The number of non-zero terms is the expansion of

\left [ (1+3\sqrt{2}\: x)^{9} +(1-3\sqrt{2}\: x)^{9}\right ] is

  • Option 1)

    9

  • Option 2)

    10

  • Option 3)

    5

  • Option 4)

    None of these

 

Answers (1)

As discussed in concept

Properties of Binomial Theorem -

\left ( x+a \right )^{n}+\left ( x-a \right )^{n}= 2\left ( ^{n}c_{0} \, x^{n}+ ^{n}c_{2}\, x^{n-2}\, a^{2}+---\right )

- wherein

Sum of odd terms or even Binomial coefficients

 

 We get

2(1+^9{C_{2}} (3\sqrt{2x})^{2}+^9{C_{4}}(3\sqrt{2x})^{4}+^9{C_{6}}(3\sqrt{2x})^{6}+^9{C_{8}}(3\sqrt{2x})^{8})

We have 5 non-zero terms


Option 1)

9

This is incorrect option

Option 2)

10

This is incorrect option

Option 3)

5

This is correct option

Option 4)

None of these

This is incorrect option

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