Alpha Question Bank for Engineering: Mathematics>Chapter 7 - Binomial Theorem>Exercise-2>Q 52

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In the expansion of ${(x + y + z)}^{25}$

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Important Questions on Binomial Theorem

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Alpha Question Bank for Engineering: Mathematics>Chapter 7 - Binomial Theorem>Exercise-2>Q 53

If

{(1 + x + 2 x^{2})}^{20} = a_{0} + a_{1} x + a_{2} x^{2} + \dots \dots \dots + a_{40} x^{40},

then

a_{0} + a_{2} + a_{4} \dots \dots + a_{38}

is equal to

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Alpha Question Bank for Engineering: Mathematics>Chapter 7 - Binomial Theorem>Exercise-2>Q 54

$n^{n} {(\frac{n + 1}{2})}^{2 n}$ is $(n \in N)$

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Alpha Question Bank for Engineering: Mathematics>Chapter 7 - Binomial Theorem>Exercise-2>Q 55

If recursion polynomials

P_{k} (x)

are defined as

P_{1} (x) = {(x - 2)}^{2}, P_{2} (x) = {({(x - 2)}^{2} - 2)}^{2}

P_{3} (x) = {({({(x - 2)}^{2} - 2)}^{2} - 2)}^{2} \dots \dots \dots .

(In general

P_{k} (x) = {(P_{k - 1} (x) - 2)}^{2},

then the constant term in

P_{k} (x)

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 7 - Binomial Theorem>Exercise-2>Q 59

Let

X

be a set containing

' n'

elements. If two subsets

A

and

B

of

X

are picked at random. The probability of

A

and

B

having same number of elements

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Alpha Question Bank for Engineering: Mathematics>Chapter 7 - Binomial Theorem>Exercise-3>Q 1

Coefficient of

t^{24}

in

{(1 + t^{2})}^{12} (1 + t^{12}) (1 + t^{24})

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 7 - Binomial Theorem>Exercise-3>Q 2

Prove that

2^{k} (\begin{array}{l} n \\ 0 \end{array}) (\begin{array}{l} n \\ k \end{array}) - 2^{k - 1} (\begin{array}{l} n \\ 1 \end{array}) (\begin{array}{l} n - 1 \\ k - 1 \end{array}) + 2^{k - 2} (\begin{array}{l} n \\ 2 \end{array}) (\begin{array}{l} n - 2 \\ k - 2 \end{array}) - \dots \dots + (- 1)^{k} (\begin{array}{l} n \\ k \end{array}) (\begin{matrix} n - k \\ 0 \end{matrix}) = (\begin{array}{l} n \\ k \end{array})

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Alpha Question Bank for Engineering: Mathematics>Chapter 7 - Binomial Theorem>Exercise-3>Q 3

If ${}^{(n - 1)}C_{r} = {(k^{2} - 3)}^{n} C_{r + 1}$ then an interval in which $k$ lies is

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Alpha Question Bank for Engineering: Mathematics>Chapter 7 - Binomial Theorem>Exercise-3>Q 4

The value of

(\begin{array}{l} 30 \\ 0 \end{array}) (\begin{array}{l} 30 \\ 10 \end{array}) - (\begin{array}{l} 30 \\ 1 \end{array}) (\begin{array}{l} 30 \\ 11 \end{array}) + (\begin{array}{l} 30 \\ 2 \end{array}) (\begin{array}{l} 30 \\ 12 \end{array}) - \dots \dots \dots + (\begin{array}{l} 30 \\ 20 \end{array}) (\begin{array}{l} 30 \\ 30 \end{array})

is