EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 30 January 2023 Shift 2>Q 123

EASY

JEE Main

IMPORTANT

Earn 100

$50^{th}$ root of a number $x$ is $12$ and $50^{th}$ root of another number $y$ is $18$ . Then the remainder obtained on dividing $(x + y)$ by $25$ is ________.

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Important Questions on Binomial Theorem

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 31 August 2021 Shift 1>Q 4

If

(\frac{3^{6}}{4^{4}}) k

is the term, independent of

x,

in the binomial expansion of

{(\frac{x}{4} - \frac{12}{x^{2}})}^{12},

then

k

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 31 August 2021 Shift 2>Q 5

If the coefficient of

a^{7} b^{8}

in the expansion of

(a + 2 b + 4 a b)^{10}

is

K \cdot 2^{16},

then

K

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 22 July 2021 Shift 1>Q 11

The number of elements in the set

{n \in {1, 2, 3, \dots, 100} ∣ (11)^{n} > (10)^{n} + (9)^{n}\}

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 _____ .

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 _____ .

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 1 September 2021 Shift 2>Q 6

If the sum of the coefficients in the expansion of

(x + y)^{n}

is

4096,

then the greatest coefficient in the expansion is _____.