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GATE Algebra Questions
Practise algebra (mathematics) for the Graduate Aptitude Test in Engineering: 10 multiple-choice questions, each with the correct answer and a worked explanation. Click an option to check it, or “New questions” for another set.
Algebra practice
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Q1.Find log₃ 243.
Show answer & explanation
Answer: B — 5
log_3(243) asks “3 to what power gives 243?” → 3^5 = 243, so the answer is 5.
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Q2.Find the sum of the first 15 terms of the AP 13, 16, 19, …
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Answer: D — 510
Sₙ = n/2 × [2a + (n − 1)d] = 15/2 × [26 + 42] = 510.
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Q3.Solve: 4x + y = -10 and x + 5y = 45
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Answer: B — x = -5, y = 10
Elimination/substitution gives x = -5, y = 10. Check: 4(-5) + 1(10) = -10 ✓ and 1(-5) + 5(10) = 45 ✓.
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Q4.Find log₃ 27.
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Answer: B — 3
log_3(27) asks “3 to what power gives 27?” → 3^3 = 27, so the answer is 3.
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Q5.Solve: x + 3y = -5 and 4x + 4y = -4
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Answer: D — x = 1, y = -2
Elimination/substitution gives x = 1, y = -2. Check: 1(1) + 3(-2) = -5 ✓ and 4(1) + 4(-2) = -4 ✓.
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Q6.Solve: x² − x − 72 = 0
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Answer: A — -8, 9
Find two roots with sum 1 and product -72: -8 and 9. So x² − x − 72 = (x + 8)(x − 9) = 0.
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Q7.Find log₅ 3,125.
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Answer: B — 5
log_5(3125) asks “5 to what power gives 3125?” → 5^5 = 3125, so the answer is 5.
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Q8.Solve: x² − 9 = 0
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Answer: A — -3, 3
Find two roots with sum 0 and product -9: -3 and 3. So x² − 9 = (x + 3)(x − 3) = 0.
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Q9.Solve: x + 4y = 33 and 2x + y = 17
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Answer: A — x = 5, y = 7
Elimination/substitution gives x = 5, y = 7. Check: 1(5) + 4(7) = 33 ✓ and 2(5) + 1(7) = 17 ✓.
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Q10.Solve: 2x + 2y = 18 and 3x + 2y = 26
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Answer: D — x = 8, y = 1
Elimination/substitution gives x = 8, y = 1. Check: 2(8) + 2(1) = 18 ✓ and 3(8) + 2(1) = 26 ✓.
How to approach algebra questions
Factorise quadratics by finding two numbers with the right sum and product; check roots by substitution. For simultaneous equations, elimination is usually faster than substitution under time pressure.
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.
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 |