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!
Q. A bag contains 4 white and 6 black balls. If two balls are drawn at random, what is the probability that both are black?
A.
0.5
B.
0.24
C.
0.36
D.
0.4
Show solution
Solution
P(both black) = (6/10) * (5/9) = 30/90 = 1/3 ≈ 0.333.
Correct Answer:
B
— 0.24
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Q. A bag contains 5 red balls and 3 blue balls. If one ball is drawn at random, what is the probability that it is blue?
A.
1/8
B.
3/8
C.
1/3
D.
3/5
Show solution
Solution
The probability of drawing a blue ball is 3/(5+3) = 3/8.
Correct Answer:
B
— 3/8
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Q. A bag contains 5 red, 3 blue, and 2 green balls. If one ball is drawn at random, what is the probability that it is not blue?
A.
0.5
B.
0.6
C.
0.7
D.
0.8
Show solution
Solution
The total number of balls is 10. The number of non-blue balls is 7 (5 red + 2 green). Thus, the probability is 7/10 = 0.7.
Correct Answer:
C
— 0.7
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Q. A box contains 3 red balls and 2 blue balls. In how many ways can 2 balls be selected from the box?
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Solution
The number of ways to choose 2 balls from 5 is 5C2 = 10.
Correct Answer:
B
— 6
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Q. A box contains 3 red, 2 blue, and 5 green balls. If one ball is drawn at random, what is the probability that it is either red or blue?
A.
0.5
B.
0.25
C.
0.625
D.
0.75
Show solution
Solution
Total balls = 3 + 2 + 5 = 10. Probability of red or blue = (3 + 2) / 10 = 5 / 10 = 0.5.
Correct Answer:
C
— 0.625
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Q. A box contains 4 white and 6 black balls. If two balls are drawn at random, what is the probability that both are white?
A.
1/15
B.
2/15
C.
1/10
D.
1/5
Show solution
Solution
The probability of drawing 2 white balls is (4/10) * (3/9) = 12/90 = 1/15.
Correct Answer:
A
— 1/15
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Q. A card is drawn from a standard deck of 52 cards. What is the probability that it is a heart or a queen?
A.
1/4
B.
1/13
C.
4/52
D.
17/52
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Solution
There are 13 hearts and 4 queens, but one queen is a heart. So, the probability is (13 + 4 - 1)/52 = 16/52 = 4/13.
Correct Answer:
D
— 17/52
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Q. A card is drawn from a standard deck of 52 cards. What is the probability that the card is a heart or a queen?
A.
1/4
B.
1/13
C.
4/52
D.
17/52
Show solution
Solution
There are 13 hearts and 4 queens, but one of the queens is a heart. Thus, the probability is (13 + 4 - 1)/52 = 16/52 = 4/13.
Correct Answer:
D
— 17/52
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Q. A group of friends consists of 10 people. If 6 like football, 4 like basketball, and 2 like both, how many like neither sport?
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Solution
Using the inclusion-exclusion principle: Total liking at least one sport = 6 + 4 - 2 = 8. Therefore, those liking neither = 10 - 8 = 2.
Correct Answer:
C
— 6
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Q. A group of friends consists of 12 people who like either football or basketball. If 7 like football and 5 like both, how many like only basketball?
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Solution
Let B be the number of basketball players. Total = Football + Basketball - Both. 12 = 7 + B - 5. Thus, B = 10, and only basketball = 10 - 5 = 5.
Correct Answer:
B
— 2
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Q. A group of friends consists of 12 people who like either football or basketball. If 7 like football and 5 like basketball, how many like both?
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Solution
Using the principle of inclusion-exclusion: Total = Football + Basketball - Both. Thus, 12 = 7 + 5 - Both, leading to Both = 0.
Correct Answer:
B
— 2
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Q. A group of friends consists of 12 people who play football, 8 who play basketball, and 5 who play both. How many play only football?
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Solution
To find the number of people who play only football, we subtract those who play both from those who play football: 12 - 5 = 7.
Correct Answer:
A
— 7
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Q. A group of friends consists of 12 who play football, 8 who play basketball, and 5 who play both. How many play only football?
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Solution
To find the number of friends who play only football, we subtract those who play both from those who play football: 12 - 5 = 7.
Correct Answer:
C
— 7
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Q. A group of friends consists of 5 people who like football, 3 who like basketball, and 2 who like both. How many like only football? (2023)
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Solution
To find the number of friends who like only football, we subtract those who like both from those who like football: 5 - 2 = 3.
Correct Answer:
A
— 3
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Q. A group of friends consists of 5 people who play football, 4 who play basketball, and 2 who play both. How many friends play only one sport?
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Solution
To find the number of friends who play only one sport, we calculate: (Football only + Basketball only) = (5 - 2) + (4 - 2) = 3 + 2 = 5.
Correct Answer:
B
— 7
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Q. A group of friends consists of 5 who like football, 4 who like basketball, and 2 who like both. How many friends like only football?
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Solution
The number of friends who like only football is calculated as: Only Football = Total Football - Both = 5 - 2 = 3.
Correct Answer:
A
— 3
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Q. A password consists of 3 letters followed by 2 digits. How many different passwords can be formed if letters can be repeated but digits cannot? (2000)
A.
17576
B.
15600
C.
13000
D.
12000
Show solution
Solution
There are 26 choices for each letter (3 letters) and 10 choices for the first digit and 9 for the second. Total = 26^3 * 10 * 9 = 17576.
Correct Answer:
A
— 17576
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Q. A student has a 70% chance of passing an exam. If he takes the exam twice, what is the probability that he passes at least once?
A.
0.49
B.
0.91
C.
0.51
D.
0.70
Show solution
Solution
The probability of passing at least once is 1 - (0.3^2) = 1 - 0.09 = 0.91.
Correct Answer:
B
— 0.91
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Q. A survey shows that 70% of people like dogs, 50% like cats, and 20% like both. What percentage of people like either dogs or cats?
A.
100%
B.
90%
C.
80%
D.
70%
Show solution
Solution
Using inclusion-exclusion, the percentage of people who like either dogs or cats is: 70% + 50% - 20% = 100%.
Correct Answer:
C
— 80%
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Q. From a group of 8 people, how many ways can a team of 4 be selected?
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Solution
The number of ways to choose 4 people from 8 is given by 8C4 = 70.
Correct Answer:
B
— 56
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Q. How many different ways can 3 men and 2 women be seated in a row?
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Solution
The number of arrangements of 5 people (3 men + 2 women) is 5! = 120.
Correct Answer:
B
— 120
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Q. How many different ways can the letters of the word 'SCHOOL' be arranged?
A.
720
B.
360
C.
480
D.
600
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Solution
The word 'SCHOOL' has 6 letters with 'O' repeated twice. The arrangements are 6! / 2! = 720 / 2 = 360.
Correct Answer:
B
— 360
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Q. How many ways can 5 different colored balls be placed in 3 different boxes if each box can hold any number of balls?
A.
243
B.
125
C.
256
D.
3125
Show solution
Solution
Each ball has 3 choices (boxes), so for 5 balls, the total arrangements = 3^5 = 243.
Correct Answer:
A
— 243
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Q. How many ways can 5 students be seated in a row of 5 chairs?
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Solution
The number of ways to arrange 5 students in 5 chairs is 5! = 120.
Correct Answer:
A
— 120
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Q. How many ways can the letters of the word 'LEVEL' be arranged?
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Solution
The word 'LEVEL' has 5 letters with 'E' repeated twice. The arrangements are 5! / 2! = 60 / 2 = 30.
Correct Answer:
B
— 30
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Q. If 15 students like both History and Geography, 25 like History, and 20 like Geography, how many students like only Geography?
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Solution
The number of students who like only Geography is: 20 - 15 = 5.
Correct Answer:
A
— 5
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Q. If 25% of a group like tea, 15% like coffee, and 5% like both, what percentage like either tea or coffee?
A.
35%
B.
30%
C.
25%
D.
20%
Show solution
Solution
Using inclusion-exclusion, the percentage who like either is 25% + 15% - 5% = 35%.
Correct Answer:
A
— 35%
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Q. If 25% of a group like tea, 35% like coffee, and 10% like both, what percentage like only tea?
A.
15%
B.
25%
C.
10%
D.
20%
Show solution
Solution
The percentage who like only tea is 25% - 10% = 15%.
Correct Answer:
A
— 15%
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Q. If 25% of a group of 200 people like sports, 15% like music, and 5% like both, what percentage of people like only sports?
A.
20%
B.
15%
C.
10%
D.
5%
Show solution
Solution
The percentage of people who like only sports is 25% - 5% = 20%.
Correct Answer:
A
— 20%
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Q. If 25% of a group of 200 people like tea, 15% like coffee, and 5% like both, what percentage like only tea?
A.
20%
B.
15%
C.
10%
D.
5%
Show solution
Solution
The number of people who like only tea is 25% of 200 - 5% of 200 = 20%.
Correct Answer:
A
— 20%
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