Chemegate
Home/Practice Tests/PYQ Archive/General Aptitude

GATE 2024 Chemical Engineering, Q3 · General Aptitude

The correct answer is A, nᵐ = mⁿ.

Question

For positive integers m and n, with m/n ≠ 1, (m/n)^(m/n) =mm/n−1.= m^{m/n − 1}. Then,

  • A. nᵐ =mn= mⁿ
  • B. nᵐ =m2n= m²ⁿ
  • C. n=m\sqrt{n} = \sqrt{m}
  • D. n1/m=m1/nn^{1/m} = m^{1/n}

Official answer: nᵐ =mn= mⁿ

Why

GATE 2024 official key: (A). Manipulating the given identity and equating exponents of the resulting power relation leads to mᵐ =nn.= nⁿ.

Explanation cross-checked for consistency. Final answer matches the official IIT answer key.

More General Aptitude PYQs →Take the Full GATE 2024 Test →