When $2^{100}$  is divided by $11$, the remainder is

Important Questions on Elements of Number Theory and Congruence

HARD

RRC Group D CBT

IMPORTANT

RRB Indian Railway Group 'D' Recruitment - General Mathematics>Chapter 16 - Elements of Number Theory and Congruence>Exercise 1>Q 79

If $100\equiv x\left|7\right|$, then the least positive values of $x$ is

MEDIUM

RRC Group D CBT

IMPORTANT

RRB Indian Railway Group 'D' Recruitment - General Mathematics>Chapter 16 - Elements of Number Theory and Congruence>Exercise 1>Q 80

$0$ and $1$ are

MEDIUM

RRC Group D CBT

IMPORTANT

RRB Indian Railway Group 'D' Recruitment - General Mathematics>Chapter 16 - Elements of Number Theory and Congruence>Exercise 1>Q 81

The least positive integer to which $79\times 91\times 125$ is congruent mod $11$ is

HARD

RRC Group D CBT

IMPORTANT

RRB Indian Railway Group 'D' Recruitment - General Mathematics>Chapter 16 - Elements of Number Theory and Congruence>Exercise 1>Q 82

The last digit in $7^{291}$ is

HARD

RRC Group D CBT

IMPORTANT

RRB Indian Railway Group 'D' Recruitment - General Mathematics>Chapter 16 - Elements of Number Theory and Congruence>Exercise 1>Q 83

If $100\equiv x\left|7\right|$ Then the least positive values of $x$ is

EASY

RRC Group D CBT

IMPORTANT

RRB Indian Railway Group 'D' Recruitment - General Mathematics>Chapter 16 - Elements of Number Theory and Congruence>Exercise 1>Q 84

$1111----1 (91$ times$)$ is

HARD

RRC Group D CBT

IMPORTANT

RRB Indian Railway Group 'D' Recruitment - General Mathematics>Chapter 16 - Elements of Number Theory and Congruence>Exercise 1>Q 85

If $P$ is a prime number and $P$ is the product of all prime numbers less than or equal to $P$, then 

HARD

RRC Group D CBT

IMPORTANT

RRB Indian Railway Group 'D' Recruitment - General Mathematics>Chapter 16 - Elements of Number Theory and Congruence>Exercise 1>Q 86

The unit digit in ${13}^{37}$ is