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 u = x y +, then the value of 2 2 2 2 2 2 u u u x xy y, x y ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ + + ∂ ∂ is - English · UPPSC GIC 2021 Q03 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 Q04 If 1 y u tan, x − = then the value of u u x y ∂ ∂ + ∂ ∂ is English · Rajasthan TGT 2015 Q05 If x = r cos θ, y = r sin θ, then the value of ∂ (x, y) (r, θ) is: English · UP PCS (Pre) 1999 Q06 If u =2(ax+by)2 –(x2 +y2) and a2 +b2 = 1, then the value of 2 2 u u x y ∂ ∂ + ∂ ∂ is: English · UP PCS (Pre) 1999