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JEE Advanced Algebra Questions
Practise algebra (mathematics) for the Joint Entrance Examination (Advanced): 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.Solve: 3x + 2y = 31 and x + 4y = 17
Show answer & explanation
Answer: B — x = 9, y = 2
Elimination/substitution gives x = 9, y = 2. Check: 3(9) + 2(2) = 31 ✓ and 1(9) + 4(2) = 17 ✓.
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Q2.Find log 1,000,000 (base 10).
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Answer: D — 6
log_10(1000000) asks “10 to what power gives 1000000?” → 10^6 = 1000000, so the answer is 6.
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Q3.Find log₅ 3,125.
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Answer: D — 5
log_5(3125) asks “5 to what power gives 3125?” → 5^5 = 3125, so the answer is 5.
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Q4.Solve: x + 2y = 8 and 4x + y = 4
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Answer: D — x = 0, y = 4
Elimination/substitution gives x = 0, y = 4. Check: 1(0) + 2(4) = 8 ✓ and 4(0) + 1(4) = 4 ✓.
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Q5.Find the sum of the first 14 terms of the AP 17, 26, 35, …
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Answer: C — 1057
Sₙ = n/2 × [2a + (n − 1)d] = 14/2 × [34 + 117] = 1,057.
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Q6.Solve: x² + 11x + 24 = 0
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Answer: D — -8, -3
Find two roots with sum -11 and product 24: -3 and -8. So x² + 11x + 24 = (x + 3)(x + 8) = 0.
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Q7.Solve: x² + 13x + 36 = 0
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Answer: A — -9, -4
Find two roots with sum -13 and product 36: -4 and -9. So x² + 13x + 36 = (x + 4)(x + 9) = 0.
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Q8.Solve: x² + 6x + 5 = 0
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Answer: A — -5, -1
Find two roots with sum -6 and product 5: -5 and -1. So x² + 6x + 5 = (x + 5)(x + 1) = 0.
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Q9.Solve: x² + 3x + 2 = 0
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Answer: C — -2, -1
Find two roots with sum -3 and product 2: -2 and -1. So x² + 3x + 2 = (x + 2)(x + 1) = 0.
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Q10.Solve: 2x + 3y = 23 and 4x + 4y = 24
Show answer & explanation
Answer: D — x = -5, y = 11
Elimination/substitution gives x = -5, y = 11. Check: 2(-5) + 3(11) = 23 ✓ and 4(-5) + 4(11) = 24 ✓.
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 JEE Advanced
Joint Entrance Examination (Advanced) — conducted by IITs (organising IIT rotates each year). The entrance exam for undergraduate programmes at the Indian Institutes of Technology.
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.
JEE Advanced practice topics
| Topic | Section | Question source |
|---|---|---|
| Algebra | Mathematics | Calculated (new numbers every set) |
| Probability & Combinatorics | Mathematics | Calculated (new numbers every set) |
| Geometry & Mensuration | Mathematics | Calculated (new numbers every set) |
| Physics | Science | Calculated + question bank |
| Chemistry | Science | Calculated + question bank |