Math

Question 1 UGC NET June-2020    
Given below are two statements:
Statement I:
5 divides n5-n whenever n is a non-negative integer.
Statement II: 6 divides n3-n whenever n is a non-negative integer.
In the light of the above statements, choose the correct answer from the options given below
A – Both Statement I and Statement II are correct
B – Both Statement I and Statement II are incorrect
C – Statement I is correct but Statement II is incorrect
D – Statement I is incorrect but Statement II is correct

Show Answer With Best Explanation

Answer: A
Explanation:
Statement I: n5 – n
Example : Take n = 2 , 25- 2 = 32 – 2 = 30 , which is divided by 5.
Take n = 3 , 35 – 3 = 243 – 3 = 240 , which is divided by 5.
Statement I is true.
Statement II: n3 – n
Example : Take n = 2 , 23- 2 = 8 – 2 = 6 , which is divided by 6.
Take n = 3 , 33 – 3 = 27 – 3 = 24 , which is divided by 6.
Statement II is true.


Question 1 UGC NET June-2020    
The number of positive integers not exceeding 100 that are either odd or the square of an integer is _.
A – 63
B – 59
C – 55
D – 50

Show Answer With Best Explanation

Answer : C


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