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Let C(n, r) = . The value of , is:

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  1. 40(2)40
  2. 40(2)39
  3. 41(2)40
  4. 41(2)39

Answer (Detailed Solution Below)

Option 4 : 41(2)39
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Detailed Solution

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Concept:

We are given the expression:

This is the sum of products of odd-index binomial coefficients weighted by their index values.

We use the identity:

Splitting it into even and odd:

For :

 

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Q1.In a binomial distribution, if the mean is 6 and the standard deviation is √2, then what are the values of the parameters n and p respectively?
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More Binomial Theorem Questions

Q1.In a binomial distribution, if the mean is 6 and the standard deviation is √2, then what are the values of the parameters n and p respectively?
Q2.What is the value of (U + V)W? 
Q3.What is V + W equal to? 
Q4.What is the remainder when 7n - 6n is divided by 36 for n = 100?
Q5.In the expansion of (1 + x)p (1 + x)q, if the coefficient of x3 is 35, then what is the value of (p + q)? 
Q6.Let C(n, r) = \(\binom{n}{r}\). The value of \(\sum_{k=0}^{20}(2 k+1) C(41,2 k+1)\), is:
Q7.The value of – 15C1 + 2. 15C2 – 3. 15C3 + …. -15. 15C1 + 14C1 + 14C3 + 14C5 + … 14C11 is
Q8.If n ≥ 2 is a positive integer, then the sum of the series n+1C2 + 2(2C2 + 3C2 + 4C2 + …. + nC2) is
Q9.The sum of all rational terms in the expansion of \(\left(2^{\frac{1}{5}} + 5^{\frac{1}{3}}\right)^{15}\) is equal to:
Q10.The term independent of x in the expansion of \(\left(\frac{3}{2} x^{2}-\frac{1}{3 x}\right)^{6}\) is
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