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GATE Practice Questions
Original practice questions for the Graduate Aptitude Test in Engineering (IISc Bengaluru and the IITs (organising institute rotates)), mixed across 5 topics with instant answers and explanations. Practise by topic below or take the timed mock test.
GATE mixed practice
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Q1.AlgebraSolve: x + 3y = 26 and x + 2y = 21
Show answer & explanation
Answer: A — x = 11, y = 5
Elimination/substitution gives x = 11, y = 5. Check: 1(11) + 3(5) = 26 ✓ and 1(11) + 2(5) = 21 ✓.
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Q2.Probability & Combinatorics2 fair coins are tossed. What is the probability of at least one head?
Show answer & explanation
Answer: A — 3/4
P(no head) = (1/2)^2 = 1/4; P(at least one head) = 1 − 1/4 = 3/4.
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Q3.PhysicsThe phenomenon responsible for the blue colour of the sky is:
Show answer & explanation
Answer: B — Rayleigh scattering
Shorter (blue) wavelengths are scattered more by air molecules.
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Q4.Logical ReasoningRavi walks 11 m north, turns right and walks 8 m, then turns right again and walks 7 m. How far is he from the start?
Show answer & explanation
Answer: D — 8.94 m
Net: 4 m north and 8 m east. Distance = √(4² + 8²) = 8.94 m.
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Q5.Vocabulary & IdiomsMeaning of the idiom “to burn the midnight oil”.
Show answer & explanation
Answer: B — To work late into the night
It means to work or study late at night.
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Q6.AlgebraSolve: 5x + 3y = 49 and 5x + 2y = 51
Show answer & explanation
Answer: A — x = 11, y = -2
Elimination/substitution gives x = 11, y = -2. Check: 5(11) + 3(-2) = 49 ✓ and 5(11) + 2(-2) = 51 ✓.
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Q7.Probability & CombinatoricsIn how many ways can a committee of 3 be chosen from 8 people?
Show answer & explanation
Answer: A — 56
Order does not matter → combinations: 8C3 = 8! / (3!·5!) = 56.
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Q8.PhysicsA body starts at 12 m/s and accelerates uniformly at 6 m/s² for 3 s. Find its final velocity.
Show answer & explanation
Answer: C — 30 m/s
v = u + at = 12 + 6×3 = 30 m/s.
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Q9.Logical ReasoningWhat day of the week was 28 December 2000?
Show answer & explanation
Answer: B — Thursday
Using odd days (or Zeller’s rule), 28 December 2000 falls on a Thursday.
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Q10.Vocabulary & IdiomsOne word for: Fear of heights.
Show answer & explanation
Answer: A — Acrophobia
Acrophobia is an extreme fear of heights.
About GATE
Graduate Aptitude Test in Engineering — conducted by IISc Bengaluru and the IITs (organising institute rotates). Tests engineering and science graduates for M.Tech admissions and PSU recruitment; every paper includes General Aptitude.
Original practice questions written for this site in the style and difficulty of each exam’s syllabus. They are not past papers and the site is not affiliated with any exam body. Exam patterns, marking schemes and syllabi change — always check the latest official notification.
Practise by topic
- Algebra questions — Factorise quadratics by finding two numbers with the right sum and product; check roots by substitution.
- Probability & Combinatorics questions — Probability = favourable ÷ total outcomes.
- Physics questions — Write the formula before substituting and keep SI units throughout.
- Logical Reasoning questions — For coding questions write the letter positions (A = 1 … Z = 26).
- Vocabulary & Idioms questions — Learn words in synonym/antonym pairs and by roots (bene = good, mal = bad, chron = time).
- GATE mock test — 25 timed questions with negative marking.
GATE practice topics
| Topic | Section | Question source |
|---|---|---|
| Algebra | Mathematics | Calculated (new numbers every set) |
| Probability & Combinatorics | Mathematics | Calculated (new numbers every set) |
| Physics | Science | Calculated + question bank |
| Logical Reasoning | Reasoning | Calculated (new numbers every set) |
| Vocabulary & Idioms | English | Question bank |