Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 8 - Binomial Theorem>Target Exercises>Q 12

HARD

JEE Advanced

IMPORTANT

Earn 100

The sum of the rational terms in the expansion of ${(\sqrt{2} + \sqrt[5]{10})}^{10}$ is

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Important Questions on Binomial Theorem

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 8 - Binomial Theorem>Target Exercises>Q 13

The coefficient of

x^{3}

in

{(\sqrt{x^{5}} + \frac{3}{\sqrt{x^{3}}})}^{6}

is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 8 - Binomial Theorem>Target Exercises>Q 14

If the coefficients of

x^{7}

and

x^{8}

in

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

are equal, then

n

is equal to

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 8 - Binomial Theorem>Target Exercises>Q 15

If

{(1 + 2 x + x^{2})}^{n} = \sum_{r = 0}^{2 n} a_{r} x^{r},

then

a_{r}

is equal to

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 8 - Binomial Theorem>Target Exercises>Q 16

If in the expansion of

(1 + x)^{m} (1 - x)^{n},

the coefficients of

x

and

x^{2}

are

3

and

- 6

respectively, then

m

is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 8 - Binomial Theorem>Target Exercises>Q 17

The coefficient of

x^{53}

in

\sum_{r = 0}^{100} {}_{r = 0}^{100}C_{r} {(x - 3)}^{100 - r} 2^{r}

is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 8 - Binomial Theorem>Target Exercises>Q 18

If the coefficients of

x^{2}

and

x^{3}

in the expansion of

(3 + k x)^{9}

are equal, then the value of

k

is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 8 - Binomial Theorem>Target Exercises>Q 20

The coefficient of

x^{13}

in the expansion of

{(1 - x)}^{5} {(1 + x + x^{2} + x^{3})}^{4}

is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 8 - Binomial Theorem>Target Exercises>Q 21

The coefficient of

x^{6} \cdot y^{- 2}

in the expansion of

{(\frac{x^{2}}{y} - \frac{y}{x})}^{12}

is