Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 7 - Binomial Theorem>Exercise>Q 40

EASY

Agniveer Vayu

IMPORTANT

Earn 100

The value of $\frac{1}{2!} + \frac{2}{3!} + . . . + \frac{999}{1000!}$ is equal to

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Important Questions on Binomial Theorem

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Agniveer Vayu

IMPORTANT

Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 7 - Binomial Theorem>Exercise>Q 1

Coefficient of

x^{2009}

in

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

is

MEDIUM

Agniveer Vayu

IMPORTANT

Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 7 - Binomial Theorem>Exercise>Q 2

If

p^{4} + q^{3} = 2 (p > 0, q > 0)

, then the maximum value of term independent of

x

in the expansion of

{(p x^{\frac{1}{12}} + q x^{- \frac{1}{9}})}^{14}

is

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Agniveer Vayu

IMPORTANT

Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 7 - Binomial Theorem>Exercise>Q 3

The coefficient of

t^{8}

in the expansion of

{(1 + 2 t^{2} - t^{3})}^{9}

is:

EASY

Agniveer Vayu

IMPORTANT

Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 7 - Binomial Theorem>Exercise>Q 4

The term independent of

x

in the expansion of

{(9 x - \frac{1}{3 \sqrt{x}})}^{18}, x > 0

is

α

times the corresponding binomial coefficient. Then

α

is

EASY

Agniveer Vayu

IMPORTANT

Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 7 - Binomial Theorem>Exercise>Q 5

The

14^{t h}

term from the end in the expansion of

(\sqrt{x} - \sqrt{y})^{17}

is

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Agniveer Vayu

IMPORTANT

Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 7 - Binomial Theorem>Exercise>Q 6

The middle term in the expansion of

{(x^{2} - \frac{2}{x})}^{10}

is

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Agniveer Vayu

IMPORTANT

Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 7 - Binomial Theorem>Exercise>Q 7

The coefficient of

x^{7}

in the expansion of

{(x^{2} + \frac{1}{x})}^{11}

is

MEDIUM

Agniveer Vayu

IMPORTANT

Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 7 - Binomial Theorem>Exercise>Q 8

The term independent of

x

in the expansion of

{(\sqrt{x} + \frac{1}{3 x^{2}})}^{10}

is