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

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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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Important Questions on Binomial Theorem

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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

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Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>EXERCISE>Q 31

The first four terms in the expansion of

{(1 - x)}^{3 / 2}

will be when

|x| < 1

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Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>EXERCISE>Q 32

If

{(a + b x)}^{- 2} = \frac{1}{4} - 3 x + \dots,

then

(a, b) =

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Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>EXERCISE>Q 33

If the third term in the binomial expansion of

{(1 + x)}^{m}

is

- \frac{1}{8} x^{2},

then the rational value of

m

is