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NIMCET Algebra Questions
Practise algebra (mathematics) for the NIT MCA 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.Find log₃ 9.
Show answer & explanation
Answer: C — 2
log_3(9) asks “3 to what power gives 9?” → 3^2 = 9, so the answer is 2.
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Q2.Solve: 5x + y = -19 and x + y = 1
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Answer: D — x = -5, y = 6
Elimination/substitution gives x = -5, y = 6. Check: 5(-5) + 1(6) = -19 ✓ and 1(-5) + 1(6) = 1 ✓.
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Q3.Solve: x² − 36 = 0
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Answer: C — -6, 6
Find two roots with sum 0 and product -36: 6 and -6. So x² − 36 = (x − 6)(x + 6) = 0.
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Q4.Find log₂ 16.
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Answer: C — 4
log_2(16) asks “2 to what power gives 16?” → 2^4 = 16, so the answer is 4.
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Q5.Solve: 4x + 3y = 77 and 2x + y = 33
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Answer: B — x = 11, y = 11
Elimination/substitution gives x = 11, y = 11. Check: 4(11) + 3(11) = 77 ✓ and 2(11) + 1(11) = 33 ✓.
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Q6.Solve: 4x + 2y = 2 and 4x + 3y = -3
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Answer: C — x = 3, y = -5
Elimination/substitution gives x = 3, y = -5. Check: 4(3) + 2(-5) = 2 ✓ and 4(3) + 3(-5) = -3 ✓.
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Q7.Solve: 2x + 2y = 14 and 5x + 4y = 31
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Answer: A — x = 3, y = 4
Elimination/substitution gives x = 3, y = 4. Check: 2(3) + 2(4) = 14 ✓ and 5(3) + 4(4) = 31 ✓.
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Q8.Solve: x² − 4x + 3 = 0
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Answer: D — 1, 3
Find two roots with sum 4 and product 3: 1 and 3. So x² − 4x + 3 = (x − 1)(x − 3) = 0.
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Q9.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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Q10.Find log 100,000 (base 10).
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Answer: B — 5
log_10(100000) asks “10 to what power gives 100000?” → 10^5 = 100000, so the answer is 5.
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 NIMCET
NIT MCA Common Entrance Test — conducted by National Institutes of Technology (organising NIT rotates). Admission to MCA programmes at participating NITs; mathematics carries the most weight.
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.
NIMCET practice topics
| Topic | Section | Question source |
|---|---|---|
| Algebra | Mathematics | Calculated (new numbers every set) |
| Probability & Combinatorics | Mathematics | Calculated (new numbers every set) |
| Logical Reasoning | Reasoning | Calculated (new numbers every set) |
| Computer Awareness | Computer knowledge | Question bank |
| English Grammar | English | Question bank |