NDA 2025 · PYQ · Number Systems / Binary · medium
If x = (1111)₂, y = (1001)₂ and z = (110)₂, then what is x³ - y³ - z³ - 3xyz equal to?
- A.(1111001)₂
- B.(1001111)₂
- C.(1)₂
- D.(0)₂✓ Correct
In decimal: x = 15, y = 9, z = 6. Note x = y + z (15 = 9 + 6). Using identity: if x = y + z, then x³ - y³ - z³ = 3yz·x (since (y+z)³ = y³ + z³ + 3yz(y+z)). So x³ - y³ - z³ = 3xyz, hence x³ - y³ - z³ - 3xyz = 0 = (0)₂.
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