Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>Assignment>Q 36

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The number of terms which are not similar in the expansion of $(I + m + n)^{6}$ is

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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 37

If sum of the coefficients in the expansion of

(2 x + 3 y - 2 z)^{n}

is

2187

then the greatest coefficient in the expansion of

(1 + x)^{n}

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Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>Assignment>Q 38

If

(1 + x)^{n} = \sum_{r = 0}^{n} C_{r} \cdot x^{r}

, then

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

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Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>Assignment>Q 39

The sum of the last eight coefficients in the expansion of

(1 + x)^{16}

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>Assignment>Q 40

If

n

is an integer greater than

1

, then

a - {}^{n}C_{1} (a - 1) + {}^{n}C_{2} (a - 2) - \dots + (- 1)^{n} (a - n) =

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Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>Assignment>Q 41

If

k = \sum_{r = 0}^{n} \frac{1}{{}^{n}C_{r}}

, then

\sum_{r = 0}^{n} \frac{r}{{}^{n}C_{r}}

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>Assignment>Q 42

\sum_{r = 1}^{n} r ({}^{n}C_{r} - {}^{n}C_{r - 1})

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>Assignment>Q 43

The coefficient of

x^{4}

in the expansion of

{(1 + x + x^{2} + x^{3})}^{11}

is

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Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>Assignment>Q 44

The number of zeroes at the end of

(101)^{11} - 1

is