EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 27 July 2022 Shift 1>Q 105

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JEE Main

IMPORTANT

Earn 100

The remainder when ${(2021)}^{2022} + {(2022)}^{2021}$ is divided by $7$ is

80% studentsanswered this correctly

Important Questions on Binomial Theorem

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 27 July 2022 Shift 2>Q 106

Let for the

9^{th}

term in the binomial expansion of

{(3 + 6 x)}^{n}

, in the increasing powers of

6 x

, to be the greatest for

x = \frac{3}{2}

, the least value of

n

is

n_{0}

. If

k

is the ratio of the coefficient of

x^{6}

to the coefficient of

x^{3}

, then

k + n_{0}

is equal to

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 28 July 2022 Shift 1>Q 107

The remainder when

7^{2022} + 3^{2022}

is divided by

5

is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 28 July 2022 Shift 2>Q 108

Let the coefficients of the middle terms in the expansion of

{(\frac{1}{\sqrt{6}} + β x)}^{4}, {(1 - 3 β x)}^{2}

and

{(1 - \frac{β}{2} x)}^{6}, β > 0

, respectively form the first three terms of an A.P. If

d

is the common difference of this A.P., then

50 - \frac{2 d}{β^{2}}

is equal to _____ .

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 28 July 2022 Shift 2>Q 109

If

1 + (2 + {}^{49}C_{1} + {}^{49}C_{2} + \dots . + {}^{49}C_{49}) ({}^{50}C_{2} + {}^{50}C_{4} + \dots . . + {}^{50}C_{50})

is equal to

2^{n} . m

, where

m

is odd, then

n + m

is equal to _____ .

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 29 July 2022 Shift 1>Q 110

Let the ratio of the fifth term from the beginning to the fifth term from the end in the binomial expansion of

{(\sqrt[4]{2} + \frac{1}{\sqrt[4]{3}})}^{n}

, in the increasing powers of

\frac{1}{\sqrt[4]{3}}

be

\sqrt[4]{6} : 1

. If the sixth term from the beginning is

\frac{α}{\sqrt[4]{3}}

, then

α

is equal to _______.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 29 July 2022 Shift 2>Q 111

If

\sum_{K = 1}^{10} K^{2} {(10_{C_{K}})}^{2} = 22000 L

, then

L

is equal to _____.

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 24 January 2023 Shift 2>Q 112

If

{({}^{30}C_{1})}^{2} + 2 {({}^{30}C_{2})}^{2} + 3 {({}^{30}C_{3})}^{2} . . . . . . . . . . 30 {({}^{30}C_{30})}^{2} = \frac{α 60!}{{(30!)}^{2}}

, then

α

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 24 January 2023 Shift 2>Q 113

Let the sum of the coefficient of first three terms in the expansion of

{(x - \frac{3}{x^{2}})}^{n}; x = 0, n \in N

be

376

. Then, the coefficient of

x^{4}

is equal to: