EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 31 January 2023 Shift 1>Q 125

HARD

JEE Main

IMPORTANT

Earn 100

The remainder on dividing $5^{99}$ by $11$ is _____ .

100% studentsanswered this correctly

Important Questions on Binomial Theorem

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 31 January 2023 Shift 2>Q 126

Let

A = [a_{\hat{i} \hat{j}}] \forall a_{i j} \in Z \cap [0, 4], 1 \leq i, j \leq 2

. The number of matrices

A

such that the sum of all entries is

a

prime number

p \in (2, 13)

is _____ .

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 31 January 2023 Shift 2>Q 127

The coefficient of

x^{- 6}

, in the expansion of

{(\frac{4 x}{5} + \frac{5}{2 x^{2}})}^{9}

, is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 31 January 2023 Shift 2>Q 128

If the constant term in the binomial expansion of

{(\frac{x^{\frac{5}{2}}}{2} - \frac{4}{x^{l}})}^{9}

is

- 84

and the coefficient of

x^{- 3 l}

is

2^{α} β

where

β < 0

is an odd number, then

|α l - β|

is equal to _____ .

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 1 February 2023 Shift 1>Q 129

The value of

$\frac{1}{1! 50!} + \frac{1}{3! 48!} + \frac{1}{5! 46!} + \dots . + \frac{1}{49! 2!} + \frac{1}{51! 1!}$ is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 1 February 2023 Shift 1>Q 130

The remainder when

19^{200} + 23^{200}

is divided by

49

, is _____ .

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 1 February 2023 Shift 2>Q 131

Let the sixth term in the binomial expansion of

{(\sqrt{2^{\log_{2} (10 - 3^{x})}} + \sqrt[5]{2^{(x - 2) \log_{2} 3}})}^{m}

powers of

2^{(x - 2) \log_{2} 3}

, be

21

. If the binomial coefficients of the second, third and fourth terms in the expansion are respectively the first, third and fifth terms of an A.P., then the sum of the squares of all possible values of

x

is _____ .

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 1 February 2023 Shift 2>Q 132

If the term without

x

in the expansion of

{(x^{\frac{2}{3}} + \frac{α}{x^{3}})}^{22}

is

7315

, then

|α|

is equal to _____ .