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 5 of 14
- A. 6
- B. 24
- C. 96
- D. 720
Explanation: The terms follow factorials: 1, 1, 2, 6, 24, 120, 720, so the sixth term should be 5! = 120, not 96.
Correct answer: 96- A. Asteroid
- B. Star
- C. Planet
- D. Comet
- E. Rocket
Explanation: Asteroids, stars, planets and comets are naturally occurring astronomical objects, whereas a rocket is a human-made vehicle.
Correct answer: Rocket- A. 9, 11, 13
- B. 11, 13, 15
- C. 13, 15, 17
- D. 7, 9, 11
- E. None of these
Explanation: Let the three consecutive odd integers be x, x + 2 and x + 4. Their condition gives (x + 2) + (x + 4) = x + 13, so x = 7 and the integers…
Correct answer: 7, 9, 11- A. 74
- B. 76
- C. 70
- D. 68
- E. None of these
Explanation: Let the smallest consecutive even number be x; the four numbers are x, x + 2, x + 4 and x + 6.
Correct answer: 70- A. 248
- B. 240
- C. 228
- D. 236
- E. None of these
Explanation: Let the least number in the five consecutive even numbers be x. Then 5x + 20 = 440, so x = 84; the second least number of the different…
Correct answer: 240- A. 8
- B. 12
- C. 6
- D. 14
- E. None of these
Explanation: Write the six consecutive even numbers as x, x + 2, x + 4, x + 6, x + 8 and x + 10.
Correct answer: 12- A. 63
- B. 511
- C. 1023
- D. 15
Explanation: Each of the five problems has four possibilities: not attempted or one of three internal choices.
Correct answer: 1023- A. 25
- B. 13
- C. 40
- D. 30
Explanation: TRIANGLE has 5 consonants, T, R, N, G and L, and 3 vowels, I, A and E. The number of selections is 5C3 x 3C2 = 10 x 3 = 30 ways.
Correct answer: 30- A. ⁹C₂
- B. ³C₂
- C. ¹⁶C₂
- D. ¹²C₂
Explanation: There are 9 + 3 + 4 = 16 balls in total, and drawing two balls without regard to order gives 16C2 = (16 x 15)/2 = 120 ways.
Correct answer: ¹⁶C₂- A. 60
- B. 360
- C. 120
- D. 240
Explanation: Only 2 is even, so the units place is fixed as 2. The remaining three places can be filled from the other 5 digits in 5 x 4 x 3 = 60 ways.
Correct answer: 60- A. 360
- B. 60
- C. 300
- D. 180
Explanation: There are 6 distinct digits and repetition is not allowed, so the four places can be filled in 6 x 5 x 4 x 3 = 360 ways.
Correct answer: 360- A. 216
- B. 243
- C. 215
- D. 729Downloading Interactive Party Trivia Games
Explanation: Each of the three rings has 6 choices, so the lock has 6 x 6 x 6 = 216 total combinations.
Correct answer: 215- A. 165
- B. 185
- C. 205
- D. 225
Explanation: There are 5 + 6 = 11 committee members, and selecting 8 without regard to order gives 11C8 = 11C3 = (11 x 10 x 9)/(3 x 2 x 1) = 165 ways.
Correct answer: 165- A. 150
- B. 200
- C. 250
- D. 300
Explanation: Choose 2 men from 5 and 3 women from 6: 5C2 x 6C3 = 10 x 20 = 200 ways.
Correct answer: 200- A. 9!/(2!)2 3!
- B. 9!/(2!)3 3!
- C. 9!/(2!)2 (3!)2
- D. 5!/(2!)2 3!
Explanation: MESMERISE has 9 letters, with E repeated 3 times, M repeated 2 times and S repeated 2 times.
Correct answer: 9!/(2!)2 3!- A. 720
- B. 144
- C. 120
- D. 36
Explanation: MEADOWS has 3 vowels, E, A and O, and 4 consonants. Placing the vowels in the even positions 2, 4 and 6 gives 3!
Correct answer: 144- A. 3
- B. 6
- C. 24
- D. 120
Explanation: Fix N in the first position and A in the last position. The remaining letters O, K and I can be arranged in the three middle positions in…
Correct answer: 6- A. 8
- B. 8!
- C. 7!
- D. 7
Explanation: THURSDAY contains 8 distinct letters, so all of them can be arranged in 8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 ways.
Correct answer: 8!- A. 12
- B. 20
- C. 16
- D. 24
Explanation: TIME has 4 distinct letters, and forming a three-letter word without repetition gives 4P3 = 4 x 3 x 2 = 24 words.
Correct answer: 24- A. 870
- B. 435
- C. 30!
- D. 29! + 1Islamic Studies Quiz
Explanation: A handshake is determined by choosing 2 people from 30, so the count is 30 x 29 / 2 = 435; division by 2 avoids counting each pair twice.
Correct answer: 435