Mathematics Crash Course JEE Main>Chapter 3 - Binomial Theorem>Level 1>Q 6

HARD

JEE Main

IMPORTANT

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Let the coefficient of the middle term of the binomial expansion of $(1 + x)^{2 n}$ be $α$ and those of two middle terms of the binomial expansion of $(1 + x)^{2 n - 1}$ be $β$ and $γ .$ Which one of the following relations is correct?

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Important Questions on Binomial Theorem

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 3 - Binomial Theorem>Level 1>Q 7

What is the term independent of

x

in the expansion of

(1 + x + 2 x^{2}) {(\frac{3 x^{- 2}}{2} - \frac{1}{3 x})}^{9}

?

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 3 - Binomial Theorem>Level 1>Q 8

Middle term in the expansion of

{(1 - 3 x + 3 x^{2} - x^{3})}^{2 n}

is

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 3 - Binomial Theorem>Level 1>Q 9

If the coefficient of the middle term in the expansion of

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

is

p

and the coefficients of middle terms in the expansion of

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

are

q

and

r,

then

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 3 - Binomial Theorem>Level 1>Q 10

The term independent of

a

in the expansion of

{(1 + \sqrt{a} + \frac{1}{\sqrt{a} - 1})}^{- 30}

is

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 3 - Binomial Theorem>Level 1>Q 11

If the sum of the coefficients in the expansion of

{(1 - 3 x + 10 x^{2})}^{n}

is

a

and sum of coefficients in the expansion of

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

is

b,

then

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 3 - Binomial Theorem>Level 1>Q 12

The fractional part of

\frac{2^{4 n}}{15}

is

(n \in N)

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 3 - Binomial Theorem>Level 1>Q 13

For the natural numbers

m, n,

if

(1 - y)^{m} (1 + y)^{n} = 1 + a_{1} y + a_{2} y^{2} + \dots . + a_{m + n} y^{m + n}

and

a_{1} = a_{2} = 10,

then the value of

m, n,

is equal to:

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 3 - Binomial Theorem>Level 1>Q 14

The solution set of

{}^{5}C_{x - 1} > 2 \cdot ({}^{5}C_{x})

is