Try this problem from I.S.I. B.Stat Entrance Objective Problem based on Binomial Expression.

Binomial Expression ( B.Stat Objective Question )


The coefficient of \(x^{2}\) in the binomial expression of \((1+x+x^{2})^{10}\) is

  • \({10 \choose 1}\)
  • \({10 \choose 1}+{10 \choose 2}\)
  • 0
  • none of these

Key Concepts


Cefficient

Binomials

Combinations

Check the Answer


But try the problem first…

Answer:\({10 \choose 1}+{10 \choose 2}\).

Source
Suggested Reading

B.Stat Objective Problem 117

Challenges and Thrills of Pre-College Mathematics by University Press

Try with Hints


First hint

\((\frac{1-x^{3}}{1-x})^{10}\)

=\((1-x^{3})^{10}(1-x)^{-10}\)

=\((1-{10 \choose 1}x^{3}\)

\(+{10 \choose 2}x^{6}+….)(1-10(-x)\)

\(+\frac{(-10)(-10)-1}{2}(-x)^{2}+…..)\)

Second Hint

coefficient of \(x^{2}\)=\(\frac{(-10)((-10)-1)}{2}\)

Final Step

=\({10 \choose 1}+{10 \choose 2}\).

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