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# Binomial Expression | TOMATO B.Stat Objective 117

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

Cefficient

Binomials

Combinations

## Check the Answer

Answer:${10 \choose 1}+{10 \choose 2}$.

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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