Q61.If z = x2 + 2y2, x = r cosθ, y = r sinθ then z ∂ ∂θ is
Correct answer: r2/sin 2θ
Q62.If x y u x, y x = φ + ψ = φ + ψ = φ + ψ = φ + ψ then the value of 2 2 2 2 2 u u u x 2xy y, x y ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ + + ∂ ∂ is:
Correct answer: 0
Q63.The function f(x,y) may have a maximum or minimum at a point, if at that point:
Correct answer: None of these
EnglishPGT-2005 UP PCS (Pre) 1997
Q64.If u=exyz, then 3 u x y z ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ is equal to:
Correct answer: xyz 2 2 2 e 1 3xyz x y z + +
EnglishNVS PGT 10-06-2019
Q65.If A = fxx (a, b), B = fxy (a, b) and C = fyy (a, b), then the function f(x, y) will have a maximum at the point (a, b) if:
Correct answer: fx = 0, fy = 0, AC > B2 and A < 0