EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 25 July 2022 Shift 1>Q 101

MEDIUM

JEE Main

IMPORTANT

Earn 100

If the maximum value of the term independent of $t$ in the expansion of ${(t^{2} x^{\frac{1}{5}} + \frac{{(1 - x)}^{^{\frac{1}{10}}}}{t})}^{15}, x \geq 0$ , is $K$ , then $8 K$ is equal to _____ .

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Important Questions on Binomial Theorem

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 25 July 2022 Shift 2>Q 102

The remainder when

{(11)}^{1011} + {(1011)}^{11}

is divided by

9

is _____ .

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 26 July 2022 Shift 2>Q 104

\sum_{\underset{i \neq j}{i, j = 0}}^{n} {}^{n}C_{i} {}^{n}C_{j}

is equal to

MEDIUM

JEE Main

IMPORTANT

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

The remainder when

{(2021)}^{2022} + {(2022)}^{2021}

is divided by

7

is

MEDIUM

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

MEDIUM

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 _____ .

MEDIUM

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 - 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

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 29 January 2023 Shift 1>Q 118

Let the coefficients of three consecutive terms in the binomial expansion of

(1 + 2 x)^{n}

be in the ratio

2 : 5 : 8

. Then the coefficient of the term, which is in the middle of these three terms, is