EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Binomial Theorem>AP EAPCET 2018 (25-APR Shift-1)>Q 9

HARD

AP EAPCET

IMPORTANT

Earn 100

The number of rational terms in the expansion of ${(3^{\frac{1}{4}} + 7^{\frac{1}{6}})}^{144}$ is

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Important Questions on Binomial Theorem

HARD

AP EAPCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Binomial Theorem>AP EAPCET 2020 (Sep-23 Shift-1)>Q 1

Let

R = (5 \sqrt{5} + 11)^{2 n + 1}

and

f = R - [R],

where

[x]

denotes the greatest integer less than or equal to

x,

then

R f =

HARD

AP EAPCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Binomial Theorem>AP EAPCET 2020 (Sep-23 Shift-1)>Q 2

If the term independent of

x

in the expansion of

{(\sqrt{x} - \frac{k}{x^{2}})}^{10}

is

405,

then

k =

HARD

AP EAPCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Binomial Theorem>AP EAPCET 2020 (Sep-23 Shift-1)>Q 3

The index of the power of

x

occurring in the

5^{th}

term from the end in the expansion of

{(\frac{x^{3}}{2} - \frac{2}{x^{2}})}^{12}

is

EASY

AP EAPCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Binomial Theorem>AP EAPCET 2020 (Sep-23 Shift-1)>Q 4

If

[x]

represents the greatest integer not greater than

x,

then

[{(1 + \frac{1}{10000})}^{10000}] =

HARD

AP EAPCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Binomial Theorem>AP EAPCET 2019 (21-Apr Shift-2)>Q 5

If

' a'

is the middle term in the expansion of

(2 x - 3 y)^{8}

and

b, c

are the middle terms in the expansion of

(3 x + 4 y)^{7},

then the value of

\frac{b + c}{a},

when

x = 2

and

y = 3,

is

HARD

AP EAPCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Binomial Theorem>AP EAPCET 2018 (25-APR Shift-1)>Q 6

\frac{1}{4} - \frac{5}{4 \cdot 8} + \frac{5 \cdot 9}{4 \cdot 8 \cdot 12} - \dots =

MEDIUM

AP EAPCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Binomial Theorem>AP EAPCET 2019 (21-Apr Shift-2)>Q 7

The first negative coefficient in the terms occurring in the expansion of

(1 + x)^{\frac{21}{5}}

is

HARD

AP EAPCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Binomial Theorem>AP EAPCET 2019 (21-Apr Shift-2)>Q 8

When

| x | < \frac{1}{2},

the coefficient of

x^{4}

in the expansion of

\frac{3 x^{2} - 5 x + 3}{(x - 1) (2 x + 1) (x + 3)}

is