Major Competitive Exams

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Major Competitive Exams

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Major Competitive Exams MCQ & Objective Questions

Major Competitive Exams play a crucial role in shaping the academic and professional futures of students in India. These exams not only assess knowledge but also test problem-solving skills and time management. Practicing MCQs and objective questions is essential for scoring better, as they help in familiarizing students with the exam format and identifying important questions that frequently appear in tests.

What You Will Practise Here

Key concepts and theories related to major subjects
Important formulas and their applications
Definitions of critical terms and terminologies
Diagrams and illustrations to enhance understanding
Practice questions that mirror actual exam patterns
Strategies for solving objective questions efficiently
Time management techniques for competitive exams

Exam Relevance

The topics covered under Major Competitive Exams are integral to various examinations such as CBSE, State Boards, NEET, and JEE. Students can expect to encounter a mix of conceptual and application-based questions that require a solid understanding of the subjects. Common question patterns include multiple-choice questions that test both knowledge and analytical skills, making it essential to be well-prepared with practice MCQs.

Common Mistakes Students Make

Rushing through questions without reading them carefully
Overlooking the negative marking scheme in MCQs
Confusing similar concepts or terms
Neglecting to review previous years’ question papers
Failing to manage time effectively during the exam

FAQs

Question: How can I improve my performance in Major Competitive Exams?
Answer: Regular practice of MCQs and understanding key concepts will significantly enhance your performance.

Question: What types of questions should I focus on for these exams?
Answer: Concentrate on important Major Competitive Exams questions that frequently appear in past papers and mock tests.

Question: Are there specific strategies for tackling objective questions?
Answer: Yes, practicing under timed conditions and reviewing mistakes can help develop effective strategies.

Start your journey towards success by solving practice MCQs today! Test your understanding and build confidence for your upcoming exams. Remember, consistent practice is the key to mastering Major Competitive Exams!

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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. {}

Solution

The intersection A ∩ B consists of common letters, which is {T}.

Correct Answer: C — {T}

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. {}

Solution

The intersection A ∩ B consists of common multiples, which is {0}.

Correct Answer: C — {0}

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}

Solution

Set A = {1, 2, 3, 4} and set B = {3, 4, 5, ...}. The intersection A ∩ B = {3, 4}.

Correct Answer: B — {3, 4}

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. {}

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}

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}

Solution

Set A = {1, 2, 3, 4} and set B = {1, 2}. Thus, A - B = {3, 4}.

Correct Answer: B — {3, 4}

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. {}

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}

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}

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}

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

Solution

Both sets A and B contain the same elements: {2, 3, 5, 7}. Therefore, A = B is True.

Correct Answer: A — True

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}

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}

Q. If A = {x | x is a prime number less than 10}, what is A?

A. {2, 3, 5, 7}
B. {1, 2, 3, 4}
C. {2, 4, 6, 8}
D. {3, 5, 7, 9}

Solution

The prime numbers less than 10 are 2, 3, 5, and 7. Therefore, A = {2, 3, 5, 7}.

Correct Answer: A — {2, 3, 5, 7}

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}

Solution

The intersection A ∩ B is empty because no letter can be both a vowel and a consonant.

Correct Answer: B — {}

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, ...}

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, ...}

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

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

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. {}

Solution

The only even prime number is 2, so A ∩ B = {2}.

Correct Answer: A — {2}

Q. If A = {x | x is an even number} 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, 1, 2, 3, ...}

Solution

The union A ∪ B includes all even numbers and all multiples of 3. Thus, A ∪ B = {0, 2, 3, 4, 6, 9, ...}.

Correct Answer: C — {0, 2, 3, 4, 6, 9, ...}

Q. If A = {x | x is an even number} and B = {x | x is a prime number}, what is A ∩ B?

A. {2}
B. {2, 3}
C. {2, 4}
D. {}

Solution

A ∩ B = {2} as 2 is the only even prime number.

Correct Answer: A — {2}

Q. If A = | 1 2 | | 3 4 |, find det(A).

A. -2
B. 2
C. 0
D. 4

Solution

det(A) = (1)(4) - (2)(3) = 4 - 6 = -2.

Correct Answer: B — 2

Q. If A = | 1 2 | | 3 4 |, what is det(A)?

A. -2
B. 2
C. 0
D. 4

Solution

det(A) = (1*4) - (2*3) = 4 - 6 = -2.

Correct Answer: B — 2

Q. If A = | 1 2 | | 3 5 |, what is det(2A)?

A. -10
B. 10
C. 20
D. 40

Solution

det(2A) = 2^2 * det(A) = 4 * (1*5 - 2*3) = 4 * (-1) = -4.

Correct Answer: C — 20

Q. If A and B invest $10,000 and $15,000 respectively, and C joins later with $25,000, what is the profit-sharing ratio after C joins?

A. 2:3:5
B. 2:5:3
C. 3:2:5
D. 5:3:2

Solution

Total investment = 10000 + 15000 + 25000 = 50000. Ratio = 10000:15000:25000 = 2:3:5.

Correct Answer: A — 2:3:5

Q. If A and B invest in a business in the ratio 3:4 and A's profit is $900, what is B's profit?

A. $1200
B. $1000
C. $800
D. $600

Solution

The profit ratio is the same as the investment ratio. If A's profit is $900, then B's profit = (4/3) * 900 = $1200.

Correct Answer: A — $1200

Q. If A and B invest in a business in the ratio of 3:4 and the total profit is $70,000, how much does B receive?

A. $30,000
B. $40,000
C. $50,000
D. $20,000

Solution

B's share = (B's ratio / Total ratio) * Total profit = (4 / 7) * 70000 = $40,000.

Correct Answer: B — $40,000

Q. If A and B invest in a business in the ratio of 3:4 and the total profit is $90,000, what is A's share?

A. $30,000
B. $36,000
C. $40,000
D. $45,000

Solution

A's share = (A's ratio / Total ratio) * Total profit = (3 / 7) * 90000 = $38,571.43.

Correct Answer: B — $36,000

Q. If A and B invest in a business with A investing $12,000 and B investing $18,000, what is the profit share of A if the total profit is $90,000?

A. $36,000
B. $30,000
C. $54,000
D. $24,000

Solution

Total investment = 12000 + 18000 = 30000. A's share = (12000 / 30000) * 90000 = $36,000.

Correct Answer: B — $30,000

Q. If A and B invest in a business with A investing $40,000 and B investing $60,000, and they agree to share profits equally, how much profit will A receive if the total profit is $20,000?

A. $10,000
B. $8,000
C. $12,000
D. $6,000

Solution

Since they share profits equally, A's share = 20000 / 2 = $10,000.

Correct Answer: A — $10,000

Q. If a bag contains 4 green and 6 yellow marbles, what is the probability of picking a green marble?

A. 2/5
B. 4/10
C. 4/6
D. 1/3

Solution

Total marbles = 4 + 6 = 10. Probability of green marble = 4/10 = 2/5.

Correct Answer: A — 2/5

Q. If a bag contains 4 green and 6 yellow marbles, what is the probability of picking a yellow marble?

A. 2/5
B. 3/5
C. 4/5
D. 1/5

Solution

Total marbles = 4 + 6 = 10. Probability of yellow = 6/10 = 3/5.

Correct Answer: B — 3/5

Q. If a basketball court is 28 meters long and 15 meters wide, what is the area of the court? (2022)

A. 420 m²
B. 300 m²
C. 450 m²
D. 350 m²

Solution

Area = Length * Width = 28 m * 15 m = 420 m².

Correct Answer: A — 420 m²

Q. If a basketball hoop is 3.05 meters high and a player jumps 0.75 meters high, how far below the hoop is the player at the peak of their jump? (2023)

A. 2.3 m
B. 2.5 m
C. 2.75 m
D. 3.05 m

Solution

Height below the hoop = height of hoop - height of jump = 3.05 m - 0.75 m = 2.3 m.

Correct Answer: B — 2.5 m

Q. If a basketball player makes 75% of his free throws and he attempts 40 free throws, how many successful free throws does he make? (2022)

A. 25
B. 30
C. 35
D. 40

Solution

Successful free throws = 75% of 40 = 0.75 * 40 = 30.

Correct Answer: B — 30

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