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# Binomial Expression | TOMATO B.Stat Objective 117

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Binomial Expression. You may use sequential hints to solve the problem.

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

But try the problem first…

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

Source

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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