How many questions are there in this paper?

There are 150 questions in this paper.

What type of questions are asked in this paper?

The questions in this paper are objective type.

Are there negative marks for wrong answers?

Yes, 1/3rd of the marks of each question will be deducted for each wrong answer.

What is the marking scheme for unanswered questions?

If a question is not attempted, one-third (1/3) part of the marks of the question shall be deducted, provided the fifth option is not darkened. If the fifth option is darkened, no marks are deducted.

What is the language of the question paper?

The question paper is available in both Hindi and English. In case of any ambiguity, the English version will be considered standard.

Is it mandatory to attempt all questions?

It is mandatory to fill one option for each question. If more than 10% of questions are left unattempted (no option darkened), the candidate may be disqualified.

What is the paper code for Mathematics Paper II?

The paper code for Mathematics Paper II is 62.

RPSC Asst. Prof. Mathematics-II Question Paper 2023 PDF

Name: RPSC Asst. Prof. Mathematics-II Question Paper 2023 PDF
Creator: RPSC
Keywords: RPSC Asst. Prof. Mathematics Paper II 2023, Asst. Prof. College Edu. Exam Mathematics Question Paper, RPSC Mathematics Paper II PDF, Rajasthan Govt Jobs Mathematics Exam, 2023 Mathematics Paper II Question 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-II
Subject	Mathematics
Duration	03 Hours
Maximum Marks	75
Number of Questions	150
Question Type	Objective (MCQ)

This is the official question paper for the Assistant Professor, Librarian, and PTI (College Education) Examination 2023 conducted by RPSC. Paper II focuses on Mathematics. The exam was held in 2023 and had a maximum of 75 marks, with a duration of 03 Hours and 10 minutes extra. It contained 150 objective-type questions. This paper is vital for candidates aspiring for these positions in Rajasthan's college education department, providing insights into the exam pattern, difficulty level, and important topics covered. Aspirants can use this paper for practice and to gauge their preparation level.

Major Topics Covered

Mathematics
Calculus
Linear Algebra
Probability
Differential Equations
Vector Calculus
Geometry

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. Paper I 2023
RPSC Librarian Exam Paper 2023
RPSC PTI Exam Paper 2023
RPSC Asst. Prof. Mathematics Paper II Answer Key 2023
RPSC Asst. Prof. Mathematics Syllabus
RPSC Asst. Prof. Exam Pattern
RPSC Asst. Prof. Exam
Rajasthan Govt Jobs

Instructions

प्रत्येक प्रश्न के लिये एक विकल्प मरना अनिवार्य है।
2 All questions carry equal marks. सभी प्रश्नों के अंक समान है। Only one answer is to be given for each question. If more than one answers з. प्रत्येक प्रश्न का मात्र एक ही उत्तर दीजिये।
एक से अधिक उत्तर देने з. are marked, it would be treated as wrong answer. की दशा में प्रश्न के उत्तर को गलत माना जाएगा।
OMR उत्तर-पत्रक इस प्रश्न पुरितका के अन्दर रखा है।
जब आपको प्रश्न directed to open the Question Booklet, take out the Answer Sheet and fill पुस्तिका खोलने को कहा जाए, तो उत्तर–पत्रक निकाल कर ध्यान से कवल नीले in the particulars carefully with BLUE BALL POINT PEN only. बॉल प्वॉइंट पेन से विवरण नरें। Please correctly fill your Roll Number in OMR Answer Sheet. Candidate
कृपया अपना रोल नम्बर ओ.एम.आर. उत्तर-पत्रक पर सावधानीपूर्वक सही गरें।
will themselves be responsible for filling wrong Roll Number. गलत रोल नम्बर मरने 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 तात्पर्य अशुद्ध एत्तर अधवा किसी भी प्रथन के एक से अधिक उत्तर से है। one answers for any question.
Each question has five options marked as 1, 2, 3, 4,
You have to प्रत्येक प्रश्न के पांच विकल्प दिये गये हैं, जिन्हें क्रमशः 1, 2, 3, 4, 5 अंकित
darken only one circle (bubble) indicating the correct answer on the किया गया है।
अभ्यर्थी 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।
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 महरा 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 प्रश्न अंक का 1/3 माग काटा जायेगा। 9, * After solving the question paper, candidate must ascertain that he/she
* प्रश्न पत्र इस करने के रापरांत अभ्यर्थी 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 अभ्यर्थी 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। nature, then out of Hindi and English Version of the question, the English
यदि किसी प्रश्न में किसी प्रकार की कोई मुद्रण या तथ्यात्मक प्रकार की त्रुटि हो, Version will be treated as standard. तो प्रश्न के हिन्दी तथा अंग्रेज़ी रूपान्तरों में से अंग्रेज़ी रूपान्तर मान्य होगा।
मोबाइल फोन अथवा इलेक्ट्रॉनिक यंत्र का परीक्षा हॉल में प्रयोग पूर्णतया वर्जित 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 अभ्यर्थी 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 (मती में अनुचित साधनों की रोकथान Public Examination (Measures for Prevention of Unfair means in अध्युपाय) अधिनियम, 2022 तथा अन्य प्रमावी कानून एवं आयोग के नियमों-प्राक्यानों Recruitment) Act, 2022, other law applicable and Commission's के तहत कार्यवाही की जाएगी।
साथ ही आयोग ऐसे अभ्यर्थी को भविष्य में होने वाली Regulations. Commission may also debar him/her permanently from all future आयोग की समस्त परीक्षाओं से विवर्जित कर सकता है। examinations. उत्तर–पत्रक में दो प्रतियां हैं – मूल प्रति और कार्बन प्रति ।
परीक्षा समापित पर परीक्षा को पूरी परीक्षाणी उत्तर–पत्रक की दोनों प्रतियां वीक्षक को सौंपैगे, परीक्षाणी स्वयं कार्बन प्रति अलग नहीं करें।
वीक्षक उत्तर–पत्रक की मूल प्रति को अपने पास कर, कार्बन प्रति को मूल प्रति से कट लाईन से मोड़कर सावधानीपूर्वक अलग कर परीसार्थी को सौंपेंगे. जिसे परीक्षार्थी अपने साथ ले जायेंगे।
परीक्षार्थी को उत्तर–पत्रक की कार्बन प्राति पाया पाया की जाता करना होगी एवं आयोग हारा मांगे जाने पर प्रस्तुत करनी होगी। 62 - 88 Page 1 of 32

The OMR Answer Sheet is inside this Question Booklet. When you are
If you are not attempting a question, then you have to darken the
A candidate who has not darkened any of the five circles in more than
Mobile Phone or any other electronic gadget in the examination hall is

Questions (page 2)

Q1. The Green's function for y''+5y'+6y = cos x, is -

(1) 2e^{2(t-x)}+3e^{3(t-x)}
(2) e^{2(t-x)}-e^{3(t-x)}
(3) 3e^{2(t-x)}-3e^{3(t-x)}
(4) e^{2(t-x)}-e^{-3(t-x)}

Q2. The plane, that has three points of contact at the origin with the curve x=t⁴-1; y=t³-1; z=t²-1, is:

(1) 3x-8y+z=0
(2) 3x+8y+6z=0
(3) 3x+8y+z=0
(4) 3x-8y+6z=0

Q3. The envelope of the plane lx+my+nz=0, where a^2l²+b^2m²+c^2n²=0, is:

(1) (x²)/(a²) + (y²)/(b²) + (z²)/(c²) = 0
(2) (x²)/(a²) + (y²)/(b²) - (z²)/(c²) = 0
(3) (x²)/(a²) - (y²)/(b²) + (z²)/(c²) = 0
(4) ((x)/(a))² + ((y)/(b))² + ((z)/(c))² = 0

Q4. The rectifying plane at any point on a curve in space contains the unit vectors (in usual notations):

(1) t, n तथा b
(2) t तथा n
(3) n तथा b
(4) b तथा n

Q5. A bag contains 2 white, 4 black and 5 red balls. Three balls are drawn from it at random. What is the probability that two balls are of the same color and the third is different?

(1) 3/35
(2) 37/55
(3) 2/11
(4) 4/165

Q6. Sturm-Liouville boundary value problem has -

(1) केवल तुच्छ हल
(2) केवल अतुच्छ हल
(3) तुच्छ तथा अतुच्छ दोनों हल
(4) इनमें से कोई नहीं

Q7. The matrix of the components of the fundamental tensor with respect to three dimensional rectangular axes is -

(1) इकाई आव्यूह
(2) पंक्ति आव्यूह
(3) स्तम्भ आव्यूह
(4) शून्य आव्यूह

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Frequently asked questions

What is the full name of the exam?

The full name of the exam is the Assistant Professor, Librarian, and PTI (College Education) Examination 2023.

Which conducting body organized this exam?

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

What is the year of this question paper?

The year of this question paper is 2023.

What is the subject of Paper II?

Paper II is for Mathematics.

What is the maximum marks for this paper?

The maximum marks for this paper are 75.

What is the total time allowed for the exam?

The time allowed is 03 Hours plus an extra 10 minutes.

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