UPSC NDA I 2016 Mathematics Solved Paper

x and y are positive numbers
x≤y2
Reflexive-
x≤x2∀ positive numbers
Hence relation is reflexive
Transitive-
x≤y2‌‌‌‌‌‌‌‌y≤z2
Let x=5,y=3,z=2
5≤(3)2‌‌‌‌‌‌‌‌(3)‌≤(2)2
but 5≮(2)2
Hence x≤y2‌‌‌‌‌‌‌‌y≤z2
x≰z2
Thus relation is not transitive
Symmetric
1≤(2)2 while 2≰(1)2
Hence relation is not symmetric.
Thus x≤y2∀ positive number is reflexive,but not transitive and symmetric