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  • If coefficient of  in <img alt="\small (1+x)^{101}\left(1-x+x^2\right)^{100}" src="https://e

If coefficient of \small x^n in \small (1+x)^{101}\left(1-x+x^2\right)^{100}  is non-zero, then n cannot be of the form  (t∈N)   
 

Option: 1

3t + 1 


Option: 2

3t


Option: 3

3t+2


Option: 4

4t+1


Answers (1)

\begin{aligned} & (1+\mathrm{x})\left(1+\mathrm{x}^3\right)^{100} \\ & =(1+\mathrm{x})\left({ }^{100} \mathrm{C}_0+{ }^{100} \mathrm{C}_1 \mathrm{x}^3\right. \\ & \left.+\ldots+{ }^{100} \mathrm{C}_{100} \mathrm{x}^{300}\right) \end{aligned}

Clearly n cannot be of the form 3 t+2.

Posted by

Sumit Saini

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