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KCET Algebra Questions
Practise algebra (mathematics) for the Karnataka 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: x² − 7x + 12 = 0
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Answer: A — 3, 4
Find two roots with sum 7 and product 12: 3 and 4. So x² − 7x + 12 = (x − 3)(x − 4) = 0.
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Q2.Solve: x² − 7x + 6 = 0
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Answer: B — 1, 6
Find two roots with sum 7 and product 6: 1 and 6. So x² − 7x + 6 = (x − 1)(x − 6) = 0.
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Q3.Solve: x² − 16 = 0
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Answer: A — -4, 4
Find two roots with sum 0 and product -16: 4 and -4. So x² − 16 = (x − 4)(x + 4) = 0.
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Q4.Find the sum of the first 13 terms of the AP 15, 23, 31, …
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Answer: D — 819
Sₙ = n/2 × [2a + (n − 1)d] = 13/2 × [30 + 96] = 819.
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Q5.Solve: x² + 4x − 5 = 0
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Answer: A — -5, 1
Find two roots with sum -4 and product -5: 1 and -5. So x² + 4x − 5 = (x − 1)(x + 5) = 0.
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Q6.Find log₅ 25.
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Answer: C — 2
log_5(25) asks “5 to what power gives 25?” → 5^2 = 25, so the answer is 2.
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Q7.Find log₂ 32.
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Answer: B — 5
log_2(32) asks “2 to what power gives 32?” → 2^5 = 32, so the answer is 5.
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Q8.Solve: x² − 1 = 0
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Answer: B — -1, 1
Find two roots with sum 0 and product -1: 1 and -1. So x² − 1 = (x − 1)(x + 1) = 0.
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Q9.Solve: x² − x − 42 = 0
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Answer: D — -6, 7
Find two roots with sum 1 and product -42: 7 and -6. So x² − x − 42 = (x − 7)(x + 6) = 0.
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Q10.Solve: 4x + y = 17 and 3x + 4y = 42
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Answer: D — x = 2, y = 9
Elimination/substitution gives x = 2, y = 9. Check: 4(2) + 1(9) = 17 ✓ and 3(2) + 4(9) = 42 ✓.
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 KCET
Karnataka Common Entrance Test — conducted by Karnataka Examinations Authority (KEA). State entrance for professional courses in Karnataka.
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.
KCET practice topics
| Topic | Section | Question source |
|---|---|---|
| Algebra | Mathematics | Calculated (new numbers every set) |
| Geometry & Mensuration | Mathematics | Calculated (new numbers every set) |
| Physics | Science | Calculated + question bank |
| Chemistry | Science | Calculated + question bank |
| Biology | Science | Question bank |