Q1. Suppose the correlation coefficient between x and y is denoted by R,
and that between x and (y + x), by R1.
Then, ( A ) R1 > R ; ( B ) R1 = R ;
(C ) R1 < R ( D ) none of these.
For lack of characters i'll use the letter T to represent the triangle operator mentioned in the question
now T is a linear operator and
T^2(f(x))= T(T(f(x)))
=T(f(x+1)-f(x))
=T(f(x+1))-T(f(x))
=f(x+2)-2f(x+1)+f(x)
now compare this with the options below for k=2 and you can see that options b and d are incorrect
now find T^3(f(x)) and again compare with the remaining options for k=3..you will get c as answer