RAS RTS 2016 Mains Paper-I Question Paper PDF | RPSC Exam

Rajasthan Government Jobs Other Jobs 2016

  • Year 2016
  • Conducted By RPSC

Exam Details

Detail Information
Examination RAS/RTS Combined Competitive Exam 2016
Year 2016
Conducting Body RPSC
Paper Paper-I
Question Type Mixed

This document contains the official question paper for the RAS/RTS Combined Competitive Exam 2016 Mains, Paper-I, conducted by the Rajasthan Public Service Commission (RPSC). The exam date was 17.12.2018-18.12.2018. This paper is a vital resource for aspirants preparing for the RAS/RTS examinations, offering insights into the exam structure, question types, and difficulty level. Analyzing previous years' papers like this one is a key strategy for effective preparation, helping candidates understand the syllabus and refine their study approach for the Mains examination.

Major Topics Covered

  • RAS/RTS Combined Competitive Exam 2016
  • Paper-I
  • RPSC
  • 2016 question paper
  • previous year paper
  • PDF download

Why This Paper is Important

  • Useful for RAS/RTS COMB. COMP. 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

  • RAS/RTS Combined Competitive Exam 2018 Mains Paper-I
  • RAS/RTS Combined Competitive Exam 2015 Mains Paper-I
  • RAS/RTS Combined Competitive Exam 2016 Prelims Paper-I
  • RAS RTS 2016 Mains Paper-I Answer Key
  • RPSC Mains Exam 2016 Answer Key
  • RAS Mains Syllabus
  • RPSC Exam Syllabus
  • RAS Mains Exam Pattern

Instructions

  • PART - II Paper Code 100026 P-1 Roll No.
  • Name of the candidate PART-I CONTRACT Paper Code STORY P-1 Date of Birth (DD/MM/YYYY) Party COST SIZAIRE Father's Name STATE Signature of the candidate 00026 TO BE FILLED BY THE CANDIDATE Roll No. ^\copyright ^\copyright ^\copyright \odot ^\copyright ^\copyright \odot \odot \odot \odot \odot \begin{picture}(40,4) \put(0,0){\line(1,0){150}} \put(0,0){\line(1,0){150}} \put(0,0){\line(1,0){150}} \put(0,0){\line(1,0){150}} \put(0,0){\line(1,0){150}} \put(0,0){\line(1,0){150}} \put(0,0){\line(1,0){150}} \put(0,0){\line(1,0){150}} \put(0,0){\line(1,0){150}} \put(0,0){\line(1,0){150}} \put(0,0){\line(1,0){150}} \put(0,0){\line(1, \odot \ddot{\circ} \odot \odot \circledS \circledS \circledS \circledS \circledS \circledcirc ^\circledR ^\circledR ^\circledR ^\circledR \circledS \circledS \circledS \circledS \circledS \circledS ^\circledR \circledS \circledS ^\circledR \circledcirc \circledcirc ^\copyright \circledcirc ^\copyright ^\circledR \circledcirc ^\circledR ^{\circ} ^\circledR ^\circledR ^\circledR ◉ ^{\circ} \circledcirc ^\circledR ^\circledR ^{\circledR} ③ Invigilator must check the Roll No. and Photo LD. of the candidate, them Sign. here: STATE CONTROL TO BE FILLED BY INVIGILATOR If candidate found using unfair means them Invigilator should fill up this SUP bubble with black/blue ball pen & report to the Centre Superintendent: 10031 COLOR О STATE 1430_H2C-2 \blacksquare

Questions (page 2)

Q1.

(a) Let V be a vector space over the field mathbb{R} and let T: V o V be a linear transformation. If T is such that T2 - 3T + 2I = 0, where I is the identity transformation, show that T is diagonalizable.

(b) Let A = \beginpmatrix 1 & 2 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \endpmatrix. Find the Jordan canonical form of A.

(c) Let f(x) = x3 - 6x2 + 11x - 6. Find the eigenvalues and eigenvectors of the matrix A = \beginpmatrix 1 & 2 & 0 \\ 2 & 1 & 0 \\ 0 & 0 & 3 \endpmatrix.

(d) Let V be the vector space of all polynomials of degree at most 2. Define a linear transformation T: V o V by T(p(x)) = p'(x) + p(x). Find the matrix representation of T with respect to the basis {1, x, x2}.

(e) Let A be an n imes n matrix such that A2 = A. Show that A is diagonalizable.

Q2.

(a) Let f: mathbb{R}^2 o mathbb{R}^2 be defined by f(x, y) = (x+y, x-y). Show that f is a linear transformation. Find the matrix of f with respect to the standard basis.

(b) Let A = \beginpmatrix 2 & 1 \\ 1 & 2 \endpmatrix. Find the eigenvalues and eigenvectors of A.

(c) Let V be the vector space of all 2 imes 2 matrices. Define a linear transformation T: V o V by T(A) = A^T. Show that T is a linear transformation and find its eigenvalues.

Question paper preview

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RAS RTS 2016 Mains Paper-I question paper page 1 instructions and candidate details section scan PDF download
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Frequently asked questions

What is the name of the exam for which this question paper is intended?

This question paper is for the RAS/RTS Combined Competitive Exam 2016 (Mains).

Which paper does this document contain?

This document contains Paper-I of the RAS/RTS Combined Competitive Exam 2016 Mains.

Who conducts the RAS/RTS Combined Competitive Exam?

The RAS/RTS Combined Competitive Exam is conducted by the Rajasthan Public Service Commission (RPSC).

What is the exam year mentioned for this paper?

The exam year is 2016.

What is the paper code for Paper-I?

The paper code for Paper-I is 100026.

What was the exam date for this paper?

The exam date was 17.12.2018-18.12.2018.

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