Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>Assignment>Q 5

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If the second, third and fourth terms in the expansion of $(x + y)^{n}$ be $135, 30$ and $\frac{10}{3}$ respectively, then

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Important Questions on Binomial Theorem

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Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>Assignment>Q 6

\sum_{r = 0}^{6} {(- 1)}^{r} (\begin{matrix} 16 \\ r \end{matrix})

is divisible by

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Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>Assignment>Q 7

If

{(1 + 2 x + 3 x^{2})}^{10} = a_{0} + a_{1} x + a_{2} x^{2} + \dots . + a_{20} x^{20},

then

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Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>Assignment>Q 8

The maximum value of

{}^{n}C_{r}

is obtained when

r

is equal to:

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Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>Assignment>Q 9

Given that the

4^{th}

term in the expansion of

{(2 + \frac{3 x}{8})}^{10}

has the maximum numerical value, then

x

can lie in the interval(s)

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Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>Assignment>Q 10

The value of the expression

C_{0}^{2} - C_{1}^{2} + C_{2}^{2} - \dots \dots . + (- 1)^{n} C_{n}^{2}

is

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Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>Assignment>Q 11

The number

101^{100} - 1

is divisible by

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Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>Assignment>Q 12

If

n

is a positive integer and

(3 \sqrt{3} + 5)^{2 n + 1} = I + f

, where

I

is an integer and

0 < f < 1

, then

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Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>Assignment>Q 13

If

n

is a positive integer and if

{(1 + x + x^{2})}^{n} = \sum_{r = 0}^{2 n} a_{r} x^{r}

, then