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NDA 2 2025 Maths, question 3

Topic: Algebra

Q3

Let y=x!y=x! and z=(2x)!z=(2x)!. If (z/y)=120(z/y)=120, then what is the value of (3x)!(3x)!?

  1. (a) 362880362880Correct answer
  2. (b) 181440181440
  3. (c) 9072090720
  4. (d) 4536045360

Solution.

Answer: (a) 362880362880

  1. For nonnegative integer x, (2x)!/x! = (x+1)(x+2)…(2x).
  2. At x=3 this is 4×5×6=120.
  3. The ratio strictly increases for positive integer x, so this is the only solution.
  4. Therefore (3x)! = 9! = 362880.