# The ratio of the coefficient of x15 to the term independent of x in x2+215x is ______. - Mathematics

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The ratio of the coefficient of x15 to the term independent of x in x^2 + 2^15/x is ______.

• 12:32

• 1:32

• 32:12

• 32:1

#### Solution

The ratio of the coefficient of x15 to the term independent of x in x^2 + 2^15/x is 1:32.

Explanation:

Let Tr+1 be the general term of x^2 + 2^15/x

So, Tr+1 = ""^15"C"_r  (x^2)^(15 - r)  2^r/x

= ""^15"C"_r (2)^r  x^(30 - 3r)  ....(1)

Now, for the coefficient of term containing x15

30 – 3r = 15

i.e., r = 5

Therefore, 15C5 (2)5 is the coefficient of x15   ....(From (1))

To find the term independent of x

Put 30 – 3r = 0

Thus 15C10 210 is the term independent of x ....(From (1))

Now the ratio is (""^15"C"_5  2^5)/(""^15"C"_10  2^10) = 1/2^5 = 1/32

Concept: General and Middle Terms
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#### APPEARS IN

NCERT Mathematics Exemplar Class 11
Chapter 8 Binomial Theorem
Solved Examples | Q 21 | Page 141

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