select the number pair in which the two numbers are related in the same way as are the two numbers of the following number pair 16 :224
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2
Answer:
The required option is "(d) 8 : 113".
We have,
7 : 85
The patter follow,
n = n^{2} +(n-1)^{2}n=n
2
+(n−1)
2
7 = 7^{2} +(7-1)^{2} =49+36=857
2
+(7−1)
2
=49+36=85
Check options:
a) 3 : 31
3 = 3^{2} +(3-1)^{2} =9+4=133=3
2
+(3−1)
2
=9+4=13 ≠ 31, it is false
b) 2 : 9
2 = 2^{2} +(2-1)^{2} =4+1=52=2
2
+(2−1)
2
=4+1=5 ≠ 9, it is false
c) 5 : 43
5 = 5^{2} +(5-1)^{2} =25+16=415=5
2
+(5−1)
2
=25+16=41 ≠ 43, it is false
d) 8 : 113
8 = 8^{2} +(8-1)^{2} =64+49=1138=8
2
+(8−1)
2
=64+49=113 , it is true
Hence, the required option is "d) 8 : 113".
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