CA Foundation Exam > CA Foundation Questions > If 28C2r : 24C2r –4 = 225 : 11, then th...
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If 28C2r : 24 C2r –4 = 225 : 11, then the value of r is
- a)7
- b)5
- c)6
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If 28C2r : 24C2r –4 = 225 : 11, then the value of r isa)7b)5c)6d...
In the problem given it is n in place of 2r..
28Cn : 24 C(n-4) = 225 : 11
Answer = n = 11
Most Upvoted Answer
If 28C2r : 24C2r –4 = 225 : 11, then the value of r isa)7b)5c)6d...
Solution:
Given,
28C2r : 24C2r+4 = 225 : 11
To find: Value of r
Let's simplify the given expression by using the formula nCr = n!/(r!*(n-r)!)
We get,
(28!/(2r!*(28-2r)!)) : (24!/(2r+4!*(24-2r-4)!)) = 225 : 11
Simplifying further,
((28*27)/(2*1))*((2r+3)*(2r+2)*(2r+1)) : ((24*23)/(2*1))*((2r+4)*(2r+3)*(2r+2)) = 225 : 11
Canceling the common factors, we get,
(28*27*(2r+3)*(2r+2)*(2r+1))/(2*1) : (24*23*(2r+4)*(2r+3)*(2r+2))/(2*1*4*3*2) = 225 : 11
On simplifying, we get
(14*27*(2r+3)*(2r+2)*(2r+1)) : (23*(2r+4)*(2r+3)*(2r+2)) = 225 : 11
Cross multiplying, we get,
31185*(2r+4)*(2r+3)*(2r+2) = 5292*(2r+3)*(2r+2)*(2r+1)
On simplifying, we get,
(2r+4) = 7
Therefore, r = 7/2 = 3.5
But r cannot be a fraction as it represents the number of items in a combination. Hence, the value of r is 7.
Therefore, option (a) is the correct answer.
Given,
28C2r : 24C2r+4 = 225 : 11
To find: Value of r
Let's simplify the given expression by using the formula nCr = n!/(r!*(n-r)!)
We get,
(28!/(2r!*(28-2r)!)) : (24!/(2r+4!*(24-2r-4)!)) = 225 : 11
Simplifying further,
((28*27)/(2*1))*((2r+3)*(2r+2)*(2r+1)) : ((24*23)/(2*1))*((2r+4)*(2r+3)*(2r+2)) = 225 : 11
Canceling the common factors, we get,
(28*27*(2r+3)*(2r+2)*(2r+1))/(2*1) : (24*23*(2r+4)*(2r+3)*(2r+2))/(2*1*4*3*2) = 225 : 11
On simplifying, we get
(14*27*(2r+3)*(2r+2)*(2r+1)) : (23*(2r+4)*(2r+3)*(2r+2)) = 225 : 11
Cross multiplying, we get,
31185*(2r+4)*(2r+3)*(2r+2) = 5292*(2r+3)*(2r+2)*(2r+1)
On simplifying, we get,
(2r+4) = 7
Therefore, r = 7/2 = 3.5
But r cannot be a fraction as it represents the number of items in a combination. Hence, the value of r is 7.
Therefore, option (a) is the correct answer.
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If 28C2r : 24C2r –4 = 225 : 11, then the value of r isa)7b)5c)6d)none of theseCorrect answer is option 'A'. Can you explain this answer?
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If 28C2r : 24C2r –4 = 225 : 11, then the value of r isa)7b)5c)6d)none of theseCorrect answer is option 'A'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If 28C2r : 24C2r –4 = 225 : 11, then the value of r isa)7b)5c)6d)none of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 28C2r : 24C2r –4 = 225 : 11, then the value of r isa)7b)5c)6d)none of theseCorrect answer is option 'A'. Can you explain this answer?.
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