Alpha Question Bank for Engineering: Mathematics>Chapter 7 - Binomial Theorem>Exercise-1>Q 40

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Earn 100

The total number of terms in the expansion of $(x + a)^{100} + (x - a)^{100}$ after simplification is

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Important Questions on Binomial Theorem

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Alpha Question Bank for Engineering: Mathematics>Chapter 7 - Binomial Theorem>Exercise-1>Q 41

The value of

\frac{18^{3} + 7^{3} + 3 \cdot 18 \cdot 7 \cdot 25}{3^{6} + 6 \cdot 243 \cdot 2 + 15 \cdot 81 \cdot 4 + 20 \cdot 27 \cdot 8 + 15 \cdot 9 \cdot 16 + 6 \cdot 3 \cdot 32 + 64}

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 7 - Binomial Theorem>Exercise-1>Q 42

In the expansion of

{(3 - \sqrt{\frac{17}{4} + 3 \sqrt{2}})}^{15}

, the

11^{th}

term is a

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Alpha Question Bank for Engineering: Mathematics>Chapter 7 - Binomial Theorem>Exercise-1>Q 43

If the second term of the expansion

{[a^{\frac{1}{13}} + \frac{a}{\sqrt{a^{- 1}}}]}^{n}

is

14 a^{\frac{5}{2}}

, then the value of

\frac{{}^{n}C_{3}}{{}^{n}C_{2}}

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 7 - Binomial Theorem>Exercise-1>Q 44

In the expansion of

{(7^{\frac{1}{3}} + 11^{\frac{1}{9}})}^{6561},

the number of terms free from radicals is

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Alpha Question Bank for Engineering: Mathematics>Chapter 7 - Binomial Theorem>Exercise-1>Q 45

The value of

m,

for which the coefficients of the

{(2 m + 1)}^{th}

and

{(4 m + 5)}^{th}

terms in the expansion of

(1 + x)^{10}

are equal, is

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Alpha Question Bank for Engineering: Mathematics>Chapter 7 - Binomial Theorem>Exercise-1>Q 46

The co-efficient of

x

in the expansion of

(1 - 2 x^{3} + 3 x^{5}) {(1 + \frac{1}{x})}^{8}

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 7 - Binomial Theorem>Exercise-1>Q 47

Given that the term of the expansion

{(x^{\frac{1}{3}} - x^{\frac{- 1}{2}})}^{15}

which does not contain

x

is

5 m,

where

m \in N,

then

m =

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Alpha Question Bank for Engineering: Mathematics>Chapter 7 - Binomial Theorem>Exercise-1>Q 48

The term independent of

x

in the expansion of

{(x - \frac{1}{x})}^{4} {(x + \frac{1}{x})}^{3}

is