Q. If 25% of a population likes apples, 15% likes oranges, and 5% likes both, what percentage likes either fruit?
A.
35%
B.
30%
C.
25%
D.
20%
Show solution
Solution
Using inclusion-exclusion, the percentage that likes either fruit is 25% + 15% - 5% = 35%.
Correct Answer:
A
— 35%
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Q. If 25% of a population likes apples, 35% likes oranges, and 10% likes both, what percentage likes only apples?
A.
15%
B.
25%
C.
10%
D.
5%
Show solution
Solution
The percentage of people who like only apples is 25% - 10% = 15%.
Correct Answer:
A
— 15%
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Q. If 25% of a population likes reading, 15% likes writing, and 5% likes both, what percentage likes either reading or writing?
A.
35%
B.
30%
C.
25%
D.
20%
Show solution
Solution
Using inclusion-exclusion, the percentage of people who like either activity is: 25% + 15% - 5% = 35%.
Correct Answer:
A
— 35%
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Q. If 4 different books are to be arranged on a shelf, how many arrangements are possible?
Show solution
Solution
The number of arrangements of 4 distinct books is 4! = 24.
Correct Answer:
B
— 24
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Q. If 4 different books are to be arranged on a shelf, how many different arrangements are possible?
Show solution
Solution
The number of arrangements of 4 distinct books is 4! = 24.
Correct Answer:
B
— 24
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Q. If 40 students like Mathematics, 30 like Science, and 10 like both subjects, how many students like only Mathematics?
Show solution
Solution
The number of students who like only Mathematics is 40 - 10 = 30.
Correct Answer:
B
— 20
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Q. If 6 different colored balls are to be arranged in a row, how many arrangements are possible?
A.
720
B.
600
C.
360
D.
480
Show solution
Solution
The number of arrangements of 6 different colored balls is 6! = 720.
Correct Answer:
A
— 720
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Q. If 60% of students like reading fiction, 40% like reading non-fiction, and 10% like both, what percentage of students like at least one genre?
A.
90%
B.
100%
C.
80%
D.
70%
Show solution
Solution
Using inclusion-exclusion, the percentage is 60% + 40% - 10% = 90%.
Correct Answer:
A
— 90%
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Q. If 60% of students like reading, 40% like writing, and 10% like both, what percentage of students like only reading?
A.
50%
B.
40%
C.
30%
D.
20%
Show solution
Solution
The percentage of students who like only reading is 60% - 10% = 50%.
Correct Answer:
A
— 50%
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Q. If 60% of students like reading, 40% like writing, and 10% like both, what percentage of students like only writing?
A.
30%
B.
40%
C.
10%
D.
50%
Show solution
Solution
The percentage of students who like only writing is 40% - 10% = 30%.
Correct Answer:
A
— 30%
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Q. If 60% of students play cricket, 40% play football, and 10% play both, what percentage of students play only cricket?
A.
50%
B.
40%
C.
30%
D.
20%
Show solution
Solution
The percentage of students who play only cricket is 60% - 10% = 50%.
Correct Answer:
A
— 50%
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Q. If 60% of students play cricket, 40% play football, and 10% play both, what percentage of students play either cricket or football?
A.
90%
B.
80%
C.
70%
D.
60%
Show solution
Solution
Using inclusion-exclusion, the percentage of students who play either cricket or football is: 60% + 40% - 10% = 90%.
Correct Answer:
B
— 80%
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Q. If 60% of students play cricket, 40% play football, and 10% play both, what percentage of students play only one sport?
A.
90%
B.
80%
C.
70%
D.
60%
Show solution
Solution
The percentage playing only cricket is 60% - 10% = 50%, and only football is 40% - 10% = 30%. Thus, total playing only one sport is 50% + 30% = 80%.
Correct Answer:
B
— 80%
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Q. If 60% of students play cricket, 50% play football, and 30% play both, what percentage of students play either cricket or football?
A.
50%
B.
60%
C.
80%
D.
100%
Show solution
Solution
Using inclusion-exclusion, the percentage playing either is 60% + 50% - 30% = 80%.
Correct Answer:
C
— 80%
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Q. If 60% of students play football, 40% play basketball, and 10% play both, what percentage of students play either football or basketball?
A.
90%
B.
80%
C.
70%
D.
60%
Show solution
Solution
Using inclusion-exclusion, the percentage of students who play either sport is: 60% + 40% - 10% = 90%.
Correct Answer:
A
— 90%
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Q. If 60% of students play football, 40% play basketball, and 10% play both, what percentage of students play either sport?
A.
90%
B.
80%
C.
70%
D.
60%
Show solution
Solution
Using inclusion-exclusion, the percentage playing either sport is 60% + 40% - 10% = 90%.
Correct Answer:
A
— 90%
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Q. If 80% of a population likes tea, 60% likes coffee, and 30% likes both, what percentage likes at least one of the two?
A.
50%
B.
60%
C.
80%
D.
100%
Show solution
Solution
Using inclusion-exclusion, the percentage liking at least one is 80% + 60% - 30% = 110%, which is capped at 100%.
Correct Answer:
C
— 80%
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Q. If a box contains 4 defective and 16 non-defective items, what is the probability of selecting a non-defective item?
A.
1/5
B.
4/20
C.
4/16
D.
16/20
Show solution
Solution
The probability of selecting a non-defective item is 16/(4+16) = 16/20 = 4/5.
Correct Answer:
D
— 16/20
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Q. If a committee of 3 is to be formed from 5 people, how many different committees can be formed?
Show solution
Solution
The number of ways to choose 3 people from 5 is given by 5C3 = 10.
Correct Answer:
B
— 15
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Q. If a committee of 3 members is to be formed from a group of 5 people, how many different committees can be formed?
Show solution
Solution
The number of ways to choose 3 members from 5 is given by 5C3 = 10.
Correct Answer:
A
— 10
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Q. If a function is defined as f(x) = 2x + 3, what is the value of f(4)?
Show solution
Solution
Substituting x = 4 into the function gives f(4) = 2(4) + 3 = 8 + 3 = 11.
Correct Answer:
B
— 11
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Q. If a function is defined as f(x) = 3x + 2, what is the value of f(4)?
Show solution
Solution
To find f(4), substitute 4 into the function: f(4) = 3(4) + 2 = 12 + 2 = 14.
Correct Answer:
A
— 14
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Q. If a lock has 4 digits, how many different combinations can be formed if digits can be repeated?
A.
10000
B.
9000
C.
8000
D.
7000
Show solution
Solution
Each digit can be any of the 10 digits (0-9). Therefore, the total combinations = 10^4 = 10000.
Correct Answer:
A
— 10000
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Q. If a lock has 4 digits, how many different combinations can be formed using the digits 0-9?
A.
10000
B.
9000
C.
1000
D.
5000
Show solution
Solution
Each digit can be any of the 10 digits (0-9), so the total combinations = 10^4 = 10000.
Correct Answer:
A
— 10000
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Q. If a lock requires 3 different digits from 0 to 9, how many different combinations can be formed?
A.
720
B.
1000
C.
900
D.
120
Show solution
Solution
The number of ways to choose 3 different digits from 10 is 10P3 = 720.
Correct Answer:
A
— 720
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Q. If a lock requires 3 digits, how many different combinations can be formed using the digits 0-9?
A.
1000
B.
900
C.
100
D.
10
Show solution
Solution
Each digit can be any of the 10 digits, so the total combinations are 10^3 = 1000.
Correct Answer:
A
— 1000
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Q. If a lock requires a 3-digit code using the digits 0-9, how many different codes can be formed if digits cannot be repeated?
A.
720
B.
1000
C.
900
D.
800
Show solution
Solution
The first digit has 10 options, the second has 9, and the third has 8. Total = 10 * 9 * 8 = 720.
Correct Answer:
A
— 720
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Q. If a password consists of 3 letters followed by 2 digits, how many different passwords can be formed using the first 3 letters of the alphabet and the first 5 digits?
A.
150
B.
180
C.
120
D.
100
Show solution
Solution
The number of ways to choose 3 letters from 3 is 3! and 2 digits from 5 is 5P2. Total = 3! * 5P2 = 6 * 20 = 120.
Correct Answer:
B
— 180
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Q. If a password consists of 3 letters followed by 2 digits, how many different passwords can be formed using the English alphabet and digits?
A.
17576000
B.
456976
C.
100000
D.
1000
Show solution
Solution
There are 26 letters and 10 digits. The total combinations are 26^3 * 10^2 = 17576000.
Correct Answer:
A
— 17576000
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Q. If a password consists of 3 letters followed by 2 digits, how many different passwords can be formed using 26 letters and 10 digits?
A.
676000
B.
6760000
C.
67600
D.
6760
Show solution
Solution
The number of passwords is 26^3 * 10^2 = 17576000.
Correct Answer:
A
— 676000
Learn More →
Showing 31 to 60 of 329 (11 Pages)
Modern Math MCQ & Objective Questions
Modern Math is a crucial component of the curriculum for students preparing for school and competitive exams in India. Mastering this subject not only enhances problem-solving skills but also boosts confidence during exams. Practicing MCQs and objective questions is essential for effective exam preparation, as they help identify important questions and clarify key concepts.
What You Will Practise Here
Sets, Relations, and Functions
Probability and Statistics
Linear Equations and Inequalities
Quadratic Equations and Functions
Mathematical Reasoning and Proofs
Sequences and Series
Graphs and their Interpretations
Exam Relevance
Modern Math is frequently tested in various examinations, including CBSE, State Boards, NEET, and JEE. Students can expect questions that assess their understanding of concepts through problem-solving and application. Common question patterns include multiple-choice questions that require students to select the correct answer from given options, as well as numerical problems that test their analytical skills.
Common Mistakes Students Make
Misinterpreting the question stem, leading to incorrect answers.
Overlooking the importance of units in probability and statistics.
Confusing different types of functions and their properties.
Neglecting to check for extraneous solutions in equations.
Failing to apply the correct formulas in problem-solving scenarios.
FAQs
Question: What are some effective strategies for solving Modern Math MCQs?Answer: Focus on understanding the concepts, practice regularly, and review previous years' question papers to familiarize yourself with common patterns.
Question: How can I improve my speed in answering objective questions?Answer: Regular practice with timed quizzes can help enhance your speed and accuracy in answering questions.
Start your journey towards mastering Modern Math today! Solve practice MCQs to test your understanding and reinforce your knowledge. Remember, consistent practice is key to success in your exams!
