Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>EXERCISE>Q 20

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If $S_{n} = C_{0} C_{1} + C_{1} C_{2} + \dots \dots + C_{n - 1} C_{n}$ and $\frac{S_{n + 1}}{S_{n}} = \frac{15}{4}$ , then value of $n$ is equal to

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Important Questions on Binomial Theorem

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Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>EXERCISE>Q 21

If number of terms in the expansion of

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

are

45

then

n

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>EXERCISE>Q 22

Coefficient of

x^{11}

in the expansion of

{(2 x^{2} + x - 3)}^{6}

is

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Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>EXERCISE>Q 24

If

a_{r}

is the coefficient of

x^{r},

in the expansion of

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

then

a_{1} - 2 a_{2} + 3 a_{3} - \dots - 2 n a_{2 n} =

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Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>EXERCISE>Q 25

The coefficient of

x^{50}

in

{(1 + x)}^{41} {(1 - x + x^{2})}^{40}

is

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Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>EXERCISE>Q 27

Find the sum of

3 .^{n} C_{0} - 8 . {}^{n}C_{1} + 13 . {}^{n}C_{2} - 18 . {}^{n}C_{3} + \dots \dots \dots .

upto

(n + 1)

terms.

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Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>EXERCISE>Q 28

Coefficient of

x^{r}

in the expansion of

{(1 - 2 x)}^{- 1 / 2}

is

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Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>EXERCISE>Q 29

Cube root of

217

is

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Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>EXERCISE>Q 30

1 + \frac{1}{3} x + \frac{1.4}{3.6} x^{2} + \frac{1.4.7}{3.6.9} x^{3} + \dots

is equal to