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 7 of 14
- A. 4000
- B. 2160
- C. 4320
- D. 5300
Explanation: The 7 players can throw in 7! = 5040 sequences. If the youngest is last, the other 6 can be arranged in 6!
Correct answer: 4320- A. 4800
- B. 5760
- C. 2880
- D. 15000
Explanation: Treat the 5 boys as one block, giving 4 objects to arrange: the boys' block and 3 girls. These objects can be arranged in 4!
Correct answer: 2880- A. 8000
- B. 8010
- C. 8020
- D. 8040
Explanation: Rewrite the products as 2003 × 2004 minus 2001 × 2002. Using n(n + 1), the difference is (2003^2 + 2003) - (2001^2 + 2001) = (2003^2 -…
Correct answer: 8010- A. 1600
- B. 900
- C. 3600
- D. 2500Islamic Studies Quiz
Explanation: The least common multiple of 10, 12, 15 and 18 is 180 = 2² x 3² x 5. To make this a square, the factor 5 must also occur twice, so the…
Correct answer: 900- A. 143
- B. 169
- C. 260
- D. 221
Explanation: Each remainder is one less than its divisor, so the number plus 1 must be divisible by 6, 8 and 12.
Correct answer: 143- A. 5073
- B. 5016
- C. 5054
- D. 5035
Explanation: The remainders are one less than the divisors, so n + 5 must be divisible by 6, 7, 8, 9 and 10.
Correct answer: 5035- A. 210
- B. 119
- C. 126
- D. 154
Explanation: Again, every remainder is one less than its divisor, so n + 1 is divisible by 2, 3, 4, 5 and 6.
Correct answer: 119- A. 7203
- B. 2403
- C. 3603
- D. 4803
Explanation: The heap leaves remainder 3 for division by 16, 20, 25 and 45, so n - 3 must be a multiple of their least common multiple, 3600.
Correct answer: 7203- A. 9654
- B. 9666
- C. 9664
- D. 9864
Explanation: Every stated remainder is 6 less than its divisor, so n + 6 must be divisible by 10, 15, 21 and 28.
Correct answer: 9654- A. 420
- B. 515
- C. 435
- D. 518
Explanation: The conditions can be written as n + 10 divisible by 35, 25 and 15, because the remainders are 10 less than their divisors.
Correct answer: 515- A. 78
- B. 68
- C. 58
- D. None
Explanation: The value 68 gives 68 ÷ 8 a remainder of 4, 68 ÷ 12 a remainder of 8, 68 ÷ 18 a remainder of 14, and 68 ÷ 24 a remainder of 20.
Correct answer: 68- A. 1 min
- B. 2 min
- C. 3 min
- D. None
Explanation: After t minutes, the wheels make 15t, 20t and 48t revolutions. They are all back at the original position when these three quantities are…
Correct answer: 1 min- A. 9985
- B. 9960
- C. 9957
- D. 9975
Explanation: The least common multiple of 3, 4 and 5 is 60, so the required number must be a multiple of 60.
Correct answer: 9960- A. 344
- B. 355
- C. 366
- D. 377
Explanation: The least common multiple of 6, 9, 15, 20 and 24 is 360, so the number increased by 5 must be 360. Therefore, the number is 360 - 5 = 355.
Correct answer: 355- A. 245
- B. 125
- C. 485
- D. 845
Explanation: Since 5 plants remain for rows of 6, 8, 10 and 12, the number minus 5 must be a multiple of LCM(6, 8, 10, 12) = 120.
Correct answer: 845- A. 18, 20, 22
- B. 20, 22, 24
- C. 22, 24, 26
- D. 24, 26, 28
Explanation: The sum for 20, 22, and 24 is 20² + 22² + 24² = 400 + 484 + 576 = 1460.
Correct answer: 20, 22, 24- A. Al-Khwarizmi
- B. Aristotle
- C. Herodotus
- D. Isaac Newton
Explanation: Isaac Newton is commonly called one of the fathers of calculus because he developed differential and integral methods independently of…
Correct answer: Isaac Newton- A. Part
- B. Trap
- C. Cart
- D. Dart
- E. Mart
Explanation: Part, cart, dart and mart all end with the letters "art." Trap ends with "rap," so it does not follow the common letter pattern.
Correct answer: Trap- A. Tiruvanantapuram
- B. Hyderabad
- C. Calicut
- D. Bangalore
- E. Bhubaneswar
Explanation: Tiruvanantapuram, Hyderabad, Bangalore and Bhubaneswar are state capitals of India.
Correct answer: Calicut- A. CAT
- B. DOG
- C. TIGER
- D. ELEPHANT
- E. LION
Explanation: Cat, dog, tiger and lion are carnivorous mammals, while an elephant is a herbivorous mammal.
Correct answer: ELEPHANT