Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>Assignment>Q 14

HARD

JEE Main/Advance

IMPORTANT

Earn 100

The number of rational terms in the expansion of ${(\sqrt[3]{25} + \frac{1}{\sqrt[3]{25}})}^{20}$ is

64.71% studentsanswered this correctly

Important Questions on Binomial Theorem

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>Assignment>Q 15

If in the expansion of

(1 + k x)^{4}

the coefficient of

x^{3}

is

32

, then the value of

k

is equal to

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>Assignment>Q 16

In the expansion of

(x + a)^{5}, T_{2} : T_{3} = 1 : 3

, then

x : a

is equal to

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>Assignment>Q 17

If in the expansion of

{(a x^{2} + \frac{1}{b x})}^{11}

the coefficient of

x^{7}

is equal to the coefficient of

x^{- 7}

in the expansion of

{(a x - \frac{1}{b x^{2}})}^{11}

, then

a b

is equal to

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>Assignment>Q 18

Coefficient of

x^{12}

in the expansion of

{(1 + x^{2})}^{50}

{(x + \frac{1}{x})}^{- 10}

is

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>Assignment>Q 19

The term independent of

x

in the expansion of

{(\sqrt[6]{x} - \frac{2}{\sqrt[3]{x}})}^{18}

is

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>Assignment>Q 20

(1.003)^{4}

is nearly equal to

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>Assignment>Q 21

The two consecutive terms in the expansion of

(3 + 2 x)^{74}

which have equal coefficients, are

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>Assignment>Q 22

The co-efficient of

r^{t h}, {(r + 1)}^{t h}

and

(r + 2)^{t h}

terms in the expansion of

(1 + x)^{14}

are in

A . P .,

the value of

r

is equal to