The unit digit in ${13}^{37}$ 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 87

When $7^{30}$ is divided by $5$, the remainder 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 88

If $a$ and $b$ are natural numbers such that $a^2+b^2$ is a prime number, 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 89

The sum of all positive divisors of $960$excluding $1$ and itself 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 90

The unit digit in the number $7^{126}$ 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 91

The remainder in the division of $2^{50 }$by $7$ 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 92

The value of $x$ such that $3x\equiv 2 \left|7\right|$  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 93

Which of the following linear congruence has no solution ?

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 94

The digit in the unit place of the number $183!+3^{183}$ is