EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>Exercise 1>Q 139

MEDIUM

JEE Main

IMPORTANT

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Suppose $28 - p, p, 70 - α, α$ are the coefficient of four consecutive terms in the expansion of $(1 + x)^{n}$ . Then the value of $2 α - 3 p$ equals

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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>Exercise 1>Q 140

Let

α = \sum_{k = 0}^{n} (\frac{{({}^{n}C_{k})}^{2}}{k + 1})

and

β = \sum_{k = 0}^{n - 1} (\frac{{}^{n}C_{k} {}^{n}C_{k + 1}}{k + 2})

. If

5 α = 6 β

, then

n

equals

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>Exercise 1>Q 141

In the expansion of

(1 + x) (1 - x^{2}) {(1 + \frac{3}{x} + \frac{3}{x^{2}} + \frac{1}{x^{3}})}^{5}, x \neq 0

, the sum of the coefficient of

x^{3}

and

x^{- 13}

is equal to ______

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>Exercise 1>Q 142

Let the coefficient of $x^{r}$ in the expansion of ${(x + 3)}^{n - 1} + {(x + 3)}^{n - 2} (x + 2) + {(x + 3)}^{n - 3} {(x + 2)}^{2} + . ... + {(x + 2)}^{n - 1}$ be $α_{r}$ . If $\sum_{r = 0}^{n} α_{r} = β^{n} - γ^{n}, β, γ \in N$ , then the value of $β^{2} + γ^{2}$ equals _______.

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>Exercise 1>Q 143

If the coefficient of

x^{30}

in the expansion of

{(1 + \frac{1}{x})}^{6} {(1 + x^{2})}^{7} {(1 - x^{3})}^{8}; x \neq 0

is

α

, then

|α|

equals _________.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 6 - Binomial Theorem>Exercise 1>Q 144

Let $m and n$ be the coefficients of seventh and thirteenth terms respectively in the expansion of ${(\frac{1}{3} x^{\frac{1}{3}} + \frac{1}{2 x^{\frac{2}{3}}})}^{18}$ . Then ${(\frac{n}{m})}^{\frac{1}{3}}$ is: