Free Practice Questions for IESL Part I

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Exam Review

Key Facts: IESL Part I Exam

45%

Average Pass Rate

IESL

40%

Passing Score

per subject

120-150

Recommended Hours

Study time

Rs. 10,000

Estimated Exam Fee

IESL

Compulsory Subjects

Syllabus

3 hrs

Duration per Paper

Written exam

The IESL Qualifying Examination Part I has an average pass rate of 45% with a passing mark of 40% per subject. It serves as the initial academic gateway for engineering candidates seeking Associate Membership (AMIESL) in Sri Lanka. The exam covers six subjects: Mathematics for Engineers, Engineering Science, Basic Electrical/Electronics, Basic Mechanical, IT, and Environmental Engineering.

Sample IESL Part I Practice Questions

Try these sample questions to review concepts for the IESL Part I exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Find the determinant of the 2x2 matrix A = [[4, -3], [2, 5]].

A.26

B.14

C.22

D.10

Explanation: The determinant of a 2x2 matrix [[a, b], [c, d]] is calculated as ad - bc. Substituting the values, we get det(A) = (4)(5) - (-3)(2) = 20 - (-6) = 20 + 6 = 26. Thus, the determinant is 26.

2If A = [[2, 1, 5], [0, -3, 4], [1, 2, 7]] and B = [[-1, 0, 3], [2, 4, 1], [5, -2, 2]], find the trace of the matrix C = 2A + B.

A.12

B.17

C.11

D.7

Explanation: The trace of a matrix is the sum of its diagonal elements, and trace is a linear operator: tr(2A + B) = 2tr(A) + tr(B). For matrix A, the trace is 2 + (-3) + 7 = 6. For matrix B, the trace is -1 + 4 + 2 = 5. Therefore, the trace of 2A + B is 2(6) + 5 = 17.

3Find all values of k for which the matrix A = [[k - 1, 2], [3, k - 2]] is singular.

A.k = 4 or k = -1

B.k = 5 or k = -2

C.k = -4 or k = 1

D.k = 3 or k = -2

Explanation: A matrix is singular if its determinant is zero. The determinant of A is (k - 1)(k - 2) - (2)(3) = k^2 - 3k + 2 - 6 = k^2 - 3k - 4. Setting this determinant to zero gives k^2 - 3k - 4 = 0, which factors as (k - 4)(k + 1) = 0, yielding solutions k = 4 and k = -1.

4Determine the eigenvalues of the matrix A = [[3, 2], [1, 4]].

A.2 and 5

B.3 and 4

C.1 and 6

D.2 and 6

Explanation: The characteristic equation of matrix A is given by det(A - L*I) = 0, which expands to (3 - L)(4 - L) - 2 = 0. This simplifies to L^2 - 7L + 10 = 0. Solving the quadratic equation (L - 2)(L - 5) = 0 gives the eigenvalues L = 2 and L = 5.

5Consider the system of linear equations: x + y + z = 3 x + 2y + 3z = 4 x + 3y + az = b For which values of a and b does the system have infinitely many solutions?

A.a = 5, b = 5

B.a = 5, b = 6

C.a = 4, b = 5

D.a = 6, b = 5

Explanation: Write the system in augmented matrix form and perform row operations: R2 -> R2 - R1 gives y + 2z = 1, and R3 -> R3 - R1 gives 2y + (a - 1)z = b - 3. Next, eliminate y from the third row using R3 -> R3 - 2R2, which yields 0y + (a - 5)z = b - 5. For the system to have infinitely many solutions, we must have a row of zeros at the bottom, which requires a - 5 = 0 and b - 5 = 0. Thus, a = 5 and b = 5.

6Find the order and degree of the differential equation: (d^2y/dx^2)^3 + 5(dy/dx)^4 - xy = 0.

A.Order 2, Degree 3

B.Order 3, Degree 2

C.Order 2, Degree 4

D.Order 4, Degree 3

Explanation: The order of a differential equation is the order of the highest derivative present, which is d^2y/dx^2 (order 2). The degree is the power to which the highest derivative is raised, which is 3. Therefore, the order is 2 and the degree is 3.

7Solve the first-order differential equation: dy/dx = x^2 / y, with the initial condition y(0) = 2.

A.y^2 = (2/3)x^3 + 4

B.y^2 = 2x^3 + 4

C.y = (2/3)x^3 + 2

D.y^2 = (1/3)x^3 + 4

Explanation: Separating variables gives y dy = x^2 dx. Integrating both sides yields (1/2)y^2 = (1/3)x^3 + C, which simplifies to y^2 = (2/3)x^3 + 2C. Applying the initial condition y(0) = 2 gives 2^2 = 0 + 2C, so 2C = 4, which yields the solution y^2 = (2/3)x^3 + 4.

8Find the integrating factor for the first-order linear differential equation: x(dy/dx) + 2y = cos(x), for x > 0.

A.x^2

B.e^(2x)

C.x

D.e^(x^2)

Explanation: First, rewrite the differential equation in standard form dy/dx + P(x)y = Q(x) by dividing by x: dy/dx + (2/x)y = cos(x)/x. The coefficient function P(x) is 2/x. The integrating factor is e^(integral P(x) dx) = e^(integral (2/x) dx) = e^(2 ln(x)) = e^(ln(x^2)) = x^2.

9Solve the second-order homogeneous linear differential equation: d^2y/dx^2 - 4dy/dx + 4y = 0, with initial conditions y(0) = 1 and y'(0) = 3.

A.y = (1 + x)e^(2x)

B.y = e^(2x) + 3xe^(2x)

C.y = c_1 e^(2x) + c_2 e^(-2x)

D.y = (1 - x)e^(2x)

Explanation: The characteristic equation is r^2 - 4r + 4 = 0, which has a repeated root r = 2. The general solution is y(x) = (C1 + C2 * x)e^(2x). Applying y(0) = 1 gives C1 = 1. The derivative is y'(x) = C2 * e^(2x) + 2(C1 + C2 * x)e^(2x); applying y'(0) = 3 gives C2 + 2C1 = 3 -> C2 + 2(1) = 3 -> C2 = 1. Thus, the solution is y(x) = (1 + x)e^(2x).

10Find the particular solution y_p(x) for the differential equation: d^2y/dx^2 + y = 3 sin(x).

A.-1.5 x cos(x)

B.1.5 x sin(x)

C.-3 x cos(x)

D.3 sin(x) - 3 cos(x)

Explanation: The complementary solution is y_c = C1 cos(x) + C2 sin(x). Since sin(x) is a solution to the homogeneous equation, the particular solution must be of the form y_p(x) = x(A cos(x) + B sin(x)). Differentiating twice and substituting into the ODE gives y_p'' + y_p = -2A sin(x) + 2B cos(x) = 3 sin(x). This yields B = 0 and -2A = 3 -> A = -1.5, so y_p(x) = -1.5 x cos(x).

About the IESL Part I Exam

The first stage of the qualifying examinations administered by the Institution of Engineers, Sri Lanka. It assesses foundational engineering knowledge across mathematics, sciences, electrical, mechanical, IT, and environmental subjects.

Exam sponsor: IESL. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Questions

100 questions

Time Limit

3 hours per paper

Passing Score

40%

Exam / Certification Fees

Rs. 10,000

Exam sponsor website

Reported exam pass rate: 45%. average pass rate across all subjects This describes exam candidates, not OpenExamPrep users or results from using our resources. Exam sponsor website

Fees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.

Official sources

Our practice resources: topics covered

We aim to reflect publicly available exam outlines and topic information in our study resources. Coverage, format, and difficulty may differ from the actual exam, and we cannot guarantee that every detail is accurate or current. Confirm exam requirements, fees, and policies with the official exam sponsor.

20%

Mathematics for Engineers

Matrices, limits, derivatives, integration, differential equations, and numerical analysis.

16%

Engineering Science

Stress-strain, elastic moduli, hydrostatics, fluid flow dynamics, and mechanics of materials.

16%

Basic Electrical/Electronics Engineering

Network theorems, AC circuits, semiconductor electronics, and electric motors/transformers.

16%

Basic Mechanical Engineering

Thermodynamic cycles (Otto, Diesel, Carnot), heat transfer modes, pumps, and gears.

16%

Information Technology

CPU architecture, basic programming logic, OSI networking layers, and SQL databases.

16%

Environmental Engineering

Water filtration, biological oxygen demand, air pollution scrubbers, waste landfills, and EIA.

Preparing for the IESL Part I Exam

What You Need to Know

Passing score: 40%
Exam length: 100 questions
Time limit: 3 hours per paper
Exam / certification fees: Rs. 10,000 Official sources

Using Our Practice Resources

Work through all 100 available questions
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IESL Part I: Suggested Study Strategy

1Dedicate at least 25-30 hours of study to each of the six subjects, emphasizing core principles.

2Practice worked calculations for engineering mathematics, structural mechanics, circuit theorems, and thermodynamic cycles.

3Review official past examination papers and model papers from the IESL Education Division.

4Consistently test yourself using practice questions to build speed and accuracy under the 3-hour exam limit.

Frequently Asked Questions

What is the passing score for the IESL Part I exam?

The passing threshold for the IESL Qualifying Examination Part I is 40% for each individual subject paper. Candidates are allowed to pass papers separately across different examination sittings.

What subjects are tested in the IESL Part I exam?

The examination tests six compulsory subjects: Mathematics for Engineers, Engineering Science, Basic Electrical and Electronics Engineering, Basic Mechanical Engineering, Information Technology, and Environmental Engineering.

How long do I have to complete each exam paper?

Each subject paper is a 3-hour written examination, which usually contains a mix of multiple-choice, short-answer, and structured calculation questions.

Is sponsorship required to register for the IESL Part I exam?

No professional sponsorship is required, but candidates must be registered student members of the Institution of Engineers, Sri Lanka (IESL) and pay the relevant registration and examination fees.