Mathematics Crash Course JEE Main>Chapter 3 - Binomial Theorem>Level 1>Q 17

MEDIUM

JEE Main

IMPORTANT

Earn 100

The number of distinct terms in the expansion of ${(x + y^{2})}^{13} + {(x^{2} + y)}^{14}$ is

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Important Questions on Binomial Theorem

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 3 - Binomial Theorem>Level 1>Q 18

Find the last two digits of

\frac{N}{1000},

if

N = 9^{100} - 1 .

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 3 - Binomial Theorem>Level 1>Q 19

The expression

{(\sqrt{2 x^{2} + 1} + \sqrt{2 x^{2} - 1})}^{6} + {(\frac{2}{\sqrt{2 x^{2} + 1} + \sqrt{2 x^{2} - 1}})}^{6}

is a polynomial of degree

MEDIUM

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 3 - Binomial Theorem>Level 1>Q 20

The coefficient of

x^{- n}

in

{(1 + x)}^{n} {(1 + \frac{1}{x})}^{n}

is

MEDIUM

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 3 - Binomial Theorem>Level 1>Q 21

If

p^{4} + q^{3} = 2 (p > 0, q > 0)

, then the maximum value of term independent of

x

in the expansion of

{(p x^{\frac{1}{12}} + q x^{- \frac{1}{9}})}^{14}

is

MEDIUM

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 3 - Binomial Theorem>Level 1>Q 22

In the binomial expansion

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

, if the ratio of the seventh term from the beginning of the expansion to the seventh term from its end is

\frac{1}{6}

, then

n =

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 3 - Binomial Theorem>Level 1>Q 23

If the coefficients of

r^{th}, {(r + 1)}^{th}

and

{(r + 2)}^{th}

terms in the binomial expansion of

{(1 + y)}^{m}

are in

AP,

then

m

and

r

satisfy the equation

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 3 - Binomial Theorem>Level 1>Q 24

If the coefficient of

x^{7}

in

{[a x^{2} + \frac{1}{b x}]}^{11}

equals the coefficient of

x^{- 7}

in

{[a x - \frac{1}{b x^{2}}]}^{11},

then

a

and

b

satisfy the relation

MEDIUM

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 3 - Binomial Theorem>Level 1>Q 25

The coefficient of the middle term in the binomial expansion in powers of

x

of

{(1 + α x)}^{4}

and of

{(1 - α x)}^{6}

is the same, if

α

equals