KVS 30-12-2018 Part B
December 30, 2024UGC NET CS 2008-june-Paper-2
December 31, 2024UGC NET CS 2008-june-Paper-2
| Question 5 |
In a set of 8 positive integers, there always exists a pair of numbers having the same remainder when divided by :
| 7 | |
| 11 | |
| 13 | |
| 15 |
Question 5 Explanation:
Given data,
— Set of positive integers=8
— A pair of numbers having the same remainder when divided by=?
Step-1: This problem, we can use pigeonhole principle.
Pigeonhole Principle: If there are ‘X’ positive integers to be placed in ‘Y’ possible remainder where Y < X, then there is at least one possible remainder which receives more than one positive integer.
Option-A: Total number of possible remainders, divided by 7 is 0,1,2,3,4,5,6.
These numbers are less than 8 only.
Option-B,C and D: Total number of possible remainders,
divided by 11, 13, 15 is greater than 8
— Set of positive integers=8
— A pair of numbers having the same remainder when divided by=?
Step-1: This problem, we can use pigeonhole principle.
Pigeonhole Principle: If there are ‘X’ positive integers to be placed in ‘Y’ possible remainder where Y < X, then there is at least one possible remainder which receives more than one positive integer.
Option-A: Total number of possible remainders, divided by 7 is 0,1,2,3,4,5,6.
These numbers are less than 8 only.
Option-B,C and D: Total number of possible remainders,
divided by 11, 13, 15 is greater than 8
Correct Answer: A
Question 5 Explanation:
Given data,
— Set of positive integers=8
— A pair of numbers having the same remainder when divided by=?
Step-1: This problem, we can use pigeonhole principle.
Pigeonhole Principle: If there are ‘X’ positive integers to be placed in ‘Y’ possible remainder where Y < X, then there is at least one possible remainder which receives more than one positive integer.
Option-A: Total number of possible remainders, divided by 7 is 0,1,2,3,4,5,6.
These numbers are less than 8 only.
Option-B,C and D: Total number of possible remainders,
divided by 11, 13, 15 is greater than 8
— Set of positive integers=8
— A pair of numbers having the same remainder when divided by=?
Step-1: This problem, we can use pigeonhole principle.
Pigeonhole Principle: If there are ‘X’ positive integers to be placed in ‘Y’ possible remainder where Y < X, then there is at least one possible remainder which receives more than one positive integer.
Option-A: Total number of possible remainders, divided by 7 is 0,1,2,3,4,5,6.
These numbers are less than 8 only.
Option-B,C and D: Total number of possible remainders,
divided by 11, 13, 15 is greater than 8
Subscribe
Login
0 Comments