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 12 of 14
- A. 18
- B. 20
- C. 21
- D. 19
Explanation: In the expansion of (a + b)^n, the number of terms is n+1.This is because the index r in the general term (n choose r) a^(n-r) b^r ranges…
Correct answer: 21- A. n
- B. n/2
- C. n - 1
- D. n + 1
Explanation: In the expansion of (a + b)^n, the number of terms is n + 1.This is because the index r in the general term (n choose r) a^(n-r) b^r…
Correct answer: n + 1- A. odd
- B. even
- C. prime
- D. none of these
Explanation: The middle term in the expansion of (a + b)^n, where n is an even number, is an even term.The general term in the expansion is given by:(n…
Correct answer: even- A. |x| < 1/4
- B. |x| > 1/4
- C. -1 ≤ x < 1
- D. |x| ≤ -1
Explanation: The binomial expansion (1 - 4x)^2 is valid when the absolute value of the ratio of the second term to the first term is less than 1.In…
Correct answer: |x| < 1/4- A. n ≥ 3
- B. n ≥ 1
- C. n ≥ 2
- D. n ≥ -1
Explanation: To determine the range of values for n where n^2 > n + 3 is true, we need to solve the inequality:n^2 > n + 3Rearranging the inequality…
Correct answer: n ≥ 3- A. 1
- B. 0
- C. 2n
- D. n
Explanation: The general term in the binomial expansion (a + b)^n is given by:(n choose r) a^(n-r) b^rThe sum of the exponents of a and b in each term…
Correct answer: n- A. |x| < 0
- B. |x| < 1/2
- C. |x| < 2
- D. |x| < 1
Explanation: The binomial expansion (1-2x)^-2 is valid when the absolute value of the ratio of the second term to the first term is less than 1.In this…
Correct answer: |x| < 1/2- A. First
- B. Second
- C. Middle
- D. Last
Explanation: The expansion of (x + 2)^8 can be written as:(x + 2)^8 = x^8 + 8x^7(2) + 28x^6(2)^2 + 56x^5(2)^3 + 70x^4(2)^4 + 56x^3(2)^5 + 28x^2(2)^6 +…
Correct answer: Last- A. (n+1)/2
- B. (n+3)/2
- C. (n-1)/2
- D. (n+1)/2 and (n+3)/2
Explanation: When n is an odd number, the expansion of (a + x)^n has two middle terms.The general term in the expansion of (a + x)^n is given by:(n…
Correct answer: (n+1)/2 and (n+3)/2- A. x ≤ 1
- B. -1 ≤ x < 1
- C. x > 1
- D. x =1
Explanation: The binomial series (1+x)^n is defined and convergent when the value of x lies between -1 and 1, i.e., -1 ≤ x < 1.When x is greater than…
Correct answer: -1 ≤ x < 1- A. 23
- B. 64
- C. 128
- D. 256
Explanation: Correct answer is"c. 128"To find the sum of the coefficients of the odd powers of \( x \) in the expansion of \( (1 + x)^n \), where \( n…
Correct answer: 128- A. 30
- B. 31
- C. 32
- D. None of these
Explanation: The correct answer is c) 32.The expansion of (x + y)^5 can be written as:(x + y)^5 = x^5 + 5x^4y + 10x^3y^2 + 10x^2y^3 + 5xy^4 + y^5The…
Correct answer: 32- A. 494
- B. 495
- C. 496
- D. 497
Explanation: The correct answer is b) 495.The general term of the binomial expansion of (a + x)^r is given as:Tr+1 = (r!(a)^(r-r)(x)^rThe given…
Correct answer: 495- A. 540x^3
- B. -22680x^3
- C. 1040x^4
- D. None of these
Explanation: The correct answer is b) -22680x^3.The expansion of (3 - 2x)^7 can be written as:(3 - 2x)^7 = 3^7 - 7(3)^6(-2x) + 21(3)^5(-2x)^2 -…
Correct answer: -22680x^3- A. 2^n
- B. n^
- C. n + 1
- D. n - 1
Explanation: Solution:The correct answer is c) n + 1.The expansion of (1 + x)^n can be written as:(1 + x)^n = 1 + nx + n(n-1)x^2/2! + n(n-1)(n-2)x^3/3!
Correct answer: n + 1- A. 60
- B. 10
- C. 6/4
- D. 2
Explanation: The general term of a Binomial expansion of (a + x)^r is given as:Tr+1 = (r!)(a)^(r-r)(x)^rFor the given expression (2 - x)^6, the general…
Correct answer: 60- A. No such term
- B. Middle Term
- C. Last Term
- D. None of these
Explanation: The correct answer is a) No such term.The expansion of (x^2 - 1/2x)^7 can be written as:(x^2 - 1/2x)^7 = x^14 - 7x^12(1/2x) +…
Correct answer: No such term- A. Optimal solution
- B. Feasible solution
- C. Linear solution
- D. Quintic solution
Explanation: The correct option is a) Optimal solution.The optimal solution is the feasible solution that maximizes or minimizes the objective…
Correct answer: Optimal solution- A. True
- B. False
- C. none of these
- D. both
Explanation: The correct answer is a) True.The feasible region for a system of inequalities in two variables (x and y) is the set of all points (x, y)…
Correct answer: True- A. x ≤ 4
- B. -4 ≤ x ≤ -1
- C. 1 ≤ x ≤ 4
- D. x ≥ 4
Explanation: The correct answer is c) 1 ≤ x ≤ 4.To find the solution set, we need to solve the inequality |3 - 2x| ≤ 5.Solving the inequality:|3 - 2x|…
Correct answer: 1 ≤ x ≤ 4