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Questions  >>  CBSE XI  >>  Math  >>  Binomial Theorem
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Q)

Expand the expression:$(101)^4$

$\begin{array}{1 1}(A)\;104060401\\(B)\;1078650\\(C)\;1020060401\\(D)\;\text{None of these}\end{array} $

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A)
Toolbox:
  • $(1+x)^n=nC_0+nC_1x+nC_2x^2+......nC_rx^r+.....+nC_xx^n$
$(101)^4=(100+1)^4$
$(100+1)^4=4C_0(100)^4+4C_1(100)^3.1+4C_2(100)^2.1^2+4C_3(100).1^3+4C_4(100)^0.1^4$
$\Rightarrow 100000000+4\times 1000000+6\times 10000+4\times 100+1$
$\Rightarrow 100000000+4000000+60000+400+1$
$\Rightarrow 104060401$
Hence (A) is the correct answer.
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