EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 25 January 2023 Shift 2>Q 116

HARD

JEE Main

IMPORTANT

Earn 100

The remainder when ${(2023)}^{2023}$ is divided by $35$ is

50% studentsanswered this correctly

Important Questions on Binomial Theorem

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 29 January 2023 Shift 1>Q 117

If the co-efficient of

x^{9}

in

{(α x^{3} + \frac{1}{β x})}^{11}

and the co-efficient of

x^{- 9}

in

{(α x - \frac{1}{β x^{3}})}^{11}

are equal, then

(α β)^{2}

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

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 29 January 2023 Shift 2>Q 119

Let

K

be the sum of the coefficients of the odd powers of

x

in the expansion of

{(1 + x)}^{99}

. Let a be the middle term in the expansion of

{(2 + \frac{1}{\sqrt{2}})}^{200}

. If

\frac{{}^{200}C_{99} K}{a} = \frac{2^{l} m}{n}

, where

m

and

n

are odd numbers, then the ordered pair

(l, n)

is equal to:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 30 January 2023 Shift 1>Q 120

If the coefficient of

x^{15}

in the expansion of

{(a x^{3} + \frac{1}{b x^{\frac{1}{3}}})}^{15}

is equal to the coefficient of

x^{- 15}

in the expansion of

{(a x^{\frac{1}{3}} - \frac{1}{b x^{3}})}^{15}

, where

a

and

b

are positive real numbers, then for each such ordered pair

(a, b)

:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 30 January 2023 Shift 1>Q 121

The coefficient of

x^{301}

in

{(1 + x)}^{500} + x {(1 + x)}^{499} + x^{2} {(1 + x)}^{498} + \dots . . + x^{500}

is:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 30 January 2023 Shift 2>Q 122

Let

x = {(8 \sqrt{3} + 13)}^{13}

and

y = {(7 \sqrt{2} + 9)}^{9}

. If

[t]

denotes the greatest integer

\leq t

, then

EASY

JEE Main

IMPORTANT

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

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 ________.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 31 January 2023 Shift 1>Q 124

Let

α > 0

, be the smallest number such that the expansion of

{(x^{\frac{2}{3}} + \frac{2}{x^{3}})}^{30}

has a term

β x^{- α}, β \in N

. Then

α

is equal to _____ .