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Sample ETEA Engineering Test Practice Questions

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

1Two vectors are given as A = 2i + 3j - k and B = -4i + 2j + p k. If vectors A and B are mutually perpendicular, what is the value of the scalar parameter p?
A.-2
B.2
C.-14
D.14
Explanation: Two non-zero vectors are perpendicular if and only if their scalar (dot) product equals zero: A · B = 0. Computing the component-wise dot product: (2)(-4) + (3)(2) + (-1)(p) = -8 + 6 - p = -2 - p. Setting -2 - p = 0 gives p = -2.
2A projectile is launched from ground level with initial speed v at an angle θ above the horizontal. If H is the maximum vertical height reached and R is the total horizontal range, what is the ratio H / R?
A.(1/4) tan θ
B.(1/2) tan θ
C.tan θ
D.4 tan θ
Explanation: The maximum height is H = (v^2 sin^2 θ) / (2g) and the horizontal range is R = (v^2 sin 2θ) / g = (2 v^2 sin θ cos θ) / g. Dividing H by R yields H / R = [(v^2 sin^2 θ) / (2g)] / [(2 v^2 sin θ cos θ) / g] = (sin θ) / (4 cos θ) = (1/4) tan θ. This relationship holds for any level-ground ballistic trajectory neglecting air resistance.
3A student of mass 70 kg stands on a spring scale inside an elevator that is accelerating downwards at 2.8 m/s^2. Taking the acceleration due to gravity g = 9.8 m/s^2, what apparent weight is registered by the scale?
A.490 N
B.686 N
C.882 N
D.196 N
Explanation: When an elevator accelerates downward with acceleration a, the normal reaction force N from the floor scale is given by N = m(g - a). Substituting the parameters gives N = 70 kg * (9.8 m/s^2 - 2.8 m/s^2) = 70 * 7.0 = 490 N. Therefore, the scale registers an apparent weight of 490 N.
4A variable force F(x) = (3x^2 + 2x) N acts along the x-axis on a particle. What is the total work done by this force as the particle moves from x = 1.0 m to x = 3.0 m?
A.34 J
B.36 J
C.28 J
D.42 J
Explanation: Work done by a variable one-dimensional force is given by the definite integral W = ∫ F(x) dx from x1 to x2. Integrating (3x^2 + 2x) dx yields [x^3 + x^2] from 1 to 3. Evaluating between the limits gives (3^3 + 3^2) - (1^3 + 1^2) = (27 + 9) - (1 + 1) = 36 - 2 = 34 J.
5A glider of mass m moving with speed v on a frictionless air track collides with a stationary glider of mass 2m. If the two gliders latch together upon impact, what fraction of the initial kinetic energy is lost in the collision?
A.2/3
B.1/3
C.1/2
D.3/4
Explanation: By conservation of linear momentum, m*v = (m + 2m)*v_f, which yields a final coupled speed of v_f = v / 3. The initial kinetic energy is K_i = (1/2) m v^2, and the final kinetic energy is K_f = (1/2)(3m)(v/3)^2 = (1/6) m v^2. The fractional kinetic energy lost is (K_i - K_f) / K_i = [(1/2) - (1/6)] / (1/2) = (1/3) / (1/2) = 2/3 (66.7%).
6A curved highway bend of radius r is engineered for a design speed v. To prevent side-skidding entirely without relying on tyre friction, the required banking angle θ must satisfy which formula?
A.tan θ = v^2 / (r g)
B.tan θ = (r g) / v^2
C.sin θ = v^2 / (r g)
D.cos θ = v / (r g)
Explanation: On a frictionless banked turn, the horizontal component of the normal force provides centripetal acceleration (N sin θ = m v^2 / r) while the vertical component supports the vehicle's weight (N cos θ = m g). Dividing these two expressions yields tan θ = v^2 / (r g). This ideal banking angle eliminates lateral shear stress on the tyres at design speed.
7A solid uniform cylinder (I = (1/2) M R^2) and a thin circular hoop (I = M R^2) of identical mass M and radius R roll from rest down an incline of height h without slipping. What is the ratio of the linear speed of the solid cylinder to that of the hoop at the base?
A.2 / √3
B.√3 / 2
C.4 / 3
D.√2
Explanation: For any rigid body rolling without slipping down height h, conservation of energy gives M g h = (1/2) M v^2 [1 + I / (M R^2)]. For the solid cylinder, 1 + 1/2 = 3/2, so v_cyl = √(4 g h / 3). For the hoop, 1 + 1 = 2, so v_hoop = √(g h). The ratio v_cyl / v_hoop is √(4/3) = 2 / √3.
8The escape velocity from the surface of Earth is v_e. If a newly discovered planet has twice the mass of Earth (M_p = 2 M_E) and half the radius of Earth (R_p = R_E / 2), what is the escape velocity from the surface of this planet?
A.2 v_e
B.4 v_e
C.√2 v_e
D.v_e / 2
Explanation: Escape velocity from the surface of a spherical body of mass M and radius R is v = √(2 G M / R). For the exoplanet, v_p = √(2 G (2 M_E) / (R_E / 2)) = √(4 * (2 G M_E / R_E)) = 2 √(2 G M_E / R_E) = 2 v_e. Doubling mass and halving radius together produce a fourfold increase inside the square root.
9A satellite moves in a circular orbit around Earth at an altitude h equal to Earth's radius R (orbital radius r = 2R). If v_0 = √(G M / R) is the circular orbital speed near the surface of Earth, what is the orbital speed of this satellite?
A.v_0 / √2
B.v_0 / 2
C.v_0 / 4
D.√2 v_0
Explanation: Orbital speed at a radial distance r from Earth's center is v = √(G M / r). At altitude h = R, the center-to-orbit distance is r = R + h = 2R. Therefore, v = √(G M / (2R)) = (1 / √2) √(G M / R) = v_0 / √2.
10Water flows smoothly through a horizontal cylindrical pipe. If the cross-sectional area narrows from 40 cm^2 to 10 cm^2 and the flow speed in the wider section is 2.0 m/s, what is the flow speed in the constricted section?
A.8.0 m/s
B.4.0 m/s
C.0.5 m/s
D.16.0 m/s
Explanation: By the equation of continuity for an incompressible fluid, A_1 * v_1 = A_2 * v_2. Substituting the values gives 40 cm^2 * 2.0 m/s = 10 cm^2 * v_2, which simplifies to v_2 = (40 * 2.0) / 10 = 8.0 m/s. The constriction forces the fluid to accelerate inversely with area to maintain constant volumetric flow.

About the ETEA Engineering Test Exam

Independent English-language practice by OpenExamPrep for ETEA engineering topics. The 2026–27 prospectus specifies standard and pre-medical applicant papers. Eligibility includes the specified intermediate or relevant DAE/equivalent route with at least 60%, with results-awaiting and domicile/seat-category rules. Pre-medical engineering applicants have separate mathematics preparation and assessment requirements. This selected-topic bank does not replace interviews, architecture drawing/writing or practical preparation. The entrance-test sources reviewed did not explicitly establish all permitted assessment languages; no official English-sitting claim is made.

Exam sponsor: Educational Testing and Evaluation Agency (ETEA), Government of Khyber Pakhtunkhwa; admitting university UET Peshawar. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

MCQs; one mark per correct answer and no negative marking. This bank offers partial practice in both optional subjects. UET admission involves interview/document verification; B.Arch additionally assesses drawing and creative writing/general knowledge. Those components are outside this bank.

Time Limit

Confirm on the current admit card; the 2026–27 entrance-test section reviewed does not state a duration.

Passing Score

No universal test pass mark stated in the reviewed section. Engineering merit uses test 50%, intermediate Part I/equivalent 40% and SSC 10%, subject to admission rules.

Exam / Certification Fees

ETEA's 7 February 2025 notification, effective until further orders, lists PKR 1,000 for engineering admission tests, possible hall charges and a disabled-candidate waiver. Confirm the current test voucher; UET admission processing is a separate fee.

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.

40 of 100 standard-paper items

Physics

Mechanics, waves, thermal physics, electricity and modern physics.

35 of 100 standard-paper items

Mathematics

Algebra, calculus, geometry, vectors and probability.

15 of 100 standard-paper items

English

Grammar, vocabulary and reading.

10 of 100 standard-paper items

Chemistry or Computer Science

The real paper uses the applicable option; this bank covers selected topics in both.

Preparing for the ETEA Engineering Test Exam

What You Need to Know

  • Passing score: No universal test pass mark stated in the reviewed section. Engineering merit uses test 50%, intermediate Part I/equivalent 40% and SSC 10%, subject to admission rules.
  • Assessment: MCQs; one mark per correct answer and no negative marking. This bank offers partial practice in both optional subjects. UET admission involves interview/document verification; B.Arch additionally assesses drawing and creative writing/general knowledge. Those components are outside this bank.
  • Time limit: Confirm on the current admit card; the 2026–27 entrance-test section reviewed does not state a duration.
  • Exam / certification fees: ETEA's 7 February 2025 notification, effective until further orders, lists PKR 1,000 for engineering admission tests, possible hall charges and a disabled-candidate waiver. Confirm the current test voucher; UET admission processing is a separate fee. Official sources

Using Our Practice Resources

  • Work through all 100 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
  • Use our AI tutor for tough concepts

ETEA Engineering Test: Suggested Study Strategy

1Check your applicant paper and optional subject.
2Practise worked physics and mathematics problems.
3Use current ETEA instructions for timing and test-day arrangements.

Frequently Asked Questions

Is the old 200-question pattern current?

The 2026–27 UET prospectus specifies 100 standard-paper items and 65 pre-medical applicant items. Follow current session instructions.

Is there negative marking?

The 2026–27 prospectus explicitly says there is no negative marking.