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The remainder, when $7^{103}$ is divided by $17,$ is

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Important Questions on Binomial Theorem

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Mathematics>Algebra>Binomial Theorem>Binomial Theorem for Positive Integral Index

Let

r

be the remainder when

2021^{2020}

is divided by

2020^{2}

. Then

r

lies between

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Mathematics>Algebra>Binomial Theorem>Binomial Theorem for Positive Integral Index

The digit at the unit place in the number

19^{2005} + 11^{2005} - 9^{2005}

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Mathematics>Algebra>Binomial Theorem>Binomial Theorem for Positive Integral Index

Let

M = 2^{30} - 2^{15} + 1,

and

M^{2}

be expressed in base

2 .

The number of

1^{'} s

in this base

2

representation of

M^{2}

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Mathematics>Algebra>Binomial Theorem>Binomial Theorem for Positive Integral Index

The number of terms which are free from fractional powers in the expansion of

{(a^{1 / 5} + b^{2 / 3})}^{45}, a \neq b

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Mathematics>Algebra>Binomial Theorem>Binomial Theorem for Positive Integral Index

If the fractional part of the number

\frac{2^{403}}{15}

\frac{k}{15},

then

k

is equal to

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Mathematics>Algebra>Binomial Theorem>Binomial Theorem for Positive Integral Index

(2021)^{3762}

is divided by

17,

then the remainder is _______.

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Mathematics>Algebra>Binomial Theorem>Binomial Theorem for Positive Integral Index

The number

(101)^{100} - 1

is divisible by

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Mathematics>Algebra>Binomial Theorem>Binomial Theorem for Positive Integral Index

The sum of all those terms which are rational numbers in the expansion of

{(2^{\frac{1}{3}} + 3^{\frac{1}{4}})}^{12}

is:

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Mathematics>Algebra>Binomial Theorem>Binomial Theorem for Positive Integral Index

{(27)}^{999}

is divided by

7

, then the remainder is

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Mathematics>Algebra>Binomial Theorem>Binomial Theorem for Positive Integral Index

{p}

denotes the fractional part of the number

p,

then

\{\frac{3^{200}}{8}\}

is equal to

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Mathematics>Algebra>Binomial Theorem>Binomial Theorem for Positive Integral Index

The remainder when

2^{2003}

is divided by

17

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Mathematics>Algebra>Binomial Theorem>Binomial Theorem for Positive Integral Index

The digit in the unit place of

7^{291}

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Mathematics>Algebra>Binomial Theorem>Binomial Theorem for Positive Integral Index

Remainder when

x = 1! + 2! + 3! + 4! + \dots + 100!

is divided by

240,

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Mathematics>Algebra>Binomial Theorem>Binomial Theorem for Positive Integral Index

If the remainder when

x

is divided by

4

3

, then the remainder when

{(2020 + x)}^{2022}

is divided by

8

is ___ .

EASY

Mathematics>Algebra>Binomial Theorem>Binomial Theorem for Positive Integral Index

x = 3^{100},

then

x

has

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Mathematics>Algebra>Binomial Theorem>Binomial Theorem for Positive Integral Index

3 \times 7^{22} + 2 \times 10^{22} - 44

when divided by

18

leaves the remainder

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Mathematics>Algebra>Binomial Theorem>Binomial Theorem for Positive Integral Index

The least positive integral value of

λ

such that

10^{50} + (3 \times {(4)}^{52}) + λ

is divisible by

9

HARD

Mathematics>Algebra>Binomial Theorem>Binomial Theorem for Positive Integral Index

If the number of integral terms in the expansion of

{(3^{\frac{1}{2}} + 5^{\frac{1}{8}})}^{n}

is exactly

33

, then the least value of

n

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Mathematics>Algebra>Binomial Theorem>Binomial Theorem for Positive Integral Index

The remainder when

2^{2000}

is divided by

17

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Mathematics>Algebra>Binomial Theorem>Binomial Theorem for Positive Integral Index

The fractional part of a real number

x

x - [x],

where

[x]

is the greatest integer less than or equal to

x .

Let

F_{1}

and

F_{2}

be the fractional parts of

{(44 - \sqrt{2017})}^{2017}

and

{(44 + \sqrt{2017})}^{2017}

respectively. Then

F_{1} + F_{2}

lies between the numbers

The remainder, when 7103 is divided by 17, is

Important Questions on Binomial Theorem

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The remainder, when $7^{103}$ is divided by $17,$ is