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 The value of

  • Option 1)

    221−210

  • Option 2)

     220−29

  • Option 3)

    220−210

  • Option 4)

     221−211

     

 

Answers (1)

best_answer

As we learnt in

Sum of Binomial Coefficients -

(x+a)^{n}= ^{n}c_{0}x^{n}a^{0}+^{n}c_{r}x^{n-1}a+^{n}c_{2}x^{n-2}a^{2}+---

x= a= 1:

\therefore c_{0}+c_{1}+c_{2}+c_{3}+----= 2^{n}

-

 

 ^{10}C_{0}+\ ^{10}C_{1}+\ ^{10}C_{2}+\ ^{10}C_{3}+........+ +\ ^{10}C_{10}=2^{10}

Thus, \ ^{10}C_{1}+\ ^{10}C_{2}+........+ +\ ^{10}C_{10}=(2^{10}-1)

Also \ ^{21}C_{0}+\ ^{21}C_{1}+\ ^{21}C_{2}+........+\ ^{21}C_{21}=2^{21}

Thus \ ^{21}C_{1}+\ ^{21}C_{2}+........+\ ^{21}C_{10}=\frac{2^{21}}{2}-1=\frac{2^{20}}{2}-1

We get (2^{20}-1)-(2^{10}-1)=2^{20}-2^{10}

 


Option 1)

221−210

This is an incorrect option.

Option 2)

 220−29

This is an incorrect option.

Option 3)

220−210

This is the correct option.

Option 4)

 221−211

 

This is an incorrect option.

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Aadil

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