EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main 16 March 2021 Shift 1>Q 22

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JEE Main

IMPORTANT

Earn 100

If $n$ is the number of irrational terms in the expansion of ${(3^{\frac{1}{4}} + 5^{\frac{1}{8}})}^{60}$ , then $(n - 1)$ is divisible by :

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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 16 March 2021 Shift 1>Q 23

Let

[x]

denote greatest integer less than or equal to

x

. If for

n \in N, {(1 - x + x^{3})}^{n} = \sum_{j = 0}^{3 n} a_{j} x^{j}

, then

\sum_{j = 0}^{[\frac{3 n}{2}]} a_{2 j} + 4 \sum_{j = 0}^{[\frac{3 n - 1}{2}]} a_{2 j + 1}

is equal to :

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main 16 March 2021 Shift 2>Q 24

Let

n

be a positive integer. Let

A = \sum_{k = 0}^{n} {(- 1)}^{k} \times {}^{n}C_{k} [{(\frac{1}{2})}^{k} + {(\frac{3}{4})}^{k} + {(\frac{7}{8})}^{k} + {(\frac{15}{16})}^{k} + {(\frac{31}{32})}^{k}]

. If

63 A = 1 - \frac{1}{2^{30}},

then

n

is equal to ______ .

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main 17 March 2021 Shift 1>Q 25

If the fourth term in the expansion of

{(x + x^{\log_{2} x})}^{7}

is

4480,

then the value of

x

where

x \in N

is equal to:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main 17 March 2021 Shift 1>Q 26

If

(2021)^{3762}

is divided by

17,

then the remainder is _______.

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main 17 March 2021 Shift 2>Q 27

The value of

\sum_{r = 0}^{6} ({}^{6}C_{r} \cdot {}^{6}C_{6 - r})

is equal to :

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main 17 March 2021 Shift 2>Q 28

Let the coefficients of third, fourth and fifth terms in the expansion of

{(x + \frac{a}{x^{2}})}^{n}, x \neq 0,

be in the ratio

12 : 8 : 3 .

Then the term independent of

x

in the expansion, is equal to _______.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main 18 March 2021 Shift 1>Q 29

Let

{(1 + x + 2 x^{2})}^{20} = a_{0} + a_{1} x + a_{2} x^{2} + \dots + a_{40} x^{40},

then

a_{1} + a_{3} + a_{5} + \dots + a_{37}

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main 18 March 2021 Shift 2>Q 30

If 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}, x \neq 1

, is equal to

k^{t h}

term, then the value of

k

is