EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Binomial Theorem>TS EAMCET - 5 August 2021 Shift 1>Q 7

MEDIUM

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IMPORTANT

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If $f (n)$ is the coefficient of $x^{n}$ in the expansion of $(1 + x) (1 - x)^{n},$ then $f (2021) =$

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Important Questions on Binomial Theorem

HARD

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Binomial Theorem>TS EAMCET - 5 August 2021 Shift 1>Q 8

If

p

and

q

are respectively the coefficient of

x^{- 3}

and

x^{- 5}

in the expansion of

{(x^{1 / 3} + \frac{1}{2 x^{1 / 3}})}^{21}, x > 0,

then

\frac{5 p}{4 q} =

HARD

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Binomial Theorem>TS EAMCET - 5 August 2021 Shift 2>Q 9

If

(\sqrt{3} + i)^{8} - (\sqrt{3} - i)^{8} = α + i β,

then

α - \frac{\sqrt{3}}{2} β =

HARD

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Binomial Theorem>TS EAMCET - 5 August 2021 Shift 2>Q 10

In the binomial expansion of

(1 + x)^{2 k},

if its middle term is the only numerically greatest term, then

x

lies in the interval

MEDIUM

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Binomial Theorem>TS EAMCET - 5 August 2021 Shift 2>Q 11

Sum of the coefficients of $x^{r}, (r = 0, 1, 2, 3, . . ., 15)$ in the expansion of $(3 x - 1)^{15}$ is equal to the sum of the binomial coefficients of which of the following expansions?

$(a)$ $(1 + x)^{15}$

$(b)$ $(1 + x)^{16} + (1 - x)^{16}$

$(c)$ $(1 + x)^{16} - (1 - x)^{16}$

EASY

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Binomial Theorem>TS EAMCET 2020 (9-Sep Shift-1)>Q 12

If

y = \frac{3}{4} + \frac{3 \cdot 5}{4 \cdot 8} + \frac{3 \cdot 5 \cdot 7}{4 \cdot 8 \cdot 12} + \dots \infty

then

EASY

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Binomial Theorem>TS EAMCET 2020 (9-Sep Shift-1)>Q 13

If the coefficient of

x^{13}

in the expansion of

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

is

A \times 2^{10}

, then

A =

MEDIUM

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Binomial Theorem>TS EAMCET 2021 (04-Aug Shift-2)>Q 14

In the expansion of

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

the coefficient of

x^{10}

is equal to the coefficient of

x^{10}

in

{(1 + a x)}^{n}, n \in N

then

n a =

MEDIUM

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Binomial Theorem>TS EAMCET 2021 (04-Aug Shift-2)>Q 15

For

x > 0,

if

p^{th}

term is the first negative term in the expansion of

{(1 + \frac{3 x}{5})}^{22 / 3}

and in the expansion of

{(1 - \frac{3 x}{5})}^{22 / 3}

from

r^{t h}

term onwards all the terms are positive, then the number of terms in the expansion of

{(p x + \frac{r}{x})}^{p r}

is