EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 12th January 2019 Shift 1>Q 68

EASY

JEE Main

IMPORTANT

Earn 100

A ratio of the $5^{t h}$ term from the beginning to the $5^{t h}$ term from the end in the binomial expansion of ${(2^{\frac{1}{3}} + \frac{1}{2 {(3)}^{\frac{1}{3}}})}^{10}$ is

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Important Questions on Binomial Theorem

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 12th January 2019 Shift 2>Q 69

The total number of irrational terms in the binomial expansion of

{(7^{\frac{1}{5}} - 3^{\frac{1}{10}})}^{60}

is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 8th April 2018>Q 70

The sum of the co-efficient of all odd degree terms in the expansion of

{(x + \sqrt{x^{3} - 1})}^{5} + {(x - \sqrt{x^{3} - 1})}^{5}, (x > 1)

is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 15th April 2018>Q 71

If

n

is the degree of the polynomial,

{[\frac{2}{\sqrt{5 x^{3} + 1} - \sqrt{5 x^{3} - 1}}]}^{8} + {[\frac{2}{\sqrt{5 x^{3} + 1} + \sqrt{5 x^{3} - 1}}]}^{8}

and

m

is the coefficient of

x^{n}

in it, then the ordered pair

(n, m)

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 16th April 2018>Q 72

The coefficient of

x^{2}

in the expansion of the product

(2 - x^{2}) \{{(1 + 2 x + 3 x^{2})}^{6} + {(1 - 4 x^{2})}^{6}\}

is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 2nd April 2017>Q 73

The value of

(^{21} C_{1} -^{10} C_{1}) + (^{21} C_{2} -^{10} C_{2}) + (^{21} C_{3} -^{10} C_{3}) + (^{21} C_{4} -^{10} C_{4}) + \dots + (^{21} C_{10} -^{10} C_{10})

is

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 8th April 2017>Q 74

If

{(27)}^{999}

is divided by

7

, then the remainder is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 9th April 2017>Q 75

The coefficient of

x^{- 5}

in the binomial expansion of

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

where

x \neq 0,1

is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 9th April 2016>Q 76

For

x \in R, x \neq - 1,

if

{(1 + x)}^{2016} + x {(1 + x)}^{2015} + x^{2} {(1 + x)}^{2014} + \dots + x^{2016} = \sum_{i = 0}^{2016} a_{i} x_{i}

, then

a_{17}

is equal to