The 11th term in the expansion of x -1- x 14 isA- 999- XB- 1001- xC-D- x-1001

The correct option is B 1001/x nbsp;General term in the expansion is T_r+1= ^14C_r(x)^14 r (1/√(x))^r Put r=10, we get nbsp; T_11= ^14C_10(x)^14 10 (1/√(x ...

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Standard XII

Mathematics

Numerically Greatest Term

The 11th term...

Question

The $11^{th}$ term in the expansion of ${(x + \frac{1}{\sqrt{x}})}^{14}$ is

\frac{999}{x}

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\frac{1001}{x}

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i

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\frac{x}{1001}

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Solution

The correct option is B $\frac{1001}{x}$
General term in the expansion is
$T_{r + 1} =^{14} C_{r} (x)^{14 - r} {(\frac{1}{\sqrt{x}})}^{r}$
Put $r = 10,$ we get
$T_{11} =^{14} C_{10} (x)^{14 - 10} {(\frac{1}{\sqrt{x}})}^{10}$
$= \frac{1001}{x}$

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Similar questions

Q. The coefficient of

x^{50}

in the expansion of

(1 + x)^{1000} + 2 x (1 + x)^{999} + 3 x^{2} (1 + x)^{998} + . . . . . . + 1001 x^{1000}

Q. Coefficient of

x^{50}

{(1 + x)}^{1001} - x^{1001}

Q. Coefficient of

x^{2001}

in the expansion of

(1 + x + x^{2} + x^{3} + x^{4})^{1001} (1 - x)^{1002}

Q. Coefficient of

x^{2009}

(1 + x + x^{2} + x^{3} + x^{4})^{1001} (1 - x)^{1002}

Q. Find the coefficient of

x^{50}

in the expression

(1 + x)^{1000} + 2 x (1 + x)^{999} + 3 x^{2} (1 + x)^{998} + \dots \dots \dots + 1001 x^{1000}

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The 11th term in the expansion of (x+1√x)14 is

The correct option is B 1001x General term in the expansion is Tr+1= 14Cr(x)14−r(1√x)r Put r=10, we get T11= 14C10(x)14−10(1√x)10 =1001x

The $11^{th}$ term in the expansion of ${(x + \frac{1}{\sqrt{x}})}^{14}$ is

The correct option is B $\frac{1001}{x}$
General term in the expansion is
$T_{r + 1} =^{14} C_{r} (x)^{14 - r} {(\frac{1}{\sqrt{x}})}^{r}$
Put $r = 10,$ we get
$T_{11} =^{14} C_{10} (x)^{14 - 10} {(\frac{1}{\sqrt{x}})}^{10}$
$= \frac{1001}{x}$