Math Chapter Wise question with answer

Q01 If 2 xy z = e,x = tcost,y = tsint, then the value of dz π at,t = is - dt 2 English · UPPSC Polytechnic Lecturer 2021 (I) Q02 If x = rcosθ, y = rsinθ, Then the value of 2 2 x y ∂ θ ∂ θ ∂ θ ∂ θ ∂ θ ∂ θ ∂ θ ∂ θ + ∂ ∂ is: English · PGT 2000 Q03 If x = r cos θ, y = r sin θ, then the value of ∂ (x, y) (r, θ) is: English · UP PCS (Pre) 1999 Q04 If x = r cos θ, y = r sin θ, then 2 x y ∂ θ ∂ ∂ is: English · UP PCS (Pre) 2000 Q05 If z = x2 + 2y2, x = r cosθ, y = r sinθ then z ∂ ∂θ is English · UP PCS (Pre) 2009 Q06 Evaluate lim(x,y,z)→ → →(3,0,1)exp–xy sin(xy/z): English · JSSC PGT 2018