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 a multiple of both 8 and 14, which of the following numbers is guaranteed to be a factor of that number? (2023)
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Solution
Since any multiple of 8 and 14 must also be a multiple of their GCD, which includes 2 as a factor.
Correct Answer:
D
— 2
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Q. If a number is both a factor and a multiple of 6, which of the following could it be?
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Solution
The number 6 is a factor of itself and also a multiple of 6, making it the only valid option.
Correct Answer:
A
— 6
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Q. If a number is both a factor of 24 and a multiple of 3, which of the following could it be?
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Solution
12 is a factor of 24 and also a multiple of 3, as 12 = 3 * 4.
Correct Answer:
D
— 12
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Q. If a number is both a factor of 36 and a multiple of 4, which of the following could be that number?
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Solution
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. Among these, 12 is a multiple of 4.
Correct Answer:
B
— 12
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Q. If a number is both a factor of 36 and a multiple of 6, which of the following is the largest such number?
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Solution
The factors of 36 that are also multiples of 6 are 6, 12, and 18. Among these, 18 is the largest.
Correct Answer:
C
— 18
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Q. If a number is both a multiple of 4 and a factor of 48, which of the following numbers could it be?
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Solution
The multiples of 4 that are also factors of 48 are 4, 8, 12, and 16. Among the options, 8 is valid.
Correct Answer:
A
— 8
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Q. If a number is composite, which of the following must be true?
A.
It has exactly two factors
B.
It has more than two factors
C.
It is even
D.
It is greater than 1
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Solution
A composite number has more than two factors.
Correct Answer:
B
— It has more than two factors
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Q. If a number is congruent to 0 modulo 6, which of the following could be a possible value?
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Solution
A number congruent to 0 mod 6 must be a multiple of 6. 12 is a multiple of 6.
Correct Answer:
B
— 12
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Q. If a number is divided by 11 and gives a remainder of 7, what is the remainder when this number is divided by 3? (2023)
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Solution
The number can be expressed as 11k + 7. When divided by 3, the remainder is 1 (7 % 3 = 1).
Correct Answer:
B
— 1
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Q. If a number is divided by 12 and gives a remainder of 7, what is the possible range of this number? (2023)
A.
7 to 19
B.
19 to 31
C.
31 to 43
D.
43 to 55
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Solution
The number can be expressed as 12k + 7, where k is a non-negative integer. For k=0, the number is 7; for k=1, it is 19.
Correct Answer:
A
— 7 to 19
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Q. If a number is divided by 12 and gives a remainder of 7, what will be the remainder when this number is divided by 3?
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Solution
Since 7 divided by 3 gives a remainder of 1, the answer is 1.
Correct Answer:
B
— 1
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Q. If a number is divided by 12 and gives a remainder of 7, what will be the remainder when the same number is divided by 3? (2023)
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Solution
The number can be expressed as 12k + 7. When divided by 3, the remainder is 1 (7 % 3 = 1).
Correct Answer:
B
— 1
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Q. If a number is divided by 12 and gives a remainder of 7, which of the following numbers could it be?
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Solution
23 gives a remainder of 7 when divided by 12 (12*1 + 7 = 19).
Correct Answer:
B
— 23
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Q. If a number is divided by 12 and leaves a remainder of 7, what is the remainder when the same number is divided by 3? (2023)
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Solution
Since 7 mod 3 = 1, the remainder when the number is divided by 3 is 1.
Correct Answer:
B
— 1
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Q. If a number is divided by 15 and gives a remainder of 10, which of the following could be the number?
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Solution
25 gives a remainder of 10 when divided by 15 (15*1 + 10 = 25).
Correct Answer:
A
— 25
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Q. If a number is divided by 15 and gives a remainder of 7, what will be the remainder when this number is divided by 3?
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Solution
The remainder when the number is divided by 3 is 1, since 7 mod 3 = 1.
Correct Answer:
B
— 1
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Q. If a number is divided by 15 and gives a remainder of 8, which of the following numbers will also give the same remainder when divided by 15?
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Solution
23 gives a remainder of 8 when divided by 15.
Correct Answer:
A
— 23
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Q. If a number is divided by 15 and leaves a remainder of 10, what will be the remainder when this number is divided by 5? (2023)
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Solution
Since 10 is greater than 5, the remainder when 10 is divided by 5 is 0.
Correct Answer:
A
— 0
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Q. If a number is divided by 3 and the result is 5, what is the number?
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Solution
Let the number be x. Then, x/3 = 5, so x = 5 × 3 = 15.
Correct Answer:
C
— 15
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Q. If a number is divided by 5, the remainder is 3. What will be the remainder when the same number is divided by 10? (2019)
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Solution
Let the number be n. Then n = 5k + 3 for some integer k. When divided by 10, n = 5k + 3 gives a remainder of 3.
Correct Answer:
C
— 3
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Q. If a number is divided by 6 and gives a remainder of 2, what will be the remainder when the same number is divided by 3? (2023)
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Solution
If the number gives a remainder of 2 when divided by 6, it will give a remainder of 2 when divided by 3 as well.
Correct Answer:
B
— 1
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Q. If a number is divided by 6 and gives a remainder of 2, what will be the remainder when this number is divided by 3? (2023)
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Solution
Since 2 is less than 3, the remainder when 2 is divided by 3 is 2.
Correct Answer:
A
— 0
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Q. If a number is divided by 8 and gives a remainder of 5, what will be the remainder when this number is divided by 4?
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Solution
The number can be expressed as 8k + 5, which gives a remainder of 1 when divided by 4.
Correct Answer:
B
— 1
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Q. If a number is divided by 8 and leaves a remainder of 5, what will be the remainder when this number is divided by 4? (2023)
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Solution
The number can be expressed as 8k + 5. When divided by 4, the remainder is 5 mod 4 = 1.
Correct Answer:
D
— 3
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Q. If a number is divided by 9 and gives a remainder of 2, which of the following numbers will also give the same remainder when divided by 9?
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Solution
29 gives a remainder of 2 when divided by 9 (9*3 + 2 = 29).
Correct Answer:
C
— 29
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Q. If a number is divisible by 10, which of the following must be true?
A.
It is divisible by 2
B.
It is divisible by 5
C.
It is even
D.
All of the above
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Solution
A number divisible by 10 is always divisible by 2 and 5, and it is also even.
Correct Answer:
D
— All of the above
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Q. If a number is divisible by 12, which of the following must also be true?
A.
It is divisible by 3
B.
It is divisible by 5
C.
It is divisible by 10
D.
It is a prime number
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Solution
A number divisible by 12 is also divisible by both 3 and 4.
Correct Answer:
A
— It is divisible by 3
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Q. If a number is divisible by 15, which of the following must also be true?
A.
It is divisible by 3
B.
It is divisible by 5
C.
It is even
D.
Both 0 and 1 are factors
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Solution
A number divisible by 15 must be divisible by both 3 and 5.
Correct Answer:
A
— It is divisible by 3
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Q. If a number is divisible by 15, which of the following must it also be divisible by?
A.
3
B.
5
C.
15
D.
All of the above
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Solution
A number divisible by 15 is also divisible by both 3 and 5, as 15 is the product of these two primes.
Correct Answer:
D
— All of the above
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Q. If a number is divisible by 2 and 3, is it prime or composite?
A.
Prime
B.
Composite
C.
Neither
D.
Cannot be determined
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Solution
A number divisible by 2 and 3 is composite, as it has divisors other than 1 and itself.
Correct Answer:
B
— Composite
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