100+ Free ECAT Practice Questions

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The efficiency of a Carnot engine operating between a hot reservoir at 400 K and a cold reservoir at 300 K is:

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Key Facts: ECAT Exam

ECAT is UET Lahore's engineering entry test: 100 MCQs in 100 minutes (400 marks max), split Maths 30, Physics 30, Chemistry/CS 30, English 10, based on the FSc Pre-Engineering syllabus.

Sample ECAT Practice Questions

Try these sample questions to test your ECAT exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1What is the derivative of f(x) = 3x^3 - 2x^2 + 5x - 11 with respect to x?

A.9x^2 - 4x + 5

B.9x^2 - 2x + 5

C.6x^2 - 4x + 5

D.3x^2 - 4x + 5

Explanation: Differentiate term by term using the power rule d/dx(x^n) = n·x^(n-1): 3x^3 gives 9x^2, -2x^2 gives -4x, 5x gives 5, and the constant -11 gives 0. So f'(x) = 9x^2 - 4x + 5.

2Evaluate the integral ∫ (2x + 3) dx.

A.2x^2 + 3x + C

B.x^2 + 3x + C

C.x^2 + 3 + C

D.2x^2 + 3 + C

Explanation: Integrate term by term using ∫x^n dx = x^(n+1)/(n+1): ∫2x dx = x^2 and ∫3 dx = 3x. Adding the constant of integration gives x^2 + 3x + C.

3If sinθ = 3/5 and θ is in the first quadrant, what is cosθ?

A.3/4

B.5/4

C.4/5

D.5/3

Explanation: Using the identity sin^2θ + cos^2θ = 1, cos^2θ = 1 - (3/5)^2 = 1 - 9/25 = 16/25, so cosθ = 4/5. Since θ is in the first quadrant, cosθ is positive.

4What is the value of the limit lim(x→0) (sin x)/x?

A.0

B.Undefined

C.∞

D.1

Explanation: This is a standard fundamental limit in calculus. As x approaches 0 (in radians), the ratio (sin x)/x approaches 1, which is the basis for differentiating trigonometric functions.

5What is the sum of the first n terms of an arithmetic series with first term a and common difference d?

A.n [a + (n-1)d]

B.n/2 [2a + (n-1)d]

C.n/2 [a + (n-1)d]

D.n [2a + (n-1)d]

Explanation: The sum of an arithmetic series is S_n = n/2 [2a + (n-1)d], where a is the first term, d the common difference, and n the number of terms. This equals n/2 times the sum of the first and last terms.

6In how many ways can the letters of the word 'EXAM' be arranged?

A.12

B.16

C.24

D.4

Explanation: The word EXAM has 4 distinct letters. The number of arrangements (permutations) of 4 distinct objects is 4! = 4 × 3 × 2 × 1 = 24.

7What is the modulus of the complex number z = 3 + 4i?

A.1

B.7

C.25

D.5

Explanation: The modulus of z = a + bi is |z| = √(a^2 + b^2). Here |z| = √(3^2 + 4^2) = √(9 + 16) = √25 = 5.

8If A is a 2×2 matrix with det(A) = 5, what is det(2A)?

A.20

B.10

C.5

D.25

Explanation: For an n×n matrix, det(kA) = k^n · det(A). For a 2×2 matrix, det(2A) = 2^2 · det(A) = 4 × 5 = 20.

9What is the distance between the points (1, 2) and (4, 6) in the coordinate plane?

A.25

B.7

C.5

D.3

Explanation: Using the distance formula d = √[(x2-x1)^2 + (y2-y1)^2] = √[(4-1)^2 + (6-2)^2] = √[9 + 16] = √25 = 5.

10What is the dot product of vectors a = 2i + 3j and b = 4i - j?

A.-3

B.11

C.8

D.5

Explanation: The dot product a·b = (a1·b1) + (a2·b2) = (2)(4) + (3)(-1) = 8 - 3 = 5. The dot product yields a scalar.

About the ECAT Exam

The Engineering Colleges Admission Test (ECAT) is conducted by the University of Engineering and Technology (UET), Lahore, and is required for admission to undergraduate engineering programs at UET and its affiliated colleges across Punjab. The paper-based test has 100 single-best-answer MCQs to be solved in 100 minutes, with each correct answer worth 4 marks for a maximum of 400. The questions are distributed as Mathematics 30, Physics 30, Chemistry (or Computer Science/Statistics for ICS students) 30, and English 10. The content follows the FSc Pre-Engineering intermediate curriculum based on the Punjab textbook board. Each correct answer scores 4 marks; UET announced no negative marking for Fall 2026, though earlier sittings deducted 1 mark per wrong answer. ECAT scores combine with FSc and matriculation results to form the merit aggregate used for engineering admissions.

Questions

100 scored questions

Time Limit

100 minutes (1 hour 40 minutes)

Passing Score

No fixed pass mark; admission is merit-based on a 400-mark scale, with ECAT typically weighted around 30% of the UET aggregate.

Exam Fee

Rs. 3,000 registration fee (Fall 2026) (University of Engineering and Technology (UET), Lahore)

ECAT Exam Content Outline

30%

Mathematics

Algebra, functions and limits, differentiation and integration, trigonometry, analytic geometry, vectors, sequences and series, permutations/combinations/probability, complex numbers, and matrices.

30%

Physics

Mechanics, waves and oscillations, thermodynamics, electricity and magnetism, electromagnetism, modern/atomic physics, and electronics.

30%

Chemistry / Computer Science / Statistics

Chemistry covers atomic structure, bonding, states of matter, thermochemistry, equilibrium, electrochemistry, organic chemistry, and s/p/d-block elements; ICS students may instead choose Computer Science or Statistics.

10%

English

Grammar, vocabulary, sentence correction, prepositions, and reading comprehension.

How to Pass the ECAT Exam

What You Need to Know

Passing score: No fixed pass mark; admission is merit-based on a 400-mark scale, with ECAT typically weighted around 30% of the UET aggregate.
Exam length: 100 questions
Time limit: 100 minutes (1 hour 40 minutes)
Exam fee: Rs. 3,000 registration fee (Fall 2026)

Keys to Passing

Complete 500+ practice questions
Score 80%+ consistently before scheduling
Focus on highest-weighted sections
Use our AI tutor for tough concepts

ECAT Study Tips from Top Performers

1Master the full FSc Part I and Part II syllabus for Physics, Chemistry, and Mathematics, since ECAT draws directly from the Punjab textbook board content.

2Practice solving MCQs under a strict 100-minute timer to build speed and accuracy for 100 questions.

3Memorize key formulas (kinematics, work-energy, calculus rules, trigonometric identities, gas laws) and rehearse rapid mental calculation.

4Don't neglect the 10 English MCQs; quick wins in grammar, vocabulary, and comprehension can raise your merit.

5Check the latest UET notification each year for changes to negative marking and subject combinations before test day.

6Solve past papers chapter-wise to recognise the recurring question styles for each subject.

Frequently Asked Questions

Who conducts the ECAT and where is it valid?

ECAT is conducted by the University of Engineering and Technology (UET), Lahore. It is required for admission to engineering programs at UET and its affiliated public and private colleges across Punjab. Universities such as NUST, GIKI, FAST, and PIEAS use their own separate entry tests instead.

How is the ECAT structured and marked?

ECAT has 100 single-best-answer MCQs to be completed in 100 minutes. The questions are split into Mathematics 30, Physics 30, Chemistry/Computer Science/Statistics 30, and English 10. Each correct answer earns 4 marks, giving a maximum of 400 marks.

Is there negative marking in ECAT?

It depends on the sitting. For Fall 2026, UET announced that no negative marking would be applied. In some earlier years a deduction of 1 mark was made for each wrong answer, so candidates should always confirm the rule on the current admit card and official notification.

What syllabus does ECAT follow?

ECAT is based on the FSc Pre-Engineering (intermediate) curriculum aligned with the Punjab textbook board, covering both Part I and Part II of Physics, Chemistry, and Mathematics, plus intermediate-level English. Pre-medical or ICS candidates may substitute Biology, Computer Science, or Statistics for the optional subject.

How much does the ECAT cost in 2026?

The ECAT registration fee for Fall 2026 is Rs. 3,000, paid at HBL branches after registering online at ecat.uet.edu.pk. Some admission cycles use a combined challan of around Rs. 5,500 that also covers the admission application processing fee.