Beta Question Bank for Engineering: Mathematics>Chapter 8 - Binomial Theorem>EXERCISE-2>Q 15

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IMPORTANT

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The binomial expansion of ${(x^{k} + \frac{1}{x^{2 k}})}^{3 n}, n \in N$ contains a term independent of $x$

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Important Questions on Binomial Theorem

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 8 - Binomial Theorem>EXERCISE-2>Q 16

Let

n \in N

. If

{(1 + x)}^{n} = a_{o} + a_{1} x + a_{2} x^{2} + . . . . + a_{n} x^{n}

and

a_{n - 3}, a_{n - 2}, a_{n - 1}

are in

A . P

, then

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Beta Question Bank for Engineering: Mathematics>Chapter 8 - Binomial Theorem>EXERCISE-2>Q 17

If the coefficients of three consecutive terms in the expansion of

{(1 + x)}^{n}

are in ratio of

1 : 7 : 42,

then

n

is divisible by

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 8 - Binomial Theorem>EXERCISE-2>Q 18

In the expansion of

{(\sqrt[3]{4} + \frac{1}{\sqrt[4]{6}})}^{20}

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Beta Question Bank for Engineering: Mathematics>Chapter 8 - Binomial Theorem>EXERCISE-2>Q 19

If

{(1 + x + x^{2} + x^{3})}^{100} = a_{0} + a_{1} x + a_{2} x^{2} + . . . + a_{300} x^{300}

, then

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Beta Question Bank for Engineering: Mathematics>Chapter 8 - Binomial Theorem>EXERCISE-2>Q 20

The number

101^{100} - 1

is divisible by

HARD

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 8 - Binomial Theorem>EXERCISE-2>Q 21

If

{(9 + \sqrt{80})}^{n} = l + f

where

l, n

are integers and

0 < f < 1

, then

HARD

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 8 - Binomial Theorem>EXERCISE-2>Q 22

In the expansion of

{(x^{\frac{2}{3}} - \frac{1}{\sqrt{x}})}^{30}

, a term containing the power

x^{13}

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 8 - Binomial Theorem>EXERCISE-2>Q 23

The co-efficient of the middle term in the expansion of

{(1 + x)}^{2 n}

is