Let a1,a2,....an be n nonzero real numbers, of which p are positive and remaining are negative. The number of ordered pairs (j,k), j<k, for which ajak is positive, is 55. Similarly, the number of ordered pairs (j,k), j<k, for which ajak is negative is 50. Then the value of p2+(n–p)2 is
The correct option is D 125
There are p positive numbers and (n−p) negative numbers.
The number of pairs for ajak to be negative,
The number of pairs for ajak to be positive,
using equation (i),
Assuming the (p+50p)=y
[∵y cannot be negative]