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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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