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 6 of 14
- A. 120
- B. 720
- C. 4320
- D. 2160
Explanation: Treat the three vowels O, I and A as one block, giving 5 objects to arrange, which can be done in 5! ways.
Correct answer: 720- A. 40
- B. 400
- C. 5040
- D. 2520
Explanation: LOGARITHMS contains 10 distinct letters, and four positions can be filled without repetition in 10 x 9 x 8 x 7 = 5040 ways.
Correct answer: 5040- A. 63
- B. 90
- C. 126
- D. 45
Explanation: Choose 5 of the 7 men in 7C5 = 21 ways and 2 of the 3 women in 3C2 = 3 ways.
Correct answer: 63- A. 9
- B. 12
- C. 14
- D. 18
Explanation: There are 4! = 24 total arrangements. If A and B are together, treat them as one block, giving 3! x 2!
Correct answer: 12- A. One
- B. Zero
- C. Three
- D. Cannot be determined
Explanation: Picking one host from 12 people each month does not guarantee a fixed number of selections for any particular member, because the lots are…
Correct answer: Cannot be determined- A. 11
- B. 30
- C. 14
- D. 20
Explanation: Without the restriction, choose 1 male from 5 and 1 female from 3, giving 5 x 3 = 15 committees.
Correct answer: 14- A. 4
- B. 12
- C. 18
- D. None of these
Explanation: The principal must be chosen from the 2 eligible candidates, giving 2 choices.
Correct answer: None of these- A. 5
- B. 6
- C. 7
- D. 18
Explanation: There are 5C2 = 10 unrestricted pairs of subjects. The three invalid pairs are Mathematics 2 with commerce, economics or statistics…
Correct answer: 7- A. 36
- B. 81
- C. 91
- D. 116
Explanation: There are 6 x 6 x 6 = 216 outcomes for three dice. Outcomes with no 2 have 5 choices for each die, giving 5 x 5 x 5 = 125, so outcomes…
Correct answer: 91- A. 19
- B. 120
- C. 624
- D. 1024
Explanation: Each of the 4 questions has 5 choices, so there are 5 x 5 x 5 x 5 = 625 answer patterns.
Correct answer: 624- A. 120
- B. 240
- C. 360
- D. 480
Explanation: The six players can be arranged in 6! = 720 ways. Arrangements with Asim and Raheem together treat them as one block, giving 5! x 2!
Correct answer: 480- A. 5
- B. 6
- C. 7
- D. 8
Explanation: There are 5C3 = 10 groups of 3 boys. Groups containing both C and D are formed by choosing the third boy from A, B or E, so there are 3…
Correct answer: 7- A. 20
- B. 40
- C. 512
- D. 1024
Explanation: Each of the 10 questions has 2 possible answers, true or false, so the multiplication principle gives 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x…
Correct answer: 1024- A. 29
- B. 32
- C. 55
- D. 30
Explanation: Lines joining one point from each parallel line give 6 x 5 = 30 lines. The two original parallel lines add 2 more, so the total is 30 + 2…
Correct answer: 32- A. ²²C₁₀
- B. ²²C₁₀ + 1
- C. ²²C₉ + ¹⁰C₁
- D. ²²C₁₀ - 1Quiz Mode Feature
Explanation: There are 22 people altogether, so selecting any 10 gives ²²C₁₀ groups.
Correct answer: ²²C₁₀ - 1Quiz Mode Feature- A. ¹²C₅ * 10
- B. ¹²C₇ * 10
- C. ¹²C₇ * ¹⁰C₅
- D. 12 * ¹⁰C₅
Explanation: The 5 seniors can be selected in ¹²C₅ ways, and independently the 5 juniors can be selected in ¹⁰C₅ ways.
Correct answer: ¹²C₇ * ¹⁰C₅- A. 300
- B. 450
- C. 600
- D. 750
Explanation: Choose the required people independently: ⁴C₃ = 4 ways for men, ⁶C₂ = 15 ways for women, and ⁵C₃ = 10 ways for children.
Correct answer: 600- A. 300
- B. 600
- C. 750
- D. 900
Explanation: The selections are ⁴C₂ = 6 ways for men, ⁶C₃ = 20 ways for women, and ⁵C₁ = 5 ways for the child.
Correct answer: 600- A. 720
- B. 1440
- C. 1860
- D. 2160
Explanation: MATERIAL has 4 vowels, A, E, I, A, which must form one block, along with the 4 consonants. These 5 objects can be arranged in 5!
Correct answer: 1440- A. 20
- B. 54
- C. 42
- D. 60
Explanation: The two specified ladies are already included, so 3 more members must be chosen from the remaining 1 lady and 5 gentlemen, giving 6 people…
Correct answer: 20