Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 8 - Binomial Theorem>Exercises>Q 60

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The value of $\frac{^{n} C_{0}}{n} + \frac{^{n} C_{1}}{n + 1} + \frac{^{n} C_{2}}{n + 2} + . . . + \frac{^{n} C_{n}}{2 n}$ is equal to

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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 61

The value of

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

is equal to

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 8 - Binomial Theorem>Exercises>Q 62

If

\sum_{r = 0}^{n} (\frac{r + 2}{r + 1})^{n} C_{r} = \frac{2^{8} - 1}{6},

then

n

is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 8 - Binomial Theorem>Exercises>Q 63

The value of

\sum_{r = 0}^{10} {(- 1)}^{r} \cdot 4^{10 - r} \cdot^{30} C_{r} \cdot^{30 - r} C_{10 - r}

is equal to

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 8 - Binomial Theorem>Exercises>Q 64

The value of

\sum_{r = 0}^{10} r^{10} C_{r} 3^{r} {(- 2)}^{10 - r}

is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 8 - Binomial Theorem>Exercises>Q 65

The value of

^{15} {C_{0}}^{2} -^{15} {C_{1}}^{2} +^{15} {C_{2}}^{2} - . . . -^{15} {C_{15}}^{2}

is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 8 - Binomial Theorem>Exercises>Q 66

If

{(1 + x)}^{n} = C_{0} + C_{1} x + C_{2} x^{2} + . .. + C_{n} x^{n},

then

C_{0} C_{2} + C_{1} C_{3} + C_{2} C_{4} + . .. + C_{n - 2} C_{n} =

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 8 - Binomial Theorem>Exercises>Q 67

^{404} C_{4} -^{4} C_{1}^{303} C_{4} +^{4} {C_{2}}^{202} C_{4} -^{4} C_{3}^{101} C_{4}

is equal to

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 8 - Binomial Theorem>Exercises>Q 68

The value of

\sum_{r = 0}^{40} r^{40} {C_{r}}^{30} C_{r}

is