EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 9th April 2019 Shift 1>Q 53

HARD

JEE Main

IMPORTANT

Earn 100

If the fourth term in the Binomial expansion of ${(\frac{2}{x} + x^{{l o g}_{8} x})}^{6}, (x > 0)$ is $20 \times 8^{7},$ then a value of $x$ is

75% studentsanswered this correctly

Important Questions on Binomial Theorem

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 9th April 2019 Shift 2>Q 54

If some three consecutive coefficients in the binomial expansion of

{(x + 1)}^{n}

in powers of

x

are in the ratio

2 : 15 : 70,

then the average of these three coefficients is:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 9th January 2019 Shift 1>Q 55

If the fractional part of the number

\frac{2^{403}}{15}

is

\frac{k}{15},

then

k

is equal to

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 9th January 2019 Shift 2>Q 56

The coefficient of

t^{4}

in the expansion of

{(\frac{1 - t^{6}}{1 - t})}^{3}

is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 8th April 2019 Shift 1>Q 57

The sum of the co-efficient of all even degree terms in

x

in the expansion of

{(x + \sqrt{x^{3} - 1})}^{6} {+ (x - \sqrt{x^{3} - 1})}^{6}, (x > 1)

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 8th April 2019 Shift 1>Q 58

The sum of the series

{2 .}^{20} C_{0} + {5 .}^{20} C_{1} + {8 .}^{20} C_{2} + {11 .}^{20} C_{3} + . . . . . . . + {62 .}^{20} C_{20}

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 8th April 2019 Shift 2>Q 59

If the fourth term in the binomial expansion of

{(\sqrt{x^{\frac{1}{1 + {l o g}_{10} x}}} + x^{\frac{1}{12}})}^{6}

is equal to

200,

and

x > 1,

then the value of

x

is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 10th April 2019 Shift 1>Q 60

If the coefficients of

x^{2}

and

x^{3}

, are both zero, in the expansion of the expression

(1 + a x + b x^{2}) {(1 - 3 x)}^{15}

, in powers of

x

, then the ordered pair

(a, b)

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 10th April 2019 Shift 2>Q 61

The smallest natural number

n

, such that the coefficient of

x

in the expansion of

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

is

{}^{n}C_{23}

, is