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NUST NET (Engineering) MCQs with answers

Practise NUST NET (Engineering) (Engineering) with 618 exam-style MCQs, each with the answer and a short explanation. Every test is marked the moment you finish and shows your score chapter by chapter, so you know what to revise next. It is free and needs no sign-up.

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NUST NET (Engineering) MCQs with answers

Practise NUST NET (Engineering) (Engineering) with 618 exam-style MCQs, each with the answer and a short explanation. Every test is marked the moment you finish and shows your score chapter by chapter, so you know what to revise next. It is free and needs no sign-up.

618 questions · 23 chapters

What each chapter covers 23 chapters

The questions follow the syllabus chapter by chapter. You can test the whole subject or one chapter at a time.

  1. Maths · Numbers, sets and functions 21 questionsComplex numbers, Sets and functions
  2. Maths · Matrices and determinants 14 questionsMatrices and determinants
  3. Maths · Quadratic equations 14 questionsQuadratic equations
  4. Maths · Sequences, series and the binomial theorem 23 questionsSequences and series, Binomial theorem and partial fractions
  5. Maths · Permutations, combinations and probability 16 questionsPermutations and combinations, Probability
  6. Maths · Trigonometry 24 questionsTrigonometric ratios and identities, Trigonometric graphs, triangles and equations
  7. Maths · Functions and limits 11 questionsLimits and continuity
  8. Maths · Differentiation 26 questionsRules of differentiation, Applications of derivatives
  9. Maths · Integration 26 questionsMethods of integration, Definite integrals and areas
  10. Maths · Analytic geometry 30 questionsStraight lines, Circles and conic sections, Linear inequalities and linear programming
  11. Maths · Vectors 14 questionsVectors in space
  12. Physics · Measurement, vectors and equilibrium 28 questionsMeasurement, Vectors and equilibrium
  13. Physics · Mechanics 61 questionsMotion and force, Work, energy and power, Circular and rotational motion, Fluid dynamics
  14. Physics · Oscillations, waves and light 42 questionsOscillations, Waves and sound, Physical optics and optical instruments
  15. Physics · Heat and thermodynamics 14 questionsKinetic theory and thermodynamics
  16. Physics · Electricity 30 questionsElectrostatics, Current electricity
  17. Physics · Magnetism and alternating current 42 questionsElectromagnetism, Electromagnetic induction, Alternating current
  18. Physics · Solids and electronics 28 questionsPhysics of solids, Electronics
  19. Physics · Modern and nuclear physics 42 questionsDawn of modern physics, Atomic spectra, Nuclear physics
  20. English · Vocabulary 32 questionsSynonyms and antonyms, Words in context
  21. English · Sentence completion 20 questionsSentence completion
  22. English · Grammar and usage 32 questionsIdentifying errors, Improving sentences
  23. English · Reading comprehension 28 questionsShort passages
Sample NUST NET (Engineering) MCQs with answers 12 questions

12 questions from the test, one or two from each chapter. Try each one, then open the answer.

1. A complex number z satisfies z + z̄ = 6 and z − z̄ = 8i. The value of |z| is

  1. A
    5
  2. B
    10
  3. C
    7
  4. D
    25
Show answer

Answer: A. If z = x + iy, then z + z̄ = 2x = 6 and z − z̄ = 2iy = 8i, so z = 3 + 4i and |z| = √(9 + 16) = 5. Forgetting the factor 2 gives z = 6 + 8i and |z| = 10.

2. The value of the determinant with rows [1 2 3], [4 5 6] and [2 4 6] is

  1. A
    0
  2. B
    6
  3. C
    −6
  4. D
    12
Show answer

Answer: A. The third row is 2 times the first row. A determinant with two proportional rows is 0, so no expansion is needed.

3. The real solutions of (x + 1)(x + 2)(x + 3)(x + 4) = 24 are

  1. A
    0 and 5
  2. B
    −1 and −4
  3. C
    1 and −6
  4. D
    0 and −5
Show answer

Answer: D. Pair the outer and inner factors: (x2 + 5x + 4)(x2 + 5x + 6) = 24. With y = x2 + 5x this is y2 + 10y = 0, so y = 0 (x = 0 or −5) or y = −10, and x2 + 5x + 10 = 0 has no real roots.

4. For |x| < 1/3, the first three terms of the expansion of (1 + 3x)1/3 are

  1. A
    1 + x − x2
  2. B
    1 + x + x2
  3. C
    1 + x − 2x2
  4. D
    1 − x + x2
Show answer

Answer: A. (1 + y)1/3 = 1 + y/3 + [(1/3)(−2/3)/2!]y2 = 1 + y/3 − y2/9. With y = 3x this is 1 + x − x2; forgetting the 2! gives −2x2.

5. For events A and B, P(A) = 0.5, P(B) = 0.4 and P(A ∩ B) = 0.2. The probability that neither A nor B occurs is

  1. A
    0.1
  2. B
    0.7
  3. C
    0.8
  4. D
    0.3
Show answer

Answer: D. P(A ∪ B) = 0.5 + 0.4 − 0.2 = 0.7, so P(neither) = 1 − 0.7 = 0.3. Forgetting to subtract P(A ∩ B) gives 1 − 0.9 = 0.1.

6. The exact value of tan 15° is

  1. A
    2 + √3
  2. B
    2 − √3
  3. C
    √3 − 1
  4. D
    (√6 − √2)/4
Show answer

Answer: B. tan(45° − 30°) = (1 − 1/√3)/(1 + 1/√3) = (√3 − 1)/(√3 + 1) = (√3 − 1)2/2 = 2 − √3. 2 + √3 is tan 75°, and (√6 − √2)/4 is sin 15°.

7. f(x) = (x2 − 9)/(x − 3) for x ≠ 3, and f(3) = k. f is continuous at x = 3 when k equals

  1. A
    6
  2. B
    0
  3. C
    3
  4. D
    9
Show answer

Answer: A. For x ≠ 3, f(x) = x + 3, so the limit at x = 3 is 6. Continuity needs f(3) to equal this limit, so k = 6.

8. The nth derivative of y = e3x is

  1. A
    n e3x
  2. B
    3n e3x
  3. C
    3n e3x
  4. D
    e3x/3n
Show answer

Answer: C. Each differentiation multiplies by 3: 3e3x, 9e3x, 27e3x, …, so the nth derivative is 3ne3x. Dividing by 3n is what repeated integration does.

9. The area under y = ex from x = 0 to x = ln 3 is (in square units)

  1. A
    3
  2. B
    ln 3
  3. C
    2
  4. D
    e3 − 1
Show answer

Answer: C. ∫0ln 3 ex dx = eln 3 − e0 = 3 − 1 = 2. Forgetting the lower limit gives 3.

10. The directrices of the ellipse x2/25 + y2/9 = 1 are

  1. A
    x = ±25/4
  2. B
    x = ±4
  3. C
    y = ±25/4
  4. D
    x = ±15/4
Show answer

Answer: A. c = √(25 − 9) = 4, so e = 4/5 and the directrices are x = ±a/e = ±5 ÷ (4/5) = ±25/4. The lines x = ±4 pass through the foci.

11. The magnitude of the vector 2i − 3j + 6k is

  1. A
    5
  2. B
    √11
  3. C
    7
  4. D
    49
Show answer

Answer: C. √(22 + (−3)2 + 62) = √(4 + 9 + 36) = √49 = 7. The value 49 forgets the square root.

12. In a pendulum experiment g is found from g = 4π2l/T2. The length l is measured with an uncertainty of 1% and the period T with an uncertainty of 2%. The percentage uncertainty in g is

  1. A
    1%
  2. B
    3%
  3. C
    4%
  4. D
    5%
Show answer

Answer: D. Percentage uncertainties add, each multiplied by its power: 1% + 2 × 2% = 5%. Forgetting the square on T gives 3%, and 4% leaves out the 1% from l.

Try 606 more questions

Ways to practise 5 ways

When you get a question wrong, a short note called "The idea behind this" explains the topic it belongs to, with the rules to remember and a worked example.

Topics explained 45 topics

Each topic has a short explanation, the rules to remember, a worked example and practice questions.

Complex numbersSets and functionsMatrices and determinantsQuadratic equationsSequences and seriesBinomial theorem and partial fractionsPermutations and combinationsProbabilityTrigonometric ratios and identitiesTrigonometric graphs, triangles and equationsLimits and continuityRules of differentiationApplications of derivativesMethods of integrationDefinite integrals and areasStraight linesCircles and conic sectionsLinear inequalities and linear programmingVectors in spaceMeasurementVectors and equilibriumMotion and forceWork, energy and powerCircular and rotational motionFluid dynamicsOscillationsWaves and soundPhysical optics and optical instrumentsKinetic theory and thermodynamicsElectrostaticsCurrent electricityElectromagnetismElectromagnetic inductionAlternating currentPhysics of solidsElectronicsDawn of modern physicsAtomic spectraNuclear physicsSynonyms and antonymsWords in contextSentence completionIdentifying errorsImproving sentencesShort passages

All NUST NET (Engineering) rules on one page

NUST NET (Engineering): frequently asked questions

Is this NUST NET (Engineering) test free?

Yes. Every test, answer and explanation is free, and you do not need an account. Sign in only if you want your results kept across devices.

How many NUST NET (Engineering) questions are there?

618 MCQs with answers, covering 23 chapters of the syllabus. Each test draws new questions, so you can practise many times.

How much of NUST NET does this cover?

NET (Engineering) is weighted Mathematics 50%, Physics 30% and English 20%. Our NUST NET (Engineering) test covers every unit of the syllabus.

Are these NUST NET (Engineering) past paper questions?

No. The 618 MCQs are our own, written to the syllabus in the style of the exam.

How is the test marked?

Instantly. You see your score, the right answer and an explanation for every question, and the topics to work on next. Questions you got wrong are saved so you can retry them.

Can I practise one chapter or only my weak topics?

Yes. Pick a chapter, build your own test from chosen topics, or practise your weakest topics and your past mistakes.

Is there a full-length mock test?

Yes: 200 MCQs in the NUST split (Mathematics 100, Physics 60, English 40), timed for 3 hours, plus a 100-question half mock.

Can I read the explanations in Urdu?

Yes. In practice mode and on your results you can switch the explanations to Urdu.

Does it work on a phone?

Yes. It runs in the browser on any phone or computer, and you can add it to your home screen like an app.

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