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MHT CET Algebra Questions
Practise algebra (mathematics) for the Maharashtra Common Entrance Test: 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: 5x + y = 63 and x + 5y = 51
Show answer & explanation
Answer: B — x = 11, y = 8
Elimination/substitution gives x = 11, y = 8. Check: 5(11) + 1(8) = 63 ✓ and 1(11) + 5(8) = 51 ✓.
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Q2.Solve: x² + 6x − 27 = 0
Show answer & explanation
Answer: C — -9, 3
Find two roots with sum -6 and product -27: 3 and -9. So x² + 6x − 27 = (x − 3)(x + 9) = 0.
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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.Solve: 2x + 3y = 12 and 5x + 3y = 39
Show answer & explanation
Answer: D — x = 9, y = -2
Elimination/substitution gives x = 9, y = -2. Check: 2(9) + 3(-2) = 12 ✓ and 5(9) + 3(-2) = 39 ✓.
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Q5.Solve: x² − 12x + 27 = 0
Show answer & explanation
Answer: D — 3, 9
Find two roots with sum 12 and product 27: 3 and 9. So x² − 12x + 27 = (x − 3)(x − 9) = 0.
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Q6.Solve: 5x + 3y = 48 and 4x + 4y = 48
Show answer & explanation
Answer: A — x = 6, y = 6
Elimination/substitution gives x = 6, y = 6. Check: 5(6) + 3(6) = 48 ✓ and 4(6) + 4(6) = 48 ✓.
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Q7.Find the sum of the first 10 terms of the AP 5, 7, 9, …
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Answer: A — 140
Sₙ = n/2 × [2a + (n − 1)d] = 10/2 × [10 + 18] = 140.
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Q8.Find log₅ 3,125.
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Answer: C — 5
log_5(3125) asks “5 to what power gives 3125?” → 5^5 = 3125, so the answer is 5.
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Q9.Find the sum of the first 20 terms of the AP 14, 20, 26, …
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Answer: D — 1420
Sₙ = n/2 × [2a + (n − 1)d] = 20/2 × [28 + 114] = 1,420.
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Q10.Solve: 3x + y = 24 and 5x + 3y = 48
Show answer & explanation
Answer: D — x = 6, y = 6
Elimination/substitution gives x = 6, y = 6. Check: 3(6) + 1(6) = 24 ✓ and 5(6) + 3(6) = 48 ✓.
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 MHT CET
Maharashtra Common Entrance Test — conducted by State Common Entrance Test Cell, Maharashtra. State entrance for engineering, pharmacy and agriculture courses in Maharashtra.
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.
MHT CET 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 |
| Chemistry | Science | Calculated + question bank |
| Biology | Science | Question bank |