JEE Exam > JEE Questions > In a class of 100 students, 55 students have ...
Start Learning for Free
In a class of 100 students, 55 students have passed in Mathematics and 67 students have passed in Physics. Then the number of students who have passed in Physics only is:
- a)45
- b)22
- c)33
- d)10
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
In a class of 100 students, 55 students have passed in Mathematics and...
Let A be the set of students who have passed in Mathematics, and B be the set of students who have passed in Physics.
We are given that |A| = 55 and |B| = 67, where |A| and |B| represent the number of students in sets A and B, respectively.
We are also given that there are 100 students in total. We need to find the number of students who have passed in Physics only, which means we need to find |B - A|.
First, let's find the number of students who have passed in both Mathematics and Physics, which can be represented by |A ∩ B|.
Using the principle of inclusion-exclusion, we have:
|A ∪ B| = |A| + |B| - |A ∩ B|
Since there are 100 students in total, we can say that |A ∪ B| = 100.
Now, we can find |A ∩ B|:
100 = 55 + 67 - |A ∩ B|
100 = 122 - |A ∩ B|
|A ∩ B| = 22
Now, we can find the number of students who have passed in Physics only, which is |B - A|:
|B - A| = |B| - |A ∩ B|
|B - A| = 67 - 22
|B - A| = 45
so, the correct answer is 45.
We are given that |A| = 55 and |B| = 67, where |A| and |B| represent the number of students in sets A and B, respectively.
We are also given that there are 100 students in total. We need to find the number of students who have passed in Physics only, which means we need to find |B - A|.
First, let's find the number of students who have passed in both Mathematics and Physics, which can be represented by |A ∩ B|.
Using the principle of inclusion-exclusion, we have:
|A ∪ B| = |A| + |B| - |A ∩ B|
Since there are 100 students in total, we can say that |A ∪ B| = 100.
Now, we can find |A ∩ B|:
100 = 55 + 67 - |A ∩ B|
100 = 122 - |A ∩ B|
|A ∩ B| = 22
Now, we can find the number of students who have passed in Physics only, which is |B - A|:
|B - A| = |B| - |A ∩ B|
|B - A| = 67 - 22
|B - A| = 45
so, the correct answer is 45.
Most Upvoted Answer
In a class of 100 students, 55 students have passed in Mathematics and...
Solution:
Given, there are 100 students in a class, out of which 55 have passed in Mathematics and 67 have passed in Physics.
Let A be the set of students who have passed in Mathematics and B be the set of students who have passed in Physics.
Then, we have,
n(A) = 55
n(B) = 67
Now, we need to find the number of students who have passed in Physics only, i.e., the number of students in the set B but not in the set A.
Let x be the number of students who have passed in both Mathematics and Physics, i.e., the number of students in the intersection of sets A and B.
Then, we have,
n(A ∩ B) = x
Using the formula for the number of elements in a union of two sets, we have,
n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
Substituting the given values, we get,
n(A ∪ B) = 55 + 67 - x
Since the total number of students in the class is 100, we have,
n(A ∪ B) = 100
Substituting this in the above equation, we get,
100 = 55 + 67 - x
Simplifying, we get,
x = 22
Therefore, the number of students who have passed in Physics only is 67 - 22 = 45.
Hence, the correct option is (A).
Given, there are 100 students in a class, out of which 55 have passed in Mathematics and 67 have passed in Physics.
Let A be the set of students who have passed in Mathematics and B be the set of students who have passed in Physics.
Then, we have,
n(A) = 55
n(B) = 67
Now, we need to find the number of students who have passed in Physics only, i.e., the number of students in the set B but not in the set A.
Let x be the number of students who have passed in both Mathematics and Physics, i.e., the number of students in the intersection of sets A and B.
Then, we have,
n(A ∩ B) = x
Using the formula for the number of elements in a union of two sets, we have,
n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
Substituting the given values, we get,
n(A ∪ B) = 55 + 67 - x
Since the total number of students in the class is 100, we have,
n(A ∪ B) = 100
Substituting this in the above equation, we get,
100 = 55 + 67 - x
Simplifying, we get,
x = 22
Therefore, the number of students who have passed in Physics only is 67 - 22 = 45.
Hence, the correct option is (A).
Community Answer
In a class of 100 students, 55 students have passed in Mathematics and...
Total number of students is 100
passed in only physics is 100-67=33
(correct answer is option C)
passed in only physics is 100-67=33
(correct answer is option C)
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
In a class of 100 students, 55 students have passed in Mathematics and 67 students have passed in Physics. Then the number of students who have passed in Physics only is:a)45b)22c)33d)10Correct answer is option 'A'. Can you explain this answer?
Question Description
In a class of 100 students, 55 students have passed in Mathematics and 67 students have passed in Physics. Then the number of students who have passed in Physics only is:a)45b)22c)33d)10Correct answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In a class of 100 students, 55 students have passed in Mathematics and 67 students have passed in Physics. Then the number of students who have passed in Physics only is:a)45b)22c)33d)10Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a class of 100 students, 55 students have passed in Mathematics and 67 students have passed in Physics. Then the number of students who have passed in Physics only is:a)45b)22c)33d)10Correct answer is option 'A'. Can you explain this answer?.
In a class of 100 students, 55 students have passed in Mathematics and 67 students have passed in Physics. Then the number of students who have passed in Physics only is:a)45b)22c)33d)10Correct answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In a class of 100 students, 55 students have passed in Mathematics and 67 students have passed in Physics. Then the number of students who have passed in Physics only is:a)45b)22c)33d)10Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a class of 100 students, 55 students have passed in Mathematics and 67 students have passed in Physics. Then the number of students who have passed in Physics only is:a)45b)22c)33d)10Correct answer is option 'A'. Can you explain this answer?.
Solutions for In a class of 100 students, 55 students have passed in Mathematics and 67 students have passed in Physics. Then the number of students who have passed in Physics only is:a)45b)22c)33d)10Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of In a class of 100 students, 55 students have passed in Mathematics and 67 students have passed in Physics. Then the number of students who have passed in Physics only is:a)45b)22c)33d)10Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
In a class of 100 students, 55 students have passed in Mathematics and 67 students have passed in Physics. Then the number of students who have passed in Physics only is:a)45b)22c)33d)10Correct answer is option 'A'. Can you explain this answer?, a detailed solution for In a class of 100 students, 55 students have passed in Mathematics and 67 students have passed in Physics. Then the number of students who have passed in Physics only is:a)45b)22c)33d)10Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of In a class of 100 students, 55 students have passed in Mathematics and 67 students have passed in Physics. Then the number of students who have passed in Physics only is:a)45b)22c)33d)10Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice In a class of 100 students, 55 students have passed in Mathematics and 67 students have passed in Physics. Then the number of students who have passed in Physics only is:a)45b)22c)33d)10Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup