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NDA 1 2025 Maths, question 7

Topic: Algebra

Q7

If x=(1111)2x = (1111)_{2}, y=(1001)2y = (1001)_{2} and z=(110)2z = (110)_{2}, then what is x3−y3−z3−3xyzx^{3} - y^{3} - z^{3} - 3xyz equal to?

  1. (a) (1111001)2(1111001)_{2}
  2. (b) (1001111)2(1001111)_{2}
  3. (c) (1)2(1)_{2}
  4. (d) (0)2(0)_{2}Correct answer

Solution.

Answer: (d) (0)2(0)_{2}

  1. Convert the binary numbers: x=15x = 15, y=9y = 9, z=6z = 6.
  2. Since x=y+zx = y + z, use (y+z)3=y3+z3+3yz(y+z)(y + z)^{3} = y^{3} + z^{3} + 3yz(y + z).
  3. The required expression is therefore 0, written (0)2(0)_{2}.