The GATE Grind

GATE Real Analysis: Multivariable Analysis – Previous Year Questions

4 GATE previous year questions on Multivariable Analysis (Real Analysis, Mathematics) with answers and explanations, from every paper.

  1. GATE 2021 MA Q50 (2 marks, Multiple choice) – The equation xy−z log y+e(xz)=1 defines y=f(x,z) near (x,y,z)=(0,1,1). Find ∇f(0,1).
  2. GATE 2024 MA Q28 (1 mark, Numerical answer) – For x,y>0, f(x,y)=(x²−y²,2xy). Let g be its local inverse near f(2,1). Find det Dg at f(2,1), to two decimals.
  3. GATE 2025 MA Q21 (1 mark, Multiple choice) – F:ℝ²→ℝ² is F(x,y)=(x3-3xy2-3x,3x2y-y3-3y). Where is the inverse function theorem applicable?
  4. GATE 2026 MA Q16 (1 mark, Multiple choice) – f: R2 R2 is f(x,y)=(ex y,ex y). Which statement is true?