Free Algebra MCQs with Answers
269 Algebra MCQs from Mathematics, each with the correct answer and a written explanation of why it is correct. Free and unlimited, with no account needed.
Algebra represents unknown quantities with symbols and uses equations, identities, patterns, and formulas to solve problems. The chapter includes linear and quadratic equations, sequences and series, and the distinction between solving an equation and finding a general rule for a sequence or sum.
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269 questions · page 1 of 14
- A. 3
- B. 5
- C. 7
- D. 9
Explanation: Subtract 7 from both sides: 3x = 15. Divide both sides by 3: x = 5. Substituting back gives 3(5) + 7 = 22, confirming the answer.
Correct answer: 5- A. 5
- B. 6
- C. 7
- D. 12
Explanation: Let the smaller number be x, so the larger number is x + 5. Their sum gives x + (x + 5) = 19, so 2x = 14 and x = 7.
Correct answer: 7- A. 12,16
- B. 18,10
- C. 15,13
- D. 14,12
Explanation: Let the larger number be x and the smaller be y. From x + y = 28 and x - y = 4, adding the equations gives 2x = 32, so x = 16 and y = 12.
Correct answer: 12,16- A. 0
- B. -2
- C. 2
- D. 1
Explanation: Division and multiplication are done before addition and subtraction, from left to right: 2 + 2 ÷ 2 × 2 - 2 = 2 + 1 × 2 - 2 = 2.
Correct answer: 2- A. a = b
- B. a ≠ b
- C. Cannot be evaluated
- D. None
Explanation: The statements a > b and b > a cannot both be true for ordinary real numbers, because greater-than is asymmetric.
Correct answer: Cannot be evaluated- A. Rs. 2800
- B. Rs. 2100
- C. Rs. 4200
- D. Rs. 8400
Explanation: Let one mixer cost m rupees and one TV cost t rupees. From 2m + t = Rs. 7,000 and m + 2t = Rs. 9,800, subtraction gives t - m = Rs.
Correct answer: Rs. 4200- A. 2
- B. 3
- C. 1/2
- D. 14
Explanation: From 17xy + 7 = 19xy, subtract 17xy to get 7 = 2xy, so xy = 7/2. Therefore, 4xy = 4 × 7/2 = 14.
Correct answer: 14- A. 19
- B. 20
- C. 21
- D. 22Pakistan Studies Quiz
Explanation: Let Khadija's current age be x years. After one year her age is x + 1 years, and ten years ago it was x − 10 years, so x + 1 = 2(x − 10)…
Correct answer: 21- A. 26
- B. 35
- C. 53
- D. Cannot be determined
Explanation: Let the original two-digit number be 10a + b. Interchanging the digits changes it by 9(b - a), so 9(b - a) = 18 and b - a = 2; together…
Correct answer: 35- A. 18
- B. 24
- C. 42
- D. 81
Explanation: The digit product 8 allows the two-digit arrangements 24 and 42. Testing the reversal condition, 24 + 18 = 42, so 24 is the required…
Correct answer: 24- A. 14
- B. 20
- C. 26
- D. 28
Explanation: Let the number be n. The statement means that multiplying it by 15 gives a result 196 greater than the number, so 15n = n + 196; hence 14n…
Correct answer: 14- A. 104
- B. 114
- C. 315
- D. 325
Explanation: Let the numbers be x and y. From x + y = 25 and x - y = 13, adding the equations gives 2x = 38, so x = 19 and y = 6; their product is 19 x…
Correct answer: 114- A. 9
- B. 12
- C. 15
- D. 18
Explanation: Let the larger and smaller numbers be x and y. Adding x + y = 33 and x - y = 15 gives 2x = 48, so x = 24; therefore y = 33 - 24 = 9.
Correct answer: 9- A. 10 Rs,
- B. 15 Rs,
- C. 20 Rs.
- D. 25 Rs.
Explanation: Let the daily earnings be A, B and C rupees. Subtracting A + C = Rs.94 from A + B + C = Rs.150 gives B = Rs.56; then B + C = Rs.76 gives C…
Correct answer: 20 Rs.- A. 432
- B. 288
- C. 144
- D. 72
- E. None of these
Explanation: Let n be the number of each type of coin. The total value is n x Rs.5 + n x Rs.2 + n x Rs.1 = 8n rupees, so 8n rupees = Rs.1,152 and n =…
Correct answer: 144- A. 4
- B. 5
- C. 6
- D. 8
- E. None of these
Explanation: Let Arslan have A marbles and Bilal have B marbles. If Bilal gives x marbles, A + x = B - x, so B - A = 2x; if Arslan gives 2x marbles, B…
Correct answer: 5- A. Rs.25
- B. Rs.22.50
- C. Rs.20
- D. Rs.17.50
- E. None of these
Explanation: The known cost is 16 x Rs.6 + 5 x Rs.45 + 7 x Rs.70 = Rs.811. The six ice-cream cups therefore cost Rs.961 - Rs.811 = Rs.150, so each…
Correct answer: Rs.25- A. 30
- B. 46
- C. 40
- D. 44
- E. None of these
Explanation: Let rabbits be r and peacocks be p, both counts of animals. From r + p = 60 and 4r + 2p = 192, doubling the first equation gives 2r + 2p =…
Correct answer: None of these- A. 600
- B. 620
- C. 500
- D. 520
- E. None of these
Explanation: If there are n children, the total supply is 2n bananas. After 360 children are absent, each of the n - 360 children receives 4 bananas…
Correct answer: None of these- A. 30 years
- B. 40 years
- C. 32 years
- D. 48 years
- E. None of these
Explanation: Let present ages be Z years and S years. The two conditions are Z - 8 = 4(S - 8)/3 and Z + 8 = 6(S + 8)/5; solving them gives S = 32 years…
Correct answer: 40 yearsAlgebra MCQs: common questions
Are these Algebra MCQs free?
Yes. All Algebra MCQs from Mathematics are free on TestUstad, with unlimited attempts and no account needed. Nothing on this page is a sample or a trial.
How many Algebra MCQs are on this page?
There are 269 Algebra MCQs in the Mathematics bank, shown 20 to a page with the correct answer and an explanation on each.
Does every Algebra MCQ have an explanation?
Yes. Each Algebra question shows the correct option and a written explanation of why it is correct, so a wrong answer teaches you something rather than just being marked wrong.
Can I take a timed Algebra test?
Yes. The practice button on this page starts a free Algebra test drawn from the Mathematics bank. It marks each answer instantly, gives you a score at the end, and can be retaken as many times as you like.