Higher Algebra>Chapter 13 - Binomial Theorem: Positive Integral Index>EXAMPLES. XIII.b.>Q 2

EASY

JEE Main

IMPORTANT

Earn 100

Find the greatest term in the expansion of $(2 x - 3 y)^{28}$ when $x = 9$ , $y = 4$ .

Important Questions on Binomial Theorem: Positive Integral Index

HARD

JEE Main

IMPORTANT

Higher Algebra>Chapter 13 - Binomial Theorem: Positive Integral Index>EXAMPLES. XIII.b.>Q 3

Find the greatest term in the expansion of

(2 a + b)^{14}

when

a = 4, b = 5

.

EASY

JEE Main

IMPORTANT

Higher Algebra>Chapter 13 - Binomial Theorem: Positive Integral Index>EXAMPLES. XIII.b.>Q 4

Find the greatest term in the expansion of

{(3 + 2 x)}^{15}

when

x = \frac{5}{2}

.

MEDIUM

JEE Main

IMPORTANT

Higher Algebra>Chapter 13 - Binomial Theorem: Positive Integral Index>EXAMPLES. XIII.b.>Q 5

Find the value of the greatest term in the expansion of $(1 + x)^{n}$ when $x = \frac{2}{3}, n = 6$ .

MEDIUM

JEE Main

IMPORTANT

Higher Algebra>Chapter 13 - Binomial Theorem: Positive Integral Index>EXAMPLES. XIII.b.>Q 6

Find the value of greatest term in the expansion of

(a + x)^{n}

where

a = \frac{1}{2}, x = \frac{1}{3}, n = 9

.

EASY

JEE Main

IMPORTANT

Higher Algebra>Chapter 13 - Binomial Theorem: Positive Integral Index>EXAMPLES. XIII.b.>Q 7

Show that the coefficient of the middle term of

(1 + x)^{2 n}

is equal to the sum of the coefficients of two middle terms of

(1 + x)^{2 n - 1}

.

MEDIUM

JEE Main

IMPORTANT

Higher Algebra>Chapter 13 - Binomial Theorem: Positive Integral Index>EXAMPLES. XIII.b.>Q 8

If

A

be the sum of the odd terms and

B

the sum of the even terms in the expansion of

(x + a)^{n}

, prove that

A^{2} - B^{2} = {(x^{2} - a^{2})}^{n}

.

MEDIUM

JEE Main

IMPORTANT

Higher Algebra>Chapter 13 - Binomial Theorem: Positive Integral Index>EXAMPLES. XIII.b.>Q 9

The

2^{nd}

,

3^{rd},

4^{th}

terms in the expansion of

(x + y)^{n}

are

240, 720, 1080

, respectively, find

x, y, n

.

HARD

JEE Main

IMPORTANT

Higher Algebra>Chapter 13 - Binomial Theorem: Positive Integral Index>EXAMPLES. XIII.b.>Q 10

Find the expansion of

{(1 + 2 x - x^{2})}^{4}

.