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UPSC NDA II 2014 Mathematics Paper

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For the next five (05) items that follow:

Consider the expansion

\left(x^2+\frac{1}{x}\right)^{15}

[NDA II 2014]

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Question : 28 of 120

Marks: +1, -0

Consider the following statements :

1. There are 15 terms in the given expansion.

2. The coefficient of

x^{12}

is equal to that of

x^{3}

Which of the above statements is/are correct?

1 only
2 only
Both 1 and 2
Neither 1 nor 2

Solution:

There are 15+1 = 16 terms in the expansion. So statement 1 is wrong.

For the term having

x^{12},30-3r=12\Rightarrow r=6

Hence coefficient of

x^{12}

is

^{15}C_{6}

For the term having

x^{3},30-3r=3\Rightarrow r=9

Hence coefficient of

x^{3}

is

^{15}C_{9}

So statement 2 is also wrong.

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