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If XAY means X² + Y² is XBY means X² -Y² is XCY means (X + Y)² is XDY means (X - Y)² is then what is true of the following?
Question

If XAY means X² + Y² is
XBY means X² -Y² is
XCY means (X + Y)² is
XDY means (X - Y)² is
then what is true of the following?

A.

(7C3) - (6D6) = -100

B.

(3C2) D (5B5) = 624

C.

(3A2) B (5C4) = 88

D.

216D256 = 1600

Correct option is D

Given:
XAY means X² + Y²
XBY means X² -Y²
XCY means (X + Y)²
XDY means (X - Y)²
Lets check by options:
Option (a): (7C3) - (6D6) = -100
= (7+3)2 - (6-6)2
= 102 - 0
= 100
So, 100 = -100 (Does not follow)
Option (b): (3C2) D (5B5) = 624
= {(3+2)2 - (52-52)}2
= {52 - 0 }2
= 252
= 625
So, 625 = 624 (Does not follow)
Option (c): (3A2) B (5C4) = 88 
= {(32 +22)}2 - {(5+4)2}2
= {(9+4)2 - {(9)2}2
= 132 - 812
= 169 - 6561
= -6392
So, -6392 = 88 (Does not follow)
Option (d): 216D256 = 1600
= (216 - 256)2
= (-40)2
= 1600
So, 1600 = 1600 (Follow)
Thus, the correct answer is (d).

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