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

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JEE Main

IMPORTANT

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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

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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 - 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

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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

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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

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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

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 10th January 2019 Shift 1>Q 62

If the third term in the binomial expansion of

{(1 + x^{\log_{2} x})}^{5}

equals

2560,

then a possible value of

x

is

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 10th January 2019 Shift 2>Q 63

If

\sum_{r = 0}^{25} \{({}^{50}C_{r}) ({}^{50 - r}C_{25 - r})\} = K ({}^{50}C_{25})

, then

K

is equal to

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 10th January 2019 Shift 2>Q 64

The positive value of

λ

for which the co-efficient of

x^{2}

in the expansion

x^{2} {(\sqrt{x} + \frac{λ}{x^{2}})}^{10}

is

720,

is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>JEE Main - 12th April 2019 Shift 1>Q 65

The coefficient of

x^{18}

in the product

(1 + x) {(1 - x)}^{10} {(1 + x + x^{2})}^{9}

is