EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 5 September 2020 Shift 1>Q 43

HARD

JEE Main

IMPORTANT

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The natural number $m$ , for which the coefficient of $x$ in the binomial expansion of ${(x^{m} + \frac{1}{x^{2}})}^{22}$ is 1540, is

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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 - 5 September 2020 Shift 2>Q 44

The coefficient of

x^{4}

in the expansion of

{(1 + x + x^{2} + x^{3})}^{6}

in powers of

x,

is

\dots . .

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 6 September 2020 Shift 1>Q 45

If

{p}

denotes the fractional part of the number

p,

then

\{\frac{3^{200}}{8}\}

is equal to

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 6 September 2020 Shift 2>Q 46

If the constant term in the binomial expansion of

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

is

405

, then

|k|

equals :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 6 September 2020 Shift 2>Q 47

Consider the data on

x

taking the values

0, 2, 4, 8, . . . . ., 2^{n}

with frequencies

{}^{n}C_{0}, {}^{n}C_{1}, {}^{n}C_{2}, . . . ., {}^{n}C_{n}

respectively. If the mean of this data is

\frac{728}{2^{n}}

, then

n

is equal to ....... .

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 7th January 2020 Shift 2>Q 48

The coefficient of

x^{7}

in the expression

{(1 + x)}^{10} + x {(1 + x)}^{9} + x^{2} {(1 + x)}^{8} + . . . . + x^{10}

, is

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 8th January 2020 Shift 2>Q 49

If

α

and

β

be the coefficients of

x^{4}

and

x^{2}

, respectively in the expansion of

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

, then

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 9th January 2020 Shift 1>Q 50

The coefficient of

x^{4}

in the expansion of

{(1 + x + x^{2})}^{10}

is ________

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 9th January 2020 Shift 2>Q 51

In the expansion of

{(\frac{x}{\cos θ} + \frac{1}{x \sin θ})}^{16},

if

l_{1}

is the least value of the term independent of

x

when

\frac{π}{8} \leq θ \leq \frac{π}{4}

and

l_{2}

is the least value of the term independent of

x

when

\frac{π}{16} \leq θ \leq \frac{π}{8},

then the ratio

l_{2} : l_{1}

is equal to: