The number of distinct terms in the expansion of x -1- x - x 2-1- x 215 is Different power of X means different termsA- 60B- 61C- 30D- 31

The correct option is B 61(x + 1x + x^2 + 1x^2)^15 = (x^3 + x + x^4 + 1x^2)^15 = (1+x+x^3+ x^4 )^15x^30 = a_0 + a_1 x + a_2x^2 + ... + a_60x^60x^30 Hence, ...

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Standard XII

Mathematics

Multinomial Expansion

The number of...

Question

The number of distinct terms in the expansion of ${(x + \frac{1}{x} + x^{2} + \frac{1}{x^{2}})}^{15}$ is
(Different power of $x$ means different terms)

60

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61

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30

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31

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Solution

The correct option is B $61$
${(x + \frac{1}{x} + x^{2} + \frac{1}{x^{2}})}^{15} = {(\frac{x^{3} + x + x^{4} + 1}{x^{2}})}^{15} = \frac{(1 + x + x^{3} + x^{4})^{15}}{x^{30}} = \frac{a_{0} + a_{1} x + a_{2} x^{2} + . . . + a_{60} x^{60}}{x^{30}}$

Hence, the total number of terms is $61$

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The number of distinct terms in the expansion of (x+1x+x2+1x2)15 is (Different power of x means different terms)

The correct option is B 61(x+1x+x2+1x2)15=(x3+x+x4+1x2)15=(1+x+x3+x4)15x30=a0+a1x+a2x2+...+a60x60x30 Hence, the total number of terms is 61

The number of distinct terms in the expansion of ${(x + \frac{1}{x} + x^{2} + \frac{1}{x^{2}})}^{15}$ is
(Different power of $x$ means different terms)

The correct option is B $61$
${(x + \frac{1}{x} + x^{2} + \frac{1}{x^{2}})}^{15} = {(\frac{x^{3} + x + x^{4} + 1}{x^{2}})}^{15} = \frac{(1 + x + x^{3} + x^{4})^{15}}{x^{30}} = \frac{a_{0} + a_{1} x + a_{2} x^{2} + . . . + a_{60} x^{60}}{x^{30}}$

Hence, the total number of terms is $61$