7. The general solution of the differential equation ∫ dz/(z sin z) = c, where c is x^2 + y^2 = 1, and y = (c1 − c2 x) e^x + c3 cos x + c4 sin x

(a) y = (c1 + c2 x) e^x − c3 cos x + c4 sin x

(b) y = (c1 + c2 x) e^x + c3 cos x + c4 sin x

(c) y = (c1 + c2 x) e^x + c3 cos x − c4 sin x

Electrical Engineering Engineering Services 2017 Prelim MCQ Questions

Central Government Jobs Engineer 2017

Year 2017
Questions 150
Maximum Marks 300
Duration Three Hours

Exam Details

Detail	Information
Examination	Engineering Services (Preliminary) Examination
Year	2017
Paper	Electrical Engineering
Subject	Electrical Engineering
Duration	Three Hours
Maximum Marks	300
Number of Questions	150

This dataset corresponds to the Electrical Engineering section of the Engineering Services (Preliminary) Examination 2017. Page 1 provides the exam header, maximum marks (300), duration (Three Hours), and instruction set (pointing to 150 MCQ items). Page 2 contains repaired objective questions spanning topics such as linear algebra (eigenvalues and minimal polynomials), differential equations, Fourier series, harmonic functions, and residues. The repaired OCR preserves numbered questions and (where present) multiple-choice options (a–d). The overall SEO metadata ties page content to topics like Fourier analysis, differential equations, matrix theory, and complex analysis, suitable for indexing and semantic search. The JSON structures include exam overview, question previews, and rich SEO artifacts including FAQs, keywords, and image metadata.

Major Topics Covered

Electrical Engineering
Engineering Services
Fourier Series
Eigenvalues
Minimal Polynomial
Differential Equations
Harmonic Functions
Residues
Complex Analysis
Matrix Theory
Linear Algebra
Calculus
Integration
Vector Functions
Polynomial Equations
Boundary Conditions
Eigenvalue Problems
Partial Differential Equations
Series Expansion
Mathematical Methods

Why This Paper is Important

Useful for Engineering Services (Preliminary) Exami preparation
Helps understand the latest exam pattern
Useful for practice and self-assessment
Covers frequently asked General Studies topics
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Instructions

THIS TEST BOOKLET DOES NOT HAVE ANY UNPRINTED OR TORN OR MISSING PAGES OR ITEMS, ETC.
IF SO, GET IT REPLACED BY A COMPLETE TEST BOOKLET.
Please note that it is the candidate's responsibility to encode and fill in the Roll Number and Test
Booklet Series Code A, B, C or D carefully and without any omission or discrepancy at the appropriate places in the OMR Answer Sheet.
Any omission/discrepancy will render the Answer Sheet liable for rejection.
You have to enter your Roll Number on the
Test Booklet in the Box provided alongside.
DO NOT write anything else on the Test Booklet.
This Test Booklet contains 150 items (questions).
Each item comprises four responses (answers).
will select the response which you want to mark on the Answer Sheet.
In case, you feel that there is more than one correct response, mark the response which you consider the best.
In any case, choose ONLY ONE response for each item.
You have to mark your responses ONLY on the separate Answer Sheet provided.
the Answer Sheet. All items carry equal marks.
Before you proceed to mark in the Answer Sheet the response to various items in the Test Booklet,
you have to fill in some particulars in the Answer Sheet as per instructions sent to you with your Admission Certificate.
After you have completed filling in all your responses on the Answer Sheet and the examination has
concluded, you should hand over to the Invigilator only the Answer Sheet.
You are permitted to take away with you the Test Booklet.
Sheets for rough work are appended in the Test Booklet at the end.
THERE WILL BE PENALTY FOR WRONG ANSWERS MARKED BY A CANDIDATE.
There are four alternatives for the answer to every question.
For each question for which a wrong answer \rm(i) has been given by the candidate, one-third (0-33) of the marks assigned to that question will be deducted as penalty.
If a candidate gives more than one answer, it will be treated as a wrong answer even if one of the given (ii) answers happens to be correct and there will be same penalty as above to that question.
If a question is left blank, i.e., no answer is given by the candidate, there will be no penalty for that (iii) question.
DO NOT OPEN THIS TEST BOOKLET UNTIL YOU ARE ASKED TO DO SO (1 - A)

Questions (page 2)

Q1.

(a) If a square matrix of order 100 has exactly 1.
5. The Fourier series expansion of the distinct eigenvalues, then the degree of the saw-toothed waveform minimal polynomial is f
(x) = x in (-π, π) of period 2π gives the series, At least 15 1-1/3 + 1/5 - 1/7 + ...
(b) At most The sum is equal to
(c) Always 15 (π)/(2) (a) \cdot
(d) Exactly 100 (π^2)/(4) (b)

Q2.

(a) The solution of the differential equation y√(1-x²) dy + x √(1-y²) dx = 0 is (π^2)/(16) \mathrmc) √(1-x²) = c (π)/(4) (d)
(b) √(1-y²) = c What is the value of m for which 2x - x² + my² 6.
(c) √(1-x²) + √(1-y²) = c is harmonic? \mathbf 1 √(1 + x²) + √(1 + y²) = c (a)
(d) (b) -1
(c) \,2
3. The general solution of the differential (d) -2 equation (d⁴y)/(dx⁴) - 2(d³y)/(dx³) + 2(d²y)/(dx²) - 2(dy)/(dx) + y = 0 is Evaluate 7. ∫ (dz)/(z sin z), where c is x² + y² = 1. y = (c₁ - c₂ x) e^x + c₃ cos x + c₄ sin x (a) y = (c₁ + c₂ x) e^x - c₃ cos x + c₄ sin x (b) y = (c₁ + c₂ x) e^x + c₃ cos x + c₄ sin x \mathbf1
(c) (a) \boldsymbol2 (b) y = (c₁ + c₂ x) e^x + c₃ cos x - c₄ sin x (d)
(c) \bf0 (d) -1 Given the Fourier series in (-π, π) for
4. f
(x) = x cos x, the value of a₀ will be The sum of residues of f(z) = (2z)/((z-1)² (z-2))
8. (a) -2/3π^2 at its singular point is (b) \bf0 -8 (a)
(c) \overline2 (b) -4 ((-1)ⁿ\ 2n)/(n²-1) (d)
(c) \pmb0 \rm(d) \bf4 MKA-S-EEN (2-A)

Q3. 3. The general solution of the differential equation d^4y/dx^4 − 2 d^3y/dx^3 + 2 d^2y/dx^2 − 2 dy/dx + y = 0

Q4. 4. f(x) = x cos x, the value of a0 will be

Q5. 5. The Fourier series expansion of the 15 distinct eigenvalues, then the degree of the saw-toothed waveform minimal polynomial is f(x) = x in (−π, π) of period 2π gives the series, At least 15

(a) 1 − 1/3 + 1/5 − 1/7 + ...
(b) At most 15
(c) Always 15
(d) Exactly 100

Q6. 6. The expression sqrt(1−x²) + sqrt(1−y²) = c is harmonic? sqrt(1+x²) + sqrt(1+y²) = c

(a) −1
(b) 2
(c) 0

Q7. 7. The general solution of the differential equation ∫ dz/(z sin z) = c, where c is x² + y² = 1, and y = (c1 − c2 x) e^x + c3 cos x + c4 sin x

(a) y = (c1 + c2 x) e^x − c3 cos x + c4 sin x
(b) y = (c1 + c2 x) e^x + c3 cos x + c4 sin x
(c) y = (c1 + c2 x) e^x + c3 cos x − c4 sin x
(d) y = (c1 − c2 x) e^x + c3 cos x + c4 sin x

Q8. 8. The sum of residues of f(z) = 2z/[(z−1)^2 (z−2)] at its singular points is

(a) −2/3 π^2
(b) 0
(c) 2
(d) 4

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