BCSE 2023 Technical Paper II PDF

PAPER II: GENERAL SUBJECT KNOWLEDGE PAPER FOR ENGINEERING ROYAL CIVIL SERVICE COMMISSION BHUTAN CIVIL SERVICE EXAMINATION (BCSE) 2023 EXAMINATION CATEGORY: TECHNICAL PAPER II: GENERAL SUBJECT KNOWLEDGE PAPER FOR...

PAPER II: GENERAL SUBJECT KNOWLEDGE PAPER FOR ENGINEERING ROYAL CIVIL SERVICE COMMISSION BHUTAN CIVIL SERVICE EXAMINATION (BCSE) 2023 EXAMINATION CATEGORY: TECHNICAL PAPER II: GENERAL SUBJECT KNOWLEDGE PAPER FOR ENGINEERING Date : October 6, 2023 Total Marks : 100 Examination Time : 90 minutes (1.5 hours) Reading Time : 15 Minutes (prior to examination time) GENERAL INSTRUCTIONS: 1. Write your Registration Number clearly and correctly on the Answer Booklet. 2. The first 15 minutes is to check the number of pages of the Question Paper, printing errors, clarify doubts and to read the instructions. You are NOT permitted to write during this time. 3. This paper consists of TWO parts: Part I & Part II. Part I consists of 70 multiple choice questions of 1 (one) mark each, and Part II consists of 10 short answer questions of 3 (three) marks each. 4. All questions are COMPULSORY 5. All answers should be written on the Answer Booklet provided to you. Candidates are not allowed to write anything on the question paper. If required, ask for additional Answer Booklet. 6. All answers should be written with correct numbering of Part, Section and Question Number in the Answer Booklet provided to you. Note that any answer written without indicating correct Part, Section and Question Number will NOT be evaluated and no marks would be awarded. 7. Begin each Part on a fresh page of the Answer Booklet. 8. You are not permitted to tear off any sheet(s) of the Answer Booklet as well as the Question Paper. 9. Use of any other paper including paper for rough work is not permitted 10. You must hand over the Answer Booklet to the Invigilator before leaving the examination hall. 11. The Question paper has 13 printed pages, including this Instruction Page. GOOD LUCK! Page 1 of 13  PAPER II: GENERAL SUBJECT KNOWLEDGE PAPER FOR ENGINEERING PART I Multiple Choice Questions [70 marks] Choose the correct answer and write down the letter of the correct answer chosen in the Answer Booklet against the question number. e.g. 71 (a). Each question carries ONE mark. Any double writing, smudgy answer or writing more than one choice shall not be evaluated. SECTION A: Mathematics 1. Let f: R → R be the functions defined by f(x) = x3 + 5. Then f-1(x) is a) (𝑥 + 5)!/# b) (5 − 𝑥)!/# c) 5 − x d) (𝑥 − 5)!/# 2. The domain of the function defined by𝑓(𝑥) = 𝑆𝑖𝑛$! √𝑥 − 1 a) [1, 2] b) [-1, 1] c) [0, 1] d) None of these (& ! $#! ) 3. Find the positive integer n in limx→3 (&$#) = 108. a) 3 b) 4 c) -2 d) 1 4. Find the value of sec2 (tan-1 2) + cosec2 (cot-1 3) a) 12 b) 5 c) 15 d) 9 ) 5. If tan-1 2x + tan-1 3x = * , then x is ! a) + b) 1 ! c) (+, -1) d) None of these 𝑥 + 𝑦 2𝑥 + 𝑧 4 7 6. If 0 5 =6 :, then the values of x, y, z and w respectively are 𝑥 − 𝑦 2𝑧 + 𝑤 0 10 a) 2, 2, 3, 4 b) 2, 3, 1, 2 c) 3, 3, 0, 1 d) None of these Page 2 of 13  PAPER II: GENERAL SUBJECT KNOWLEDGE PAPER FOR ENGINEERING 7. If A2 – A + I = O, then the inverse of A is a) I – A b) A – I c) A d) A + I 8. If the points (3, -2), (x, 2), (8, 8) are co-linear, find the value of x. a) 2 b) 5 c) 4 d) 3 9. Using determinants, find the equation of the line joining the points (1, 2) and (3, 6). a) x = 3y b) y = x c) y = 2x d) 4x – y = 5 ,- 10. If xy. yx = 16, then the value of ,. at (2, 2) is a) 0 b) 1 c) -1 d) None of these ,- 11. If y = (tan x)sin x, then ,. is equal to a) sec x + cos x b) sec x + log tan x c) (tan x)sin x d) None of these 12. It is given that at x = 1, the function x4 – 62x2 + ax + 9 attains its maximum value on the interval [0, 2]. Find the value of a. a) 120 b) 100 c) 140 d) 160 13. The area of a right-angled triangle of the given hypotenuse is maximum when the triangle is a) Scalene b) Isosceles c) Equilateral d) None of these Page 3 of 13  PAPER II: GENERAL SUBJECT KNOWLEDGE PAPER FOR ENGINEERING 14. The equation of the normal to the curves y = sin x at (0, 0) is a) x = 0 b) y = 0 c) x + y = 0 d) x – y = 0 15. Evaluate: ∫tan(x – θ) tan(x + θ) tan2x dx ! a) / log|cos2x| – log|cos(x – θ)| + log|cos(x + θ)| + c ! b) − / log|cos2x| + log|cos(x – θ)| + log|cos (x + θ)| + c ! c) − / log|cos2x| – log|cos(x – θ)| – log|cos(x + θ)| + c d) None of these 16. The solution of differential equation (ey + 1) cosx dx + ey sinx dy = 0 is a) (ey + 1) sinx = c b) ex sinx = c c) (ex + 1) cosx = c d) None of these 17. The vectors from origin to the points A and B are a