sheet using BLUE BALL POINT PEN. गोले (बबल) को उत्तर-पत्रक पर नीले बॉल प्वॉइंट पेन से गहरा करना है। If you are not attempting a question, then you have to darken the यदि आप प्रश्न का उत्तर नहीं देना चाहते हैं, तो उत्तर-पत्रक में पांचवे (5) विकल्प
circle '5'. If none of the five circles is darkened, one third (1/3) part of को गहरा करें।
यदि पांच में से कोई भी गोला गहरा नहीं किया जाता है, तो ऐसे the marks of question shall be deducted. प्रश्न के लिये प्रहन अंक का 1/3 भाग काटा जायेगा।
4 After solving the question paper, candidate must ascertain that he/she 9* प्रश्न पत्र हल करने के उपरांत अम्पर्थी अनिवार्य रूप से ओ.एम.आर. आंसर शीट has darkened one of the circles (bubbles) for each of the questions. जांच लें कि समस्त प्रश्नों के लिये एक विकल्प (गोला) भर दिया गया है।
इसके Extra time of 10 minutes beyond scheduled time is provided for this. लिये ही निर्धारित समय से 10 मिनट का अतिरिक्त समय दिया गया है।
यदि अम्यर्थी 10% से अधिक प्रश्नों में पांच विकल्प में से कोई भी विकल्प अंकित 10% questions shall be disqualified.
If there is any sort of ambiguity/mistake either of printing or factual नहीं करता है, तो उसको अयोग्य माना जायेगा।
यदि किसी प्रश्न में किसी प्रकार की कोई मुद्दण या तेव्यात्मक प्रकार की बुटि हो, nature, then out of Hindi and English Version of the question, the English Version will be treated as standard. तो प्रश्न के हिन्दी तथा अंग्रेजी रूपान्तरों में से अंग्रेजी रूपानार मान्य होगा। Mobile Phone or any other electronic gadget in the examination hall is
मीबाइल फोन अथवा इलेक्ट्रॉनिक यंत्र का परीक्षा हॉल में प्रयोग पूर्णतया वजिंत strictly prohibited. A candidate found with any of such objectionable है।
यदि किसी अभ्यर्थी के पास ऐसी कोई वर्जित सामग्री मिलती है, तो उसके material with him/her will be strictly dealt as per rules. विरुद्ध आयोग द्वारा नियमानुसार कार्यवाही की जायेगी। Warning : If a candidate is found copying or if any unauthorized material is चेतावनी : अगर कोई अभ्यथी नकल करते पकड़ा जाता है या उसके पास से कोई found in his/her possession, F.I.R. would be lodged against him/her in the अनधिकृत सामग्री पाई जाती है, तो उस अभ्यर्थी के विरुद्ध पुलिस में प्राथमिकी दर्ज Police Station and he/she would liable to be prosecuted under Rajasthan कराते हुए और राजस्थान सार्वजनिक परीक्षा (मर्ती में अनुचित साधनों की रोकथाम Public Examination (Measures for Prevention of Unfair means in अध्युपाय) अधिनियम, 2022 तथा अन्य प्रभावी कानून एवं आयोग के नियमों-प्राक्धानों Recruitment) Act, 2022, other law applicable and Commission's क तहत कायवाही की जाएगी।
साथ ही आयोग ऐसे अभ्ययों को मंदिष्य में होने वाली Regulations. Commission may also debar him/her permanently from all future आयोग की समस्त परीक्षाओं से विवजित कर सकता है। examinations. उत्तर-पत्रक में दो प्रतियां हैं – मूल प्रति और कार्बन प्रति।
परीक्षा समापित पर परीक्षा को पुले परीक्षा पति पत्र पत्र की दोनों प्रतियां वीवाक को सौंपेंगे, परीक्षार्थी रवयं कार्बन प्रति अलग नहीं करें।
वीशक उत्तर-पत्रक की मूल प्रति को अपने पास जमा कर, कार्बन प्रति को मूल प्रति से कट लाईन से गोड़कर सावधानीपूर्वक अलग कर परीक्षायी को सौंपेंगे, जिसे परीक्षायी अपने साथ ले जायेंगे।
परीक्षायी को उत्तर-पत्रक की कार्बन प्रति चयन प्रक्रिया पूर्ण होने तक सुरक्षित रखनी होगी एवं आयोग द्वारा मांगे जाने पर प्रस्तुत करनी होगी। 0 Page 1 of 32.

A candidate who has not darkened any of the five circles in more than

Questions (page 2)

Q1. Let t:R⁳ → R³ be defined by -
t(x₁, x₂, x₃) = (x₁-x₂, x₁-x₂, 0). If N(t) and R(t) denote the null space and the range space of t respectively, then -

(1) dim N(t)=2
(2) dim N(t)=0
(3) dim R(t)=2
(4) dim R(t)=1
(5) अनुत्तरित प्रश्न

Q2. If f(x,y) = (1/1) + (1)/(xy) + (log_e x - log_e y)/(x² + y²), then

(1) (\partial f)/(\partial x) + (\partial f)/(\partial y) = f
(2) (\partial f)/(\partial x) + (\partial f)/(\partial y) = 2f
(3) (\partial f)/(\partial x) + (\partial f)/(\partial y) = -f
(4) (\partial f)/(\partial x) + (\partial f)/(\partial y) = -2f
(5) अनुत्तरित प्रश्न

Q3. If the auxiliary equation of (d²y)/(dx²) + 2α (dy)/(dx) + y = 0 has two equal roots, then the values of α are -

(1) \(± 2\)
(2) \(± 1\)
(3) \(± √(2)\)
(4) \(± 3\)
(5) अनुत्तरित प्रश्न

Q4. A particle is moving in a S.H.M. having amplitude a. At what distance from the centre will its velocity be half of the maximum velocity?

(1) \(a/√(3)\)
(2) \(a/2\)
(3) \(2a\)
(4) \(a√(3)/2\)
(5) अनुत्तरित प्रश्न

Q5. The equation of the direction of the conic x²-4xy+4y²-32x+4y+16 = 0 is -

(1) 2x - y + 3 = 0
(2) x + 2y + 3 = 0
(3) x + y + 3 = 0
(4) 2x + y + 3 = 0
(5) अनुत्तरित प्रश्न

Q6. Find the remainder when f(x)=3x⁴+x³+2x²+1 is divided by g(x)=x²+4x+2 where f(x) and g(x) belong to Z₅[x].

(1) 2x-1
(2) 138x+79
(3) 2x+1
(4) -138x-79
(5) अनुत्तरित प्रश्न

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Frequently asked questions

What is the full name of the exam?

The full name of the exam is ASST. PROF., LIBRARIAN AND PTI (COLLEGE EDU.) EXAM 2023.

Which conducting body organized this exam?

The exam was conducted by RPSC (Rajasthan Public Service Commission).

What is the subject of this question paper?

This question paper is for Mathematics - Paper I.

What is the maximum marks for this paper?

The maximum marks for this paper is 75.

How many questions are there in the paper?

There are 150 questions in the booklet.

What is the time duration allowed for the exam?

The time allowed is 03 Hours + 10 Minutes Extra.

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