The value of r for which 20Cr 20C0- 20Cr-1 20C1- 20Cr-2 20C2 - - - 20C0 20Cr is maximum- is -

Let S= ^20C_r ^20C_0+ ^20C_r 1 ^20C_1+ ^20C_r 2 ^20C_2 + … + ^20C_0 ^20C_r The sum S is the coefficient of x^r in the expansion of (1+x)^20(x+1)^20=(1+x)^40 ...

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Byju's Answer

Standard XIII

Mathematics

Sum of Product of Binomial Coefficients

The value of ...

Question

The value of $r$ for which $^{20} C_{r}^{20} C_{0} +^{20} C_{r - 1}^{20} C_{1} +^{20} C_{r - 2}^{20} C_{2} + \dots +^{20} C_{0}^{20} C_{r}$ is maximum, is :

11

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Solution

The correct option is D $20$
Let $S =^{20} C_{r}^{20} C_{0} +^{20} C_{r - 1}^{20} C_{1} +^{20} C_{r - 2}^{20} C_{2} + \dots +^{20} C_{0}^{20} C_{r}$
The sum $S$ is the coefficient of $x^{r}$ in the expansion of $(1 + x)^{20} (x + 1)^{20} = (1 + x)^{40}$
$∴ S =^{40} C_{r}$
$S$ is maximum when $r = 20$

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Similar questions

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^{20} C_{r}^{20} C_{0} +^{20} C_{r - 1}^{20} C_{1} +^{20} C_{r - 2}^{20} C_{2} + \dots +^{20} C_{0}^{20} C_{r}

is maximum, is :

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is maximum, is :

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The value of r for which 20Cr 20C0+ 20Cr−1 20C1+ 20Cr−2 20C2+…+ 20C0 20Cr is maximum, is :

The correct option is D 20Let S= 20Cr 20C0+ 20Cr−1 20C1+ 20Cr−2 20C2+…+ 20C0 20Cr The sum S is the coefficient of xr in the expansion of (1+x)20(x+1)20=(1+x)40 ∴S= 40Cr S is maximum when r=20

The value of $r$ for which $^{20} C_{r}^{20} C_{0} +^{20} C_{r - 1}^{20} C_{1} +^{20} C_{r - 2}^{20} C_{2} + \dots +^{20} C_{0}^{20} C_{r}$ is maximum, is :