Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 8 - Binomial Theorem>Exercises>Q 45

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The value of ${}^{20}C_{0} + {}^{20}C_{1} + {}^{20}C_{2} + {}^{20}C_{3} + {}^{20}C_{4} + {}^{20}C_{12} + {}^{20}C_{13} + {}^{20}C_{14} + {}^{20}C_{15}$ is

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Important Questions on Binomial Theorem

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 8 - Binomial Theorem>Exercises>Q 46

The sum of the series

{}^{20}C_{0} - {}^{20}C_{1} + {}^{20}C_{2} - {}^{20}C_{3} + \dots + {}^{20}C_{10}

is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 8 - Binomial Theorem>Exercises>Q 47

If

{(3 + x^{2008} + x^{2009})}^{2010} = a_{0} + a_{1} x + a_{2} x^{2} + . . . + a_{n} x^{n},

then the value of

a_{0} - \frac{1}{2} a_{1} - \frac{1}{2} a_{2} + a_{3} - \frac{1}{2} a_{4} - \frac{1}{2} a_{5} + a_{6} - . . . .

is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 8 - Binomial Theorem>Exercises>Q 48

Value of

\sum_{k = 1}^{\infty} \sum_{r = 0}^{k} \frac{1}{3^{k}} ({}^{k}C_{r})

is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 8 - Binomial Theorem>Exercises>Q 49

The value of

\sum_{r = 0}^{10} (r) {}^{20}C_{r}

is equal to

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 8 - Binomial Theorem>Exercises>Q 50

{[({}^{n}C_{0} + {}^{n}C_{3} + . . .) - (\frac{1}{2}) ({}^{n}C_{1} + {}^{n}C_{2} + {}^{n}C_{4} + {}^{n}C_{5} + . . .)]}^{2} + (\frac{3}{4}) {({}^{n}C_{1} - {}^{n}C_{2} + {}^{n}C_{4} - {}^{n}C_{5} + . . .)}^{2} =

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 8 - Binomial Theorem>Exercises>Q 51

The value of

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

(where

r, k, n \in N

) is equal to

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 8 - Binomial Theorem>Exercises>Q 52

The sum

\sum_{0 \leq i \leq j \leq 10} (^{10} C_{j}) (^{j} C_{i})

is equal to

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 8 - Binomial Theorem>Exercises>Q 53

The value of the sum

^{1000} C_{50} +^{999} C_{49} +^{998} C_{48} + . . . +^{950} C_{0}

is