Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 7 - Binomial Theorem>DPP>Q 8

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In the expansion of ${(1 + x)}^{70}$ the sum of the coefficients of odd powers of $x$ 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 9

The sum of all the coefficients of the terms in the expansion of

(x + y + z + w)^{6}

which contains

x

but not

y

, is

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JEE Main

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

The value of

{}^{12}C_{2} +^{13} C_{3} +^{14} C_{4} + \dots +^{999} C_{989}

is

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

If

{(1 + x + x^{2})}^{25} = a_{0} + a_{1} x + a_{2} x^{2} + . . . + a_{50} x^{50}

, then

a_{0} + a_{2} + a_{4} + . . . + a_{50}

is

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

If the sum of the coefficients in the expansion of ${(q + r)}^{20} {(1 + (p - 2) x)}^{20}$ is equal to square of the sum of coefficients in the expansion of ${[2 r q x - (r + q) . y]}^{10}$ , where $p, q, r$ are positive constants, then:

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

The sum

S_{n} = Σ_{k = 0}^{n} {(- 1)}^{k} \cdot^{3 n} C_{k}

, where

n = 1, 2, . . . .

is

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

If

1 + (1 + x) + {(1 + x)}^{2} + \dots + {(1 + x)}^{n} = \sum_{k = 0}^{n} a_{k} x^{k}

, then which of the following is not true?

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

Given

{}^{8}C_{1} x {(1 - x)}^{7} + 2 \cdot {}^{8}C_{2} x^{2} {(1 - x)}^{6} + 3 \cdot^{8} C_{3} x^{3} {(1 - x)}^{5} + \dots + 8 \cdot x^{8} = a x + b

, then

a + b

is

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IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 7 - Binomial Theorem>DPP>Q 2

The value of

99^{50} - \frac{99}{1} \cdot 98^{50} + \frac{99 \cdot 98}{1 \cdot 2} \cdot 97^{50} - \dots . . . - \frac{99 \cdot 98}{1.2} \cdot 2^{50} + \frac{99}{1} \cdot 1^{50}

is