EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 20 July 2021 Shift 1>Q 7

MEDIUM

JEE Main

IMPORTANT

Earn 100

The coefficient of $x^{256}$ in the expansion of ${(1 - x)}^{101} {(x^{2} + x + 1)}^{100}$ 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 - 20 July 2021 Shift 1>Q 8

The number of rational terms in the binomial expansion of

{(4^{\frac{1}{4}} + 5^{\frac{1}{6}})}^{120}

is_______.

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 20 July 2021 Shift 2>Q 9

For the natural numbers

m, n,

if

(1 - y)^{m} (1 + y)^{n} = 1 + a_{1} y + a_{2} y^{2} + \dots . + a_{m + n} y^{m + n}

and

a_{1} = a_{2} = 10,

then the value of

m, n,

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 10

If the constant term, in binomial expansion of

{(2 x^{r} + \frac{1}{x^{2}})}^{10}

is

180,

then

r

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 ___________.

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 25 July 2021 Shift 1>Q 12

If

b

is very small as compared to the value of

a

, so that the cube and other higher powers of

\frac{b}{a}

can be neglected in the identity

$\frac{1}{a - b} + \frac{1}{a - 2 b} + \frac{1}{a - 3 b} + \dots . + \frac{1}{a - n b} = α n + β n^{2} + γ n^{3}$

then the value of $γ$ is :

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 25 July 2021 Shift 1>Q 13

The ratio of the coefficient of the middle term in the expansion of $(1 + x)^{20}$ and the sum of the coefficients of two middle terms in expansion of $(1 + x)^{19}$ is .

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 25 July 2021 Shift 1>Q 14

The term independent of

x

in the expansion of

{(\frac{x + 1}{x^{2 / 3} - x^{1 / 3} + 1} - \frac{x - 1}{x - x^{1 / 2}})}^{10},

where

x \neq 0, 1

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 25 July 2021 Shift 2>Q 15

The sum of all those terms which are rational numbers in the expansion of

{(2^{\frac{1}{3}} + 3^{\frac{1}{4}})}^{12}

is: