Q. If A = [[1, 0], [0, 1]] and B = [[2, 3], [4, 5]], what is AB?
A.
[2, 3], [4, 5]
B.
[1, 0], [0, 1]
C.
[0, 0], [0, 0]
D.
[6, 8], [12, 15]
Show solution
Solution
AB = [[1*2 + 0*4, 1*3 + 0*5], [0*2 + 1*4, 0*3 + 1*5]] = [[2, 3], [4, 5]].
Correct Answer:
A
— [2, 3], [4, 5]
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Q. If A = [[1, 0], [0, 1]] is the identity matrix, what is A^n for any integer n?
A.
A
B.
0
C.
I
D.
None of the above
Show solution
Solution
A^n = I for any integer n, where I is the identity matrix.
Correct Answer:
C
— I
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Q. If A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]], what is A + B?
A.
[6, 8], [10, 12]
B.
[1, 2], [3, 4]
C.
[5, 6], [7, 8]
D.
[8, 10], [10, 12]
Show solution
Solution
A + B = [[1+5, 2+6], [3+7, 4+8]] = [[6, 8], [10, 12]].
Correct Answer:
A
— [6, 8], [10, 12]
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Q. If A = [[1, 2], [3, 4]], find A^2.
A.
[7, 10], [15, 22]
B.
[1, 2], [3, 4]
C.
[10, 13], [22, 29]
D.
[-1, -2], [-3, -4]
Show solution
Solution
A^2 = A * A = [[1*1 + 2*3, 1*2 + 2*4], [3*1 + 4*3, 3*2 + 4*4]] = [[7, 10], [15, 22]].
Correct Answer:
A
— [7, 10], [15, 22]
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Q. If A = [[1, 2], [3, 4]], find the determinant of A.
Show solution
Solution
The determinant of A is (1*4) - (2*3) = 4 - 6 = -2.
Correct Answer:
B
— 2
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Q. If A = [[1, 2], [3, 4]], what is A^2?
A.
[7, 10; 15, 22]
B.
[1, 2; 3, 4]
C.
[10, 14; 22, 30]
D.
[-1, -2; -3, -4]
Show solution
Solution
A^2 = A * A = [[1*1 + 2*3, 1*2 + 2*4], [3*1 + 4*3, 3*2 + 4*4]] = [[7, 10], [15, 22]].
Correct Answer:
A
— [7, 10; 15, 22]
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Q. If A = [[1, 2], [3, 4]], what is the adjoint of A?
A.
[[4, -2], [-3, 1]]
B.
[[1, 3], [2, 4]]
C.
[[2, 1], [4, 3]]
D.
[[0, 0], [0, 0]]
Show solution
Solution
The adjoint of A is [[4, -2], [-3, 1]].
Correct Answer:
A
— [[4, -2], [-3, 1]]
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Q. If A = [[1, 2], [3, 4]], what is the determinant of A?
Show solution
Solution
The determinant of A is (1*4) - (2*3) = 4 - 6 = -2.
Correct Answer:
A
— -2
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Q. If A = [[1, 2], [3, 4]], what is the eigenvalue of A?
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Solution
The eigenvalues are found from the characteristic polynomial λ^2 - 5λ + 2 = 0, which gives λ = 5.
Correct Answer:
A
— 5
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Q. If A = [[1, 2], [3, 4]], what is the inverse of A?
A.
[[4, -2], [-3, 1]]
B.
[[-2, 1], [1.5, -0.5]]
C.
[[-2, 1], [1.5, -0.5]]
D.
[[4, -2], [-3, 1]]
Show solution
Solution
The inverse of A is (1/det(A)) * adj(A) = (1/(-2)) * [[4, -2], [-3, 1]] = [[-2, 1], [1.5, -0.5]].
Correct Answer:
A
— [[4, -2], [-3, 1]]
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Q. If A = [[1, 2], [3, 4]], what is the trace of A?
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Solution
The trace of A is the sum of the diagonal elements: 1 + 4 = 5.
Correct Answer:
A
— 5
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Q. If A = [[2, 0], [0, 3]], what is the eigenvalue of A?
Show solution
Solution
The eigenvalues of A are the diagonal elements: 2 and 3.
Correct Answer:
B
— 3
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Q. If A = {1, 2, 3, 4} and B = {2, 4, 6, 8}, what is A ∪ B?
A.
{1, 2, 3, 4, 6, 8}
B.
{2, 4}
C.
{1, 3, 5, 7}
D.
{1, 2, 3, 4, 5}
Show solution
Solution
The union A ∪ B includes all elements from both sets, which are {1, 2, 3, 4, 6, 8}.
Correct Answer:
A
— {1, 2, 3, 4, 6, 8}
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Q. If A = {1, 2, 3} and B = {1, 2, 3, 4, 5}, what is A ⊆ B?
A.
True
B.
False
C.
Depends on the context
D.
None of the above
Show solution
Solution
Set A is a subset of set B because all elements of A are contained in B. Therefore, A ⊆ B is True.
Correct Answer:
A
— True
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Q. If A = {1, 2, 3} and B = {1, 2, 3, 4}, what is the cardinality of A × B?
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Solution
The cardinality of the Cartesian product A × B is given by |A| * |B|. Here, |A| = 3 and |B| = 4, so |A × B| = 3 * 4 = 12.
Correct Answer:
B
— 6
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Q. If A = {1, 2, 3} and B = {1, 2, 3}, what is A × B?
A.
{(1,1), (2,2), (3,3)}
B.
{(1,2), (2,3), (3,1)}
C.
{(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)}
D.
{}
Show solution
Solution
A × B = {(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)} as it is the Cartesian product of A and B.
Correct Answer:
C
— {(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)}
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Q. If A = {1, 2, 3} and B = {3, 4, 5}, what is A - B?
A.
{1, 2}
B.
{3}
C.
{4, 5}
D.
{1, 2, 3, 4, 5}
Show solution
Solution
The difference of sets A and B, A - B, contains elements that are in A but not in B. Here, A - B = {1, 2}.
Correct Answer:
A
— {1, 2}
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Q. If A = {1, 2, 3} and B = {3, 4, 5}, what is A Δ B (symmetric difference)?
A.
{1, 2}
B.
{4, 5}
C.
{1, 2, 4, 5}
D.
{3}
Show solution
Solution
The symmetric difference A Δ B includes elements in either A or B but not in both, which are {1, 2, 4, 5}.
Correct Answer:
C
— {1, 2, 4, 5}
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Q. If A = {1, 2, 3} and B = {3, 4, 5}, what is A ∪ (A ∩ B)?
A.
{1, 2, 3}
B.
{3, 4, 5}
C.
{1, 2, 3, 4, 5}
D.
{1, 2, 5}
Show solution
Solution
First, A ∩ B = {3}. Then, A ∪ {3} = {1, 2, 3}.
Correct Answer:
A
— {1, 2, 3}
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Q. If A = {x | x is a letter in the word 'MATH'} and B = {x | x is a letter in the word 'SET'}, what is A ∩ B?
A.
{M, A, T}
B.
{A, T}
C.
{T}
D.
{}
Show solution
Solution
The intersection A ∩ B consists of common letters, which is {T}.
Correct Answer:
C
— {T}
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Q. If A = {x | x is a letter in the word 'MATH'} and B = {x | x is a letter in the word 'SCIENCE'}, what is A ∩ B?
A.
{A}
B.
{M, A, T}
C.
{A, C, E}
D.
{A, T}
Show solution
Solution
The intersection A ∩ B includes letters that are common in both words. The only common letter is 'A', so A ∩ B = {A}.
Correct Answer:
A
— {A}
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Q. If A = {x | x is a multiple of 3} and B = {x | x is a multiple of 5}, what is A ∩ B?
A.
{15}
B.
{3, 5}
C.
{0}
D.
{}
Show solution
Solution
The intersection A ∩ B consists of common multiples, which is {0}.
Correct Answer:
C
— {0}
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Q. If A = {x | x is a natural number and x < 5} and B = {x | x is a natural number and x > 2}, what is A ∩ B?
A.
{1, 2}
B.
{3, 4}
C.
{2, 3, 4}
D.
{1, 2, 3, 4}
Show solution
Solution
Set A = {1, 2, 3, 4} and set B = {3, 4, 5, ...}. The intersection A ∩ B = {3, 4}.
Correct Answer:
B
— {3, 4}
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Q. If A = {x | x is a natural number less than 5} and B = {x | x is a natural number less than 3}, what is A - B?
A.
{1, 2}
B.
{3, 4}
C.
{1, 2, 3, 4}
D.
{2, 3, 4}
Show solution
Solution
Set A = {1, 2, 3, 4} and set B = {1, 2}. Thus, A - B = {3, 4}.
Correct Answer:
B
— {3, 4}
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Q. If A = {x | x is a natural number less than 5} and B = {x | x is an odd natural number}, what is A ∩ B?
A.
{1, 2, 3, 4}
B.
{1, 3}
C.
{2, 4}
D.
{1, 2, 3}
Show solution
Solution
The intersection A ∩ B includes elements that are in both A and B. Here, A = {1, 2, 3, 4} and B = {1, 3}, so A ∩ B = {1, 3}.
Correct Answer:
B
— {1, 3}
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Q. If A = {x | x is a prime number less than 10} and B = {2, 3, 5, 7}, what is A = B?
A.
True
B.
False
C.
Cannot be determined
D.
None of the above
Show solution
Solution
Both sets A and B contain the same elements: {2, 3, 5, 7}. Therefore, A = B is True.
Correct Answer:
A
— True
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Q. If A = {x | x is a prime number less than 10} and B = {2, 3, 5, 7}, what is A?
A.
{2, 3, 5, 7}
B.
{1, 2, 3, 4, 5, 6, 7, 8, 9}
C.
{2, 3, 5, 7, 11}
D.
{2, 3, 5, 7, 9}
Show solution
Solution
The set A consists of all prime numbers less than 10, which are {2, 3, 5, 7}.
Correct Answer:
A
— {2, 3, 5, 7}
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Q. If A = {x | x is a vowel} and B = {x | x is a consonant}, what is A ∩ B?
A.
{a, e, i, o, u}
B.
{}
C.
{a, b, c}
D.
{a, e, i}
Show solution
Solution
The intersection A ∩ B is empty because no letter can be both a vowel and a consonant.
Correct Answer:
B
— {}
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Q. If A = {x | x is an even integer} and B = {x | x is a multiple of 3}, what is A ∪ B?
A.
{0, 2, 4, 6, ...}
B.
{0, 3, 6, 9, ...}
C.
{0, 2, 3, 4, 6, 9, ...}
D.
{0, 2, 3, 4, 6, 8, 9, ...}
Show solution
Solution
The union of sets A and B, A ∪ B, includes all even integers and all multiples of 3. Thus, A ∪ B = {0, 2, 3, 4, 6, 9, ...}.
Correct Answer:
C
— {0, 2, 3, 4, 6, 9, ...}
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Q. If A = {x | x is an even integer} and B = {x | x is a prime number}, what is A ∩ B?
A.
{2}
B.
{2, 3}
C.
{2, 4}
D.
{}
Show solution
Solution
The only even prime number is 2, so A ∩ B = {2}.
Correct Answer:
A
— {2}
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Showing 271 to 300 of 862 (29 Pages)
Algebra MCQ & Objective Questions
Algebra is a fundamental branch of mathematics that plays a crucial role in various school and competitive exams. Mastering algebraic concepts not only enhances problem-solving skills but also boosts confidence during exams. Practicing MCQs and objective questions helps students identify important questions and reinforces their understanding, making exam preparation more effective.
What You Will Practise Here
Basic operations with algebraic expressions
Solving linear equations and inequalities
Understanding quadratic equations and their roots
Working with polynomials and factoring techniques
Graphing linear equations and interpreting graphs
Applying algebraic identities in problem-solving
Word problems involving algebraic concepts
Exam Relevance
Algebra is a significant topic in the CBSE curriculum and is also included in various State Board syllabi. It frequently appears in competitive exams like NEET and JEE, where students encounter questions that test their understanding of algebraic concepts. Common question patterns include solving equations, simplifying expressions, and applying formulas to real-world problems.
Common Mistakes Students Make
Misinterpreting the signs in equations, leading to incorrect solutions.
Overlooking the importance of order of operations when simplifying expressions.
Confusing the properties of exponents and their applications.
Failing to check solutions in the original equations.
Neglecting to practice word problems, which can lead to difficulty in translating real-life situations into algebraic expressions.
FAQs
Question: What are some important Algebra MCQ questions for exams?Answer: Important Algebra MCQ questions often include solving linear equations, factoring polynomials, and applying algebraic identities.
Question: How can I improve my Algebra skills for competitive exams?Answer: Regular practice of objective questions and understanding key concepts will significantly enhance your Algebra skills.
Don't wait! Start solving practice MCQs today to test your understanding of Algebra and prepare effectively for your exams. Your success in mastering algebraic concepts is just a few questions away!
