Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>Assignment>Q 13

HARD

JEE Main/Advance

IMPORTANT

Earn 100

The remainder when $2^{2019} + 2020$ is divided by $17$ is

77.78% studentsanswered this correctly

Important Questions on Binomial Theorem

HARD

JEE Main/Advance

IMPORTANT

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

The largest integer

k

such that

2^{k}

divides

3^{2^{n}} - 1

is

HARD

JEE Main/Advance

IMPORTANT

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

Let

f (x) = \frac{\sum_{r = 0}^{100} {}^{100}C_{r} \sin 2 r x}{\sum_{r = 0}^{100} {}^{100}C_{r} \cos 2 r x}

then

f (\frac{π}{800})

is equal

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>Assignment>Q 1

For a positive integer

n

, if the expansion of

{(\frac{5}{x^{2}} + x^{4})}^{n}

has a term independent of

x

, then

n

can be

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>Assignment>Q 2

The positive value of

a

so that the coefficients of

x^{5}

is equal to that of

x^{15}

in the expansion of

{(x^{2} + \frac{a}{x^{3}})}^{10}

is:

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>Assignment>Q 3

The sum of the coefficients of all the even powers of

x

in the expansion of

{(2 x^{2} - 3 x + 1)}^{11}

is

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>Assignment>Q 4

The term independent of

x

in the expansion of

{(x - \frac{1}{x})}^{4} {(x + \frac{1}{x})}^{3}

is

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 6 - Binomial Theorem>Assignment>Q 5

If the second, third and fourth terms in the expansion of

(x + y)^{n}

be

135, 30

and

\frac{10}{3}

respectively, then

HARD

JEE Main/Advance

IMPORTANT

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

\sum_{r = 0}^{6} {(- 1)}^{r} (\begin{matrix} 16 \\ r \end{matrix})

is divisible by