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!
Q. If a number is divisible by 2 and 3, is it prime?
A.
Yes
B.
No
C.
Only if it's 6
D.
Only if it's odd
Show solution
Solution
No, because if a number is divisible by 2 and 3, it has divisors other than 1 and itself.
Correct Answer:
B
— No
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Q. If a number is divisible by 4, which of the following must also be true?
A.
It is even
B.
It is divisible by 8
C.
It is divisible by 2
D.
It is a multiple of 10
Show solution
Solution
Any number divisible by 4 is even, as 4 itself is an even number.
Correct Answer:
A
— It is even
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Q. If a number is divisible by 4, which of the following must be true?
A.
It ends in 0
B.
It ends in 2
C.
Its last two digits form a number divisible by 4
D.
It is even
Show solution
Solution
A number is divisible by 4 if the number formed by its last two digits is divisible by 4.
Correct Answer:
C
— Its last two digits form a number divisible by 4
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Q. If a number is divisible by 7, which of the following is NOT necessarily true?
A.
It is odd
B.
It is not a prime number
C.
It can be a multiple of 14
D.
It can be a two-digit number
Show solution
Solution
A number can be divisible by 7 and still be even, such as 14.
Correct Answer:
A
— It is odd
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Q. If a number is divisible by 8, which of the following must also be true?
A.
It is divisible by 2
B.
It is divisible by 4
C.
It is a multiple of 16
D.
It is a prime number
Show solution
Solution
Any number divisible by 8 is also divisible by 4, as 8 is a multiple of 4.
Correct Answer:
B
— It is divisible by 4
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Q. If a number is divisible by 8, which of the following must be true?
A.
It is divisible by 2
B.
It is divisible by 3
C.
It is divisible by 5
D.
It is divisible by 10
Show solution
Solution
A number divisible by 8 is also divisible by 2, as 8 is a multiple of 2.
Correct Answer:
A
— It is divisible by 2
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Q. If a number is divisible by 9, what can be inferred about the sum of its digits?
A.
It is even
B.
It is divisible by 3
C.
It is divisible by 9
D.
It is a prime number
Show solution
Solution
A number is divisible by 9 if the sum of its digits is also divisible by 9.
Correct Answer:
C
— It is divisible by 9
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Q. If a number is divisible by 9, which of the following must also be true?
A.
It is divisible by 3
B.
It is divisible by 6
C.
It is divisible by 12
D.
It is divisible by 18
Show solution
Solution
Any number divisible by 9 is also divisible by 3.
Correct Answer:
A
— It is divisible by 3
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Q. If a number is divisible by both 2 and 3, which of the following is true?
A.
It is divisible by 5
B.
It is divisible by 6
C.
It is odd
D.
It is a prime number
Show solution
Solution
A number that is divisible by both 2 and 3 is also divisible by their least common multiple, which is 6.
Correct Answer:
B
— It is divisible by 6
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Q. If a number is divisible by both 2 and 3, which of the following must also be true?
A.
It is divisible by 5.
B.
It is divisible by 6.
C.
It is an odd number.
D.
It is a prime number.
Show solution
Solution
A number divisible by both 2 and 3 is also divisible by their least common multiple, which is 6.
Correct Answer:
B
— It is divisible by 6.
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Q. If a number is divisible by both 2 and 3, which of the following must it also be divisible by?
Show solution
Solution
A number divisible by both 2 and 3 is also divisible by their least common multiple, which is 6.
Correct Answer:
B
— 6
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Q. If a number is divisible by both 2 and 5, what can be said about it?
A.
It is odd
B.
It is a multiple of 10
C.
It is a prime number
D.
It is a multiple of 20
Show solution
Solution
A number divisible by both 2 and 5 must end in 0, making it a multiple of 10.
Correct Answer:
B
— It is a multiple of 10
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Q. If a number is divisible by both 2 and 5, which of the following must be true?
A.
It is divisible by 10
B.
It is divisible by 15
C.
It is divisible by 20
D.
It is divisible by 25
Show solution
Solution
A number divisible by both 2 and 5 is also divisible by 10, as 10 is the least common multiple of 2 and 5.
Correct Answer:
A
— It is divisible by 10
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Q. If a number is divisible by both 3 and 4, what is the smallest positive number it can be?
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Solution
The smallest positive number divisible by both 3 and 4 is 12.
Correct Answer:
A
— 12
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Q. If a number is divisible by both 3 and 4, which of the following must also be true?
A.
It is divisible by 12.
B.
It is divisible by 7.
C.
It is divisible by 6.
D.
It is divisible by 9.
Show solution
Solution
The least common multiple of 3 and 4 is 12, so any number divisible by both must also be divisible by 12.
Correct Answer:
A
— It is divisible by 12.
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Q. If a number is divisible by both 3 and 5, which of the following is guaranteed to be true?
A.
It is divisible by 15
B.
It is divisible by 8
C.
It is divisible by 10
D.
It is divisible by 6
Show solution
Solution
A number divisible by both 3 and 5 is also divisible by their least common multiple, which is 15.
Correct Answer:
A
— It is divisible by 15
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Q. If a number is divisible by both 3 and 5, which of the following must also be true?
A.
It is divisible by 15
B.
It is divisible by 8
C.
It is divisible by 10
D.
It is not divisible by 6
Show solution
Solution
A number divisible by both 3 and 5 is also divisible by their LCM, which is 15.
Correct Answer:
A
— It is divisible by 15
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Q. If a number is divisible by both 4 and 6, what is the least possible value of that number?
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Solution
The least common multiple (LCM) of 4 and 6 is 12.
Correct Answer:
A
— 12
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Q. If a number is divisible by both 4 and 6, what is the smallest positive integer that it can be?
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Solution
The smallest positive integer divisible by both 4 and 6 is 12.
Correct Answer:
A
— 12
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Q. If a number is divisible by both 4 and 6, what is the smallest positive integer that is also a multiple of both?
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Solution
The LCM of 4 and 6 is 12.
Correct Answer:
A
— 12
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Q. If a number is divisible by both 4 and 6, what is the smallest such number?
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Solution
The smallest number divisible by both 4 and 6 is their LCM, which is 12.
Correct Answer:
A
— 12
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Q. If a number is divisible by both 4 and 6, which of the following must also be true? (2023)
A.
It is divisible by 12.
B.
It is divisible by 24.
C.
It is divisible by 10.
D.
It is not divisible by 2.
Show solution
Solution
The least common multiple of 4 and 6 is 12, so any number divisible by both must also be divisible by 12.
Correct Answer:
A
— It is divisible by 12.
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Q. If a number is divisible by both 5 and 10, which of the following can be concluded?
A.
It is a multiple of 15.
B.
It is a multiple of 20.
C.
It is a multiple of 50.
D.
It is a multiple of 10.
Show solution
Solution
Any number divisible by 10 is also a multiple of 10.
Correct Answer:
D
— It is a multiple of 10.
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Q. If a number is divisible by both 6 and 8, which of the following must it also be divisible by?
Show solution
Solution
The least common multiple of 6 and 8 is 24, so any number divisible by both must also be divisible by 24.
Correct Answer:
B
— 24
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Q. If a number is divisible by both 8 and 12, what is the smallest number it could be?
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Solution
The least common multiple of 8 and 12 is 24, so the smallest number divisible by both is 24.
Correct Answer:
B
— 48
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Q. If a number is divisible by both 8 and 12, which of the following must also be true?
A.
It is divisible by 24.
B.
It is divisible by 16.
C.
It is divisible by 20.
D.
It is divisible by 32.
Show solution
Solution
The least common multiple of 8 and 12 is 24, so any number divisible by both must also be divisible by 24.
Correct Answer:
A
— It is divisible by 24.
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Q. If a number is divisible by both 8 and 12, which of the following must it also be divisible by?
Show solution
Solution
The least common multiple of 8 and 12 is 24, so the number must be divisible by 24.
Correct Answer:
B
— 24
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Q. If a number is divisible by both 9 and 12, which of the following is guaranteed to be true?
A.
It is divisible by 36.
B.
It is divisible by 108.
C.
It is divisible by 27.
D.
It is divisible by 18.
Show solution
Solution
The least common multiple of 9 and 12 is 36, and since 36 is divisible by 18, the number must also be divisible by 18.
Correct Answer:
D
— It is divisible by 18.
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Q. If a number is expressed as 5k + 3 for some integer k, what is the remainder when this number is divided by 5? (2023)
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Solution
The term 5k is divisible by 5, so the remainder is solely from 3, which is 3.
Correct Answer:
D
— 3
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Q. If a number is expressed as 5k + 3, where k is an integer, what is the remainder when this number is divided by 5?
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Solution
The remainder is 3, as 5k is divisible by 5.
Correct Answer:
D
— 3
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