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.
Last updated
269 questions · page 4 of 14
- A. If a < b
- B. If a ≤ b
- C. If the relationship between a and b cannot be established
- D. If a ≥ b
Explanation: a² - 9a + 20 = (a - 4)(a - 5), so a = 4 or 5. For b, 2b² - 5b - 12 = (2b + 3)(b - 4), so b = -3/2 or 4; hence every possible a is greater…
Correct answer: If a ≥ b- A. if a < b
- B. if a ≤ b
- C. if the relationship between a and b cannot be established.
- D. if a > b
Explanation: a² - 7a + 12 = (a - 3)(a - 4), so a = 3 or 4. b² - 3b + 2 = (b - 1)(b - 2), so b = 1 or 2; therefore every possible a-value is greater…
Correct answer: if a > b- A. 10
- B. 8
- C. 15
- D. 7.50
Explanation: Let the price of one notebook be p rupees, so the number bought is 300/p.
Correct answer: 10- A. 3x2 + 5x - 2 = 0
- B. 3x2 + 5x + 2 = 0
- C. 3x2 - 5x + 2 = 0
- D. 3x2 - 5x - 2 = 0
Explanation: If r is a root of 2r² + 5r + 3 = 0 and z = 1/r, substitute r = 1/z: 2/z² + 5/z + 3 = 0.
Correct answer: 3x2 + 5x + 2 = 065. Find the value of a/b + b/a, if a and b are the roots of the quadratic equation x2 + 8x + 4 = 0?
- A. 15
- B. 14
- C. 24
- D. 26
Explanation: For x² + 8x + 4 = 0, Vieta's relations give a + b = -8 and ab = 4. Therefore a/b + b/a = (a² + b²)/ab = ((a + b)² - 2ab)/ab = (64 - 8)/4 =…
Correct answer: 14- A. -21
- B. 1
- C. 61
- D. 21
Explanation: For x² - 9x + 20 = 0, the sum of roots is a + b = 9 and their product is ab = 20.
Correct answer: 61- A. 29
- B. 27
- C. 28
- D. 7
Explanation: Let the two roots be t and 3t. Their sum is t + 3t = 12, so 4t = 12 and t = 3; the roots are therefore 3 and 9, whose product is a = 3 x 9…
Correct answer: 27- A. 9, 10
- B. 10, 11
- C. 11, 12
- D. 12, 13
Explanation: Let the consecutive positive integers be n and n + 1. Their square sum exceeds their product by n² + (n + 1)² - n(n + 1) = n² + n + 1 =…
Correct answer: 9, 1069. If the roots of the equation 2x2 - 5x + b = 0 are in the ratio of 2:3, then find the value of b?
- A. 3
- B. 4
- C. 5
- D. 6Enrolling In Online Certification Courses
Explanation: If the roots are 2k and 3k, their sum is 5k = 5/2 because the sum of roots is 5/2, so k = 1/2.
Correct answer: 3- A. 10, 3
- B. -10, 3
- C. -20, 3
- D. -10, -3
Explanation: For a quadratic x² + 20x + 3 = 0, the sum of roots is -20 and the product of roots is 3, using the relations -coefficient of x and…
Correct answer: -20, 3- A. x2 + 13x - 140 = 0
- B. x2 - 13x + 140 = 0
- C. x2 - 13x - 140 = 0
- D. x2 + 13x + 140 = 0
Explanation: A monic quadratic with roots 20 and -7 is (x - 20)(x + 7) = 0. Expanding gives x² - 13x - 140 = 0, since the sum of roots is 13 and the…
Correct answer: x2 - 13x - 140 = 0- A. rational and unequal
- B. complex
- C. real and equal
- D. irrational and unequal
Explanation: The discriminant of 3x² - 12x + 10 = 0 is D = (-12)² - 4 x 3 x 10 = 144 - 120 = 24.
Correct answer: irrational and unequal- A. 3, -3/2
- B. 3/2, -3
- C. -3/2, -3
- D. 3/2, 3
Explanation: For 2x^2 + 3x - 9 = 0, factorisation gives (2x - 3)(x + 3) = 0. Hence x = 3/2 or x = -3.
Correct answer: 3/2, -3- A. -5, 3
- B. 3, 5
- C. -3, 5
- D. -3, -5
Explanation: The equation x^2 + 2x - 15 = 0 factors as (x + 5)(x - 3) = 0. Therefore the roots are x = -5 and x = 3.
Correct answer: -5, 3- A. 5/36
- B. 4/36
- C. 1/12
- D. 1/2
Explanation: Two dice have 36 equally likely outcomes, and a sum of 8 occurs in five ways: (2,6), (3,5), (4,4), (5,3) and (6,2).
Correct answer: 5/36- A. 22
- B. 32
- C. 11
- D. 19
Explanation: The terms follow an alternating pattern: 4 + 4 = 8, 8 + 1 = 9, 9 + 4 = 13, 13 + 1 = 14, and 14 + 4 = 18.
Correct answer: 19- A. 4970
- B. 4950
- C. 4900
- D. 4980
Explanation: The first 70 even numbers are 2, 4, ..., 140, which can be written as 2(1 + 2 + ... + 70). Since 1 + 2 + ...
Correct answer: 4970- A. 4900
- B. 4970
- C. 4960
- D. None of these
Explanation: The sum of the first n odd numbers is n² because the terms form 1 + 3 + 5 + ... + (2n - 1). For n = 70, the sum is 70² = 4,900.
Correct answer: 4900- A. 36
- B. 40
- C. 46
- D. 52
Explanation: The successive differences are 5, 7, 9 and 11, increasing by 2 each time. The next difference is therefore 13, giving 33 + 13 = 46.
Correct answer: 46- A. 6
- B. 9
- C. 15
- D. 18
Explanation: With three distinct flags, single-flag codes give 3 arrangements, two-flag codes give 3P2 = 3 x 2 = 6 arrangements, and three-flag codes…
Correct answer: 15