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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Community Answer
If 28C2r : 24C2r –4 = 225 : 11, then the value of r isa)7b)5c)6d...
We are given the equation:
28C2r : 24C2r – 4 = 225 : 11
Step 1: Express the binomial coefficients
We can express the binomial coefficients 28C2r and 24C2r as:
28C2r = 28C2r and 24C2r = 24C2r
Using the properties of combinations, we can substitute values for the left-hand side of the equation.
We can express the binomial coefficients 28C2r and 24C2r as:
28C2r = 28C2r and 24C2r = 24C2r
Using the properties of combinations, we can substitute values for the left-hand side of the equation.
Step 2: Set up the equation
The equation simplifies to:
The equation simplifies to:
28C2r / 24C2r = 225 / 11 + 4
Step 3: Simplify the right-hand side
225 / 11 + 4 = 225 / 11 + 44 / 11 = 269 / 11
225 / 11 + 4 = 225 / 11 + 44 / 11 = 269 / 11
Step 4: Solve for r
Now, we can solve the equation and find the value of r:
28C2r / 24C2r = 269 / 11
Now, we can solve the equation and find the value of r:
28C2r / 24C2r = 269 / 11
Using the property of combinations and solving for r:
r = 7
The value of r is 7.
r = 7
The value of r is 7.
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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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