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JEE Main Algebra Questions
Practise algebra (mathematics) for the Joint Entrance Examination (Main): 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: x² − 15x + 54 = 0
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Answer: D — 6, 9
Find two roots with sum 15 and product 54: 9 and 6. So x² − 15x + 54 = (x − 9)(x − 6) = 0.
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Q2.Find log₃ 81.
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Answer: B — 4
log_3(81) asks “3 to what power gives 81?” → 3^4 = 81, so the answer is 4.
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Q3.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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Q4.Find the sum of the first 19 terms of the AP 9, 17, 25, …
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Answer: D — 1539
Sₙ = n/2 × [2a + (n − 1)d] = 19/2 × [18 + 144] = 1,539.
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Q5.Find log₅ 25.
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Answer: D — 2
log_5(25) asks “5 to what power gives 25?” → 5^2 = 25, so the answer is 2.
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Q6.Solve: x² − 3x − 18 = 0
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Answer: A — -3, 6
Find two roots with sum 3 and product -18: -3 and 6. So x² − 3x − 18 = (x + 3)(x − 6) = 0.
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Q7.Solve: x² − 7x + 12 = 0
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Answer: D — 3, 4
Find two roots with sum 7 and product 12: 4 and 3. So x² − 7x + 12 = (x − 4)(x − 3) = 0.
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Q8.Find the sum of the first 26 terms of the AP 15, 18, 21, …
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Answer: D — 1365
Sₙ = n/2 × [2a + (n − 1)d] = 26/2 × [30 + 75] = 1,365.
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Q9.Solve: 3x + y = 8 and 4x + y = 10
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Answer: A — x = 2, y = 2
Elimination/substitution gives x = 2, y = 2. Check: 3(2) + 1(2) = 8 ✓ and 4(2) + 1(2) = 10 ✓.
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Q10.Solve: x² + 12x + 32 = 0
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Answer: B — -8, -4
Find two roots with sum -12 and product 32: -4 and -8. So x² + 12x + 32 = (x + 4)(x + 8) = 0.
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 Main
Joint Entrance Examination (Main) — conducted by National Testing Agency (NTA). India’s national engineering entrance for NITs, IIITs and other institutes, and the qualifier for JEE Advanced.
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 Main practice topics
| Topic | Section | Question source |
|---|---|---|
| Algebra | Mathematics | Calculated (new numbers every set) |
| Geometry & Mensuration | Mathematics | Calculated (new numbers every set) |
| Probability & Combinatorics | Mathematics | Calculated (new numbers every set) |
| Physics | Science | Calculated + question bank |
| Chemistry | Science | Calculated + question bank |