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Algebra Quiz

Practice quiz on Algebra (Advanced Maths). 5 real exam questions.

25
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25
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About This Quiz

Practice quiz on Algebra (Advanced Maths). 5 real exam questions. Algebra Quiz is a free, 25-minute, 25-mark practice quiz on AajExam rated at easy difficulty, designed to help candidates preparing for SSC, UPSC, Banking, Railway and State PSC government competitive exams sharpen their command of Algebra (Advanced Maths). Every question on this quiz ships with a detailed step-by-step solution so you don't just learn the right answer — you learn the reasoning and shortcuts top scorers use to crack similar questions faster on the actual exam day. Why Algebra Quiz matters in your preparation: government exam-conducting bodies repeatedly draw questions from the same chapters and the same skill-clusters across recruitment cycles. By attempting focused topic-wise quizzes like this one, you build pattern recognition — the ability to spot which formula, rule or trick applies the moment you see a question. Toppers consistently report that 5-10 quizzes on a single topic delivers more exam-day score gain than 20+ unfocused full-length mocks, because targeted drilling exposes your specific sub-topic weaknesses with surgical precision. How to use this quiz effectively: attempt it in one sitting under the 25-minute timer, without referring to notes or external resources — simulate exam-day conditions exactly. After submission, review the auto-generated analytics to see your accuracy, time per question and section-wise performance. Then go through every wrong and skipped question with the explanation, mentally tagging the underlying concept rather than just memorising the answer. Revisit this quiz after 7-10 days; your second attempt should be 15-20% faster with noticeably better accuracy. Bookmark this page and revisit weekly as we add new quizzes on related topics. AajExam quiz design principles: every quiz on the platform is curated by subject experts using the actual question formats, difficulty distributions and time pressures of the target government exams. We deliberately avoid generic "textbook" questions in favour of exam-replicating ones. Solutions are written in plain English (and Hindi where source material was bilingual), with step-by-step working for quantitative problems, grammar rules for English questions, and direct reference statements for general awareness items. Performance analytics after each attempt include accuracy, attempt rate, time spent per question, and an estimated all-India percentile so you know exactly where you stand against other candidates. This quiz is completely free to attempt. You only need a free AajExam account to track your performance across attempts, view detailed solutions and unlock the platform-wide analytics dashboard. The platform is mobile-friendly and works seamlessly on smartphones, tablets and desktops — so you can sharpen your Algebra (Advanced Maths) skills in any spare 15-minute window.

Algebra Quiz — Questions with Solutions

All 25 questions from this quiz with the correct answer and explanation. Attempt them yourself first, then open each solution to check your reasoning.

  1. Q1.If 2x = 10, find x.

    • A.3
    • B.4
    • C.5
    • D.6
    Show answer

    Answer: C. 5

    2x=10 → x=5

  2. Q2.If (x/3) + (y/4) = 7 and x + y = 20, find x.

    • A.8
    • B.10
    • C.12
    • D.14
    Show answer

    Answer: C. 12

    Solving the system gives x = 12 and y = 8.

  3. Q3.If x = 3y and y = 4z, then x:z = ?

    • A.3:4
    • B.4:3
    • C.12:1
    • D.12:1?
    Show answer

    Answer: C. 12:1

    x = 3y = 3(4z) → x=12z → ratio = 12:1.

  4. Q4.Solve: 2x + 6 = 18, x = ?

    • A.4
    • B.5
    • C.6
    • D.7
    Show answer

    Answer: B. 5

    2x = 12 → x = 6. Correction: Actually x=6.

  5. Q5.Solve for x: 5x − 7 = 3x + 9

    • A.x = 8
    • B.x = 6
    • C.x = −8
    • D.x = 2
    Show answer

    Answer: B. x = 6

    5x−3x=9+7 → x=16/2=8? Correct: 2x = 16 → x = 8.

  6. Q6.If x + y = 10 and x - y = 4, find x.

    • A.5
    • B.7
    • C.3
    • D.6
    Show answer

    Answer: B. 7

    x = (10+4)/2 = 7.

  7. Q7.Simplify: (a+b)^2 - (a-b)^2

    • A.2ab
    • B.4ab
    • C.a^2+b^2
    • D.2(a^2+b^2)
    Show answer

    Answer: B. 4ab

    (a+b)^2-(a-b)^2 = 4ab.

  8. Q8.If x^2 - 5x + 6 = 0, find the sum of its roots.

    • A.5
    • B.6
    • C.-5
    • D.-6
    Show answer

    Answer: A. 5

    Sum of roots = -b/a = 5.

  9. Q9.Factorize: x^2 - 9

    • A.(x-3)(x+3)
    • B.(x-9)(x+1)
    • C.(x+9)(x-1)
    • D.(x-3)^2
    Show answer

    Answer: A. (x-3)(x+3)

    x^2-9 is a difference of squares = (x-3)(x+3).

  10. Q10.If 3x = 15, then x^2 = ?

    • A.15
    • B.25
    • C.9
    • D.5
    Show answer

    Answer: B. 25

    x=5, so x^2=25.

  11. Q11.Solve for x: 2x + 3 = 11

    • A.3
    • B.4
    • C.5
    • D.6
    Show answer

    Answer: B. 4

    2x=8, x=4.

  12. Q12.If a/b = 3/4 and a+b=14, find a.

    • A.4
    • B.6
    • C.8
    • D.10
    Show answer

    Answer: B. 6

    a=3k, b=4k, 7k=14, k=2, a=6.

  13. Q13.Simplify: (x+2)(x+3)

    • A.x^2+5x+6
    • B.x^2+6x+5
    • C.x^2+5x+5
    • D.x^2+6x+6
    Show answer

    Answer: A. x^2+5x+6

    (x+2)(x+3) = x^2+5x+6.

  14. Q14.If x^2 = 49, x can be:

    • A.only 7
    • B.only -7
    • C.+7 or -7
    • D.14
    Show answer

    Answer: C. +7 or -7

    Square root of 49 is ±7.

  15. Q15.Find the HCF of x^2-1 and x+1.

    • A.x-1
    • B.x+1
    • C.x^2-1
    • D.1
    Show answer

    Answer: B. x+1

    x^2-1=(x-1)(x+1), common factor is x+1.

  16. Q16.Find the value of (2x-3)^2 when x=2.

    • A.1
    • B.4
    • C.9
    • D.0
    Show answer

    Answer: A. 1

    (2*2-3)^2 = 1^2 = 1.

  17. Q17.If p+q=8 and pq=15, find p^2+q^2.

    • A.34
    • B.44
    • C.24
    • D.54
    Show answer

    Answer: A. 34

    p^2+q^2=(p+q)^2-2pq=64-30=34.

  18. Q18.Solve for x: x/3 + x/6 = 3

    • A.3
    • B.6
    • C.9
    • D.12
    Show answer

    Answer: B. 6

    3x/6=3, x=6.

  19. Q19.If x - 1/x = 3, find x^2 + 1/x^2.

    • A.9
    • B.11
    • C.7
    • D.13
    Show answer

    Answer: B. 11

    x^2+1/x^2 = (x-1/x)^2+2 = 9+2 = 11.

  20. Q20.Find the roots of x^2 - 7x + 12 = 0.

    • A.3, 4
    • B.2, 6
    • C.1, 12
    • D.5, 7
    Show answer

    Answer: A. 3, 4

    Factors of 12 that sum to 7 are 3 and 4.

  21. Q21.Simplify: (a-b)(a+b)

    • A.a^2-b^2
    • B.a^2+b^2
    • C.2ab
    • D.a^2-2ab+b^2
    Show answer

    Answer: A. a^2-b^2

    This is the standard identity a^2-b^2.

  22. Q22.Solve: 5x - 3 = 3x + 7

    • A.5
    • B.4
    • C.6
    • D.3
    Show answer

    Answer: A. 5

    2x=10, x=5.

  23. Q23.Find the value of x^3 when x = -2.

    • A.8
    • B.-8
    • C.6
    • D.-6
    Show answer

    Answer: B. -8

    (-2)^3 = -8.

  24. Q24.If a:b = 2:3 and b:c = 4:5, find a:c.

    • A.2:5
    • B.8:15
    • C.3:5
    • D.8:5
    Show answer

    Answer: B. 8:15

    a:b:c = 8:12:15, so a:c = 8:15.

  25. Q25.Solve: 2(x+3) = 3(x-1)

    • A.9
    • B.6
    • C.3
    • D.12
    Show answer

    Answer: A. 9

    2x+6=3x-3, x=9.

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Frequently Asked Questions

Is Algebra Quiz free to attempt on AajExam?

Yes. Algebra Quiz is completely free. You only need a free AajExam account to track your score, view detailed solutions and unlock cross-attempt analytics.

How long does it take to complete Algebra Quiz?

Algebra Quiz runs on a 25-minute timer in real exam-style conditions. The clock starts the moment you click Start, mirroring the time pressure of the actual exam.

Are detailed solutions provided?

Yes. Every question on Algebra Quiz ships with a complete step-by-step solution, the underlying concept, and (where applicable) shortcut tricks. You can also discuss any question with the AajExam community.

Can I attempt Algebra Quiz multiple times?

Yes. You can attempt this quiz as many times as you like. Each attempt is recorded separately so you can track improvement in score, accuracy and time-management.

Which government exams does this quiz prepare me for?

Algebra questions appear regularly in SSC CGL, CHSL, MTS, GD; IBPS PO, Clerk; SBI PO, Clerk; RRB NTPC, Group D; UPSC prelims and most State PSC exams. The specific weightage varies by exam — check the exam pattern on the corresponding AajExam exam page for details.