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MHT CET202519 Apr 2025Evening ShiftMathematicsFunctionsActual

The domain of the function f (x)= ^ 7-x P _ x-1

Options

  1. AR
  2. Bx R - 1
  3. C1,2,3,4
  4. D1,2,3,4,5,6

Correct answer

C. 1,2,3,4

Step-by-step solution

The domain of f(x) = ^ 7-x P _ x-1 requires that both 7-x and x-1 be non-negative integers with 7-x x-1 . Since 7-x 0 implies x 7 and x-1 0 gives x 1 , we also require 7-x x-1 , which simplifies to x 4 . The integer solutions satisfying 1 x 4 are verified to yield valid permutations. Verification confirms x = 1, 2, 3, 4 produce defined values: ⁶ P ₀ = 1 , ⁵ P ₁ = 5 , ⁴ P ₂ = 12 , and ³ P ₃ = 6 , respectively. The domain is 1,2,3,4 .

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