Consider the expansion x2-1-x15- What is the independent term in the given expansion-

The correct option is B 3003 The genral term can be written as T_r+1=^15C_r.x^2(15 r).1x^r=^15C_r.x^30 3r As we have to find that term which is indepe ...

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Standard IX

Mathematics

Algebraic Identities

Consider the ...

Question

Consider the expansion ${(x^{2} + \frac{1}{x})}^{15}$ . What is the independent term in the given expansion?

2103

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3003

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4503

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None of the above

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Solution

The correct option is B $3003$
The genral term can be written as $T_{r + 1} =^{15} C_{r} . x^{2 (15 - r)} . \frac{1}{x^{r}} =^{15} C_{r} . x^{30 - 3 r}$
As we have to find that term which is independent of x
So $\Rightarrow$ $30 - 3 r = 0$ $\Rightarrow$ $r = 10$
So the term is $^{15} C_{10} = 3003$

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Consider the expansion (x2+1x)15. What is the independent term in the given expansion?

The correct option is B 3003The genral term can be written as Tr+1=15Cr.x2(15−r).1xr=15Cr.x30−3rAs we have to find that term which is independent of xSo ⇒ 30−3r=0 ⇒ r=10So the term is 15C10=3003

Consider the expansion ${(x^{2} + \frac{1}{x})}^{15}$ . What is the independent term in the given expansion?

The correct option is B $3003$
The genral term can be written as $T_{r + 1} =^{15} C_{r} . x^{2 (15 - r)} . \frac{1}{x^{r}} =^{15} C_{r} . x^{30 - 3 r}$
As we have to find that term which is independent of x
So $\Rightarrow$ $30 - 3 r = 0$ $\Rightarrow$ $r = 10$
So the term is $^{15} C_{10} = 3003$