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?
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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 A ⊆ B?
A.
True
B.
False
C.
Depends on A
D.
Not enough information
Show solution
Solution
A is a subset of B if all elements of A are in B. Here, all elements of A are in B, so 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, 4}, what is the number of subsets of A ∪ B?
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Solution
A ∪ B = {1, 2, 3, 4}, which has 4 elements. The number of subsets is 2^4 = 16.
Correct Answer:
B
— 16
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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 = {1, 2}, what is the number of elements in A × B?
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Solution
The number of elements in the Cartesian product A × B is the product of the number of elements in A and B. Here, |A| = 3 and |B| = 2, so |A × B| = 3 * 2 = 6.
Correct Answer:
D
— 4
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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 = {1, 2, 3} and B = {3, 4}, what is the Cartesian product A × B?
A.
{(1, 3), (2, 4)}
B.
{(1, 3), (1, 4), (2, 3), (2, 4), (3, 3), (3, 4)}
C.
{(1, 3), (1, 4), (2, 3), (2, 4), (3, 3), (3, 4), (1, 1), (2, 2), (3, 3)}
D.
{}
Show solution
Solution
The Cartesian product A × B is the set of all ordered pairs (a, b) where a ∈ A and b ∈ B, which is {(1, 3), (1, 4), (2, 3), (2, 4), (3, 3), (3, 4)}.
Correct Answer:
B
— {(1, 3), (1, 4), (2, 3), (2, 4), (3, 3), (3, 4)}
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Q. If A = {1, 2, 3}, how many subsets does A have?
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Solution
The number of subsets of a set with n elements is 2^n. Here, n = 3, so 2^3 = 8.
Correct Answer:
D
— 8
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Q. If A = {1, 2, 3}, what is the power set of A?
A.
{∅, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}
B.
{∅, {1, 2, 3}}
C.
{1, 2, 3}
D.
{1, 2, 3, ∅}
Show solution
Solution
The power set of a set with n elements has 2^n subsets. Here, n=3, so the power set has 2^3 = 8 subsets.
Correct Answer:
A
— {∅, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}
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Q. If A = {1, 2} and B = {x | x is an odd integer}, what is A × B?
A.
{(1, 1), (2, 1)}
B.
{(1, 3), (2, 3)}
C.
{(1, 1), (1, 3), (2, 1), (2, 3)}
D.
{(1, 2), (2, 2)}
Show solution
Solution
The Cartesian product A × B consists of all ordered pairs (a, b) where a ∈ A and b ∈ B. Thus, A × B = {(1, x), (2, x)} for all odd integers x.
Correct Answer:
C
— {(1, 1), (1, 3), (2, 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 '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 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 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 10} and B = {x | x is a prime number}, what is A ∩ B?
A.
{2, 3, 5, 7}
B.
{1, 2, 3, 4}
C.
{2, 4, 6, 8}
D.
{}
Show solution
Solution
The intersection A ∩ B includes 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 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 a prime number}, what is A ∩ B?
A.
{1, 2, 3, 4}
B.
{2, 3}
C.
{3, 5}
D.
{}
Show solution
Solution
The natural numbers less than 5 are {1, 2, 3, 4} and the prime numbers are {2, 3}. Their intersection is {2, 3}.
Correct Answer:
B
— {2, 3}
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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 multiple of 4}, what is A ⊆ B?
A.
True
B.
False
C.
Depends on x
D.
None of the above
Show solution
Solution
A is the set of all even integers, while B is the set of multiples of 4. Not all even integers are multiples of 4 (e.g., 2 is even but not a multiple of 4), hence A is not a subset of B.
Correct Answer:
B
— False
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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 1081 to 1110 of 2847 (95 Pages)
Mathematics Syllabus (JEE Main) MCQ & Objective Questions
The Mathematics Syllabus for JEE Main is crucial for students aiming to excel in competitive exams. Understanding this syllabus not only helps in grasping key concepts but also enhances your ability to tackle objective questions effectively. Practicing MCQs and important questions from this syllabus is essential for solid exam preparation, ensuring you are well-equipped to score better in your exams.
What You Will Practise Here
Sets, Relations, and Functions
Complex Numbers and Quadratic Equations
Permutations and Combinations
Binomial Theorem
Sequences and Series
Limits and Derivatives
Statistics and Probability
Exam Relevance
The Mathematics Syllabus (JEE Main) is not only relevant for JEE but also appears in CBSE and State Board examinations. Students can expect a variety of question patterns, including direct MCQs, numerical problems, and conceptual questions. Mastery of this syllabus will prepare you for similar topics in NEET and other competitive exams, making it vital for your overall academic success.
Common Mistakes Students Make
Misinterpreting the questions, especially in word problems.
Overlooking the importance of units and dimensions in problems.
Confusing formulas related to sequences and series.
Neglecting to practice derivations, leading to errors in calculus.
Failing to apply the correct methods for solving probability questions.
FAQs
Question: What are the key topics in the Mathematics Syllabus for JEE Main? Answer: Key topics include Sets, Complex Numbers, Permutations, Binomial Theorem, and Calculus.
Question: How can I improve my performance in Mathematics MCQs? Answer: Regular practice of MCQs and understanding the underlying concepts are essential for improvement.
Now is the time to take charge of your exam preparation! Dive into solving practice MCQs and test your understanding of the Mathematics Syllabus (JEE Main). Your success is just a question away!
