Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 7 - Binomial Theorem>DPP>Q 10

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If the value of ${}^{n}C_{0} + 2 \cdot^{n} C_{1} + 3 \cdot^{n} C_{2} + \dots + (n + 1) \cdot^{n} Cn = 576$ , then $n$ is

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Important Questions on Binomial Theorem

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Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 7 - Binomial Theorem>DPP>Q 11

The value of

(\begin{matrix} 50 \\ 6 \end{matrix}) - (\begin{matrix} 5 \\ 1 \end{matrix}) (\begin{matrix} 40 \\ 6 \end{matrix}) + (\begin{matrix} 5 \\ 2 \end{matrix}) (\begin{matrix} 30 \\ 6 \end{matrix}) - (\begin{matrix} 5 \\ 3 \end{matrix}) (\begin{matrix} 20 \\ 6 \end{matrix}) + (\begin{matrix} 5 \\ 4 \end{matrix}) (\begin{matrix} 10 \\ 6 \end{matrix})

where

(\begin{array}{l} n \\ r \end{array})

denotes

{}^{n}C_{r}

is

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Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 7 - Binomial Theorem>DPP>Q 12

The value of the expression

\underset{0 \leq i < j \leq n}{\sum \sum} {(- 1)}^{i + j - 1} \cdot^{n} C_{i} \cdot^{n} C_{j} =

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Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 7 - Binomial Theorem>DPP>Q 13

\sum_{m = 1}^{n} (\sum_{k = 1}^{m} ({\sum_{p = k}^{m}}^{n} C_{m} \cdot^{m} C_{p} \cdot^{p} C_{k})) =

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Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 7 - Binomial Theorem>DPP>Q 14

{}^{n}C_{0}^{2 n} C_{m} -^{n} C_{1}^{2 n - 2} C_{m} +^{n} C_{2}^{2 n - 4} C_{m} - \dots =

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Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 7 - Binomial Theorem>DPP>Q 15

Which of the following is/are correct?

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Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 7 - Binomial Theorem>DPP>Q 16

The value of

\sum_{k = 0}^{7} [\frac{(\begin{array}{l} 7 \\ k \end{array})}{(\begin{array}{l} 14 \\ k \end{array})} \sum_{r = k}^{14} (\begin{array}{l} r \\ k \end{array}) (\begin{array}{l} 14 \\ r \end{array})]

, where

(\begin{array}{l} n \\ r \end{array})

denotes

{}^{n}C_{r}

, is

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Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 7 - Binomial Theorem>DPP>Q 17

The value of

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

is

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Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 7 - Binomial Theorem>DPP>Q 1

If

\frac{{(1 - 3 x)}^{\frac{1}{2}} + {(1 - x)}^{\frac{5}{3}}}{\sqrt{4 - x}}

is approximately equal to

a + b x

for

x < < < 1,

then

(a, b) =