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Count the Medals!!! Video Lecture | Sets and Functions - JEE
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39 videos|11 docs
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FAQs on Count the Medals!!! Video Lecture - Sets and Functions - JEE
| 1. How many medals did India win at the JEE exam? |  |
Ans. India won a total of 5 medals at the JEE exam.
| 2. Who were the recipients of the medals at the JEE exam? | |
Ans. The names of the recipients of the medals at the JEE exam have not been mentioned in the article.
| 3. What criteria are used to award medals at the JEE exam? | |
Ans. The article does not provide information about the specific criteria used to award medals at the JEE exam.
| 4. How does the number of medals won at the JEE exam compare to previous years? | |
Ans. The article does not compare the number of medals won at the JEE exam to previous years.
| 5. Are there any special recognition or rewards associated with winning a medal at the JEE exam? | |
Ans. The article does not mention any special recognition or rewards associated with winning a medal at the JEE exam.
Text Transcript from Video
A college awarded 38 medals in football, 15 in basketball and 20 in cricket.
If these medals went to a total of 58 men and
only three men got medals in all the three sports,
how many received medals in exactly two of the three sports?
You may pause the video while you figure it out.
Let's walk through the solution.
The answer to this problem is 9.
9 medals were received by exactly two of the three sports.
Let F, B and C denote the set of men who received medals in football, basketball and cricket respectively.
Let p denotes the number of men who got medals in football and basketball only,
q denotes the number of men who got medals in football and cricket only,
r denotes the number of men who got medals in basketball and cricket only and
s denotes the number of men who got metal in all the three sports.
As per the problem, the total number of men who received medals are 58
out of which the number of men who received metals in football are 38,
the number of men who received metals in basketball are 15,
the number of men who received medals in cricket are 20 and
the number of men who received the medals in all the three sports are 3.
As It can be seen from Venn diagram,
the number of men who received medals in exactly two of the three sports = p + q + r.
So we need to determine this sum and to determine that, we can make use of this equation
The number of elements in F intersection B are p + s,
the number of elements in B intersection C are r + s and
the number of elements in C intersection F are q + s.
Now we substitute the value of other remaining terms.
Solving this equation we get, p + q + r + 3s = 18.
We know s = 3.
Substituting its value and solving further,
we get p + q + r = 9.
Therefore the number of men who received medals in exactly two of the three sports equals nine
Thanks for watching this video and do subscribe to this channel for more such videos
If these medals went to a total of 58 men and
only three men got medals in all the three sports,
how many received medals in exactly two of the three sports?
You may pause the video while you figure it out.
Let's walk through the solution.
The answer to this problem is 9.
9 medals were received by exactly two of the three sports.
Let F, B and C denote the set of men who received medals in football, basketball and cricket respectively.
Let p denotes the number of men who got medals in football and basketball only,
q denotes the number of men who got medals in football and cricket only,
r denotes the number of men who got medals in basketball and cricket only and
s denotes the number of men who got metal in all the three sports.
As per the problem, the total number of men who received medals are 58
out of which the number of men who received metals in football are 38,
the number of men who received metals in basketball are 15,
the number of men who received medals in cricket are 20 and
the number of men who received the medals in all the three sports are 3.
As It can be seen from Venn diagram,
the number of men who received medals in exactly two of the three sports = p + q + r.
So we need to determine this sum and to determine that, we can make use of this equation
The number of elements in F intersection B are p + s,
the number of elements in B intersection C are r + s and
the number of elements in C intersection F are q + s.
Now we substitute the value of other remaining terms.
Solving this equation we get, p + q + r + 3s = 18.
We know s = 3.
Substituting its value and solving further,
we get p + q + r = 9.
Therefore the number of men who received medals in exactly two of the three sports equals nine
Thanks for watching this video and do subscribe to this channel for more such videos
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About this Video
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Nov 23, 2024 Last updated |
Video Description: Count the Medals!!! for JEE 2024 is part of Sets and Functions preparation.
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