The number of terms in the expansion of - a 3 - 1 a 3 -1 - 100 is

The correct option is A 201 (a^3+1/a^3+1)^100 1/a^300(1+a^3+a^6)^100 Here, terms will be in the form, a^0 ; a^3, a^6⋯ and highest power term ...

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Standard XII

Mathematics

Binomial Coefficients

The number of...

Question

The number of terms in the expansion of ${[a^{3} + \frac{1}{a^{3}} + 1]}^{100}$ is

201

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300

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200

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^{100} C_{3}

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Solution

The correct option is A $201$

${(a^{3} + \frac{1}{a^{3}} + 1)}^{100}$

$\frac{1}{a^{300}} {(1 + a^{3} + a^{6})}^{100}$

Here, terms will be in the form,

$a^{0}; a^{3}, a^{6} \dots$

and highest power term will be ${(a^{6})}^{100}$

This forms a A.P of powers,

$∴ 600 = 0 + (n - 1) 3$

$∴ n = 201$

$Option (a)$

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Similar questions

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The number of terms in the expansion of [a3+1a3+1]100 is

The correct option is A 201(a3+1a3+1)1001a300(1+a3+a6)100Here, terms will be in the form,a0;a3,a6⋯and highest power term will be (a6)100This forms a A.P of powers,∴600=0+(n−1)3∴n=201 Option (a)

The number of terms in the expansion of ${[a^{3} + \frac{1}{a^{3}} + 1]}^{100}$ is