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 = sin–1 2 2 + y x, then x ∂ ∂ u u + y y x is equal to – English · UP PGT 2021 UP PCS (Pre) 1994 Rajsthan TGT 2011 Q03 If L= → 2 2 (x,y) (0,0) sin(x + y) lim x + y and () → 2 2 (x,y) (0,0) x – y M = lim,then - x + y English · UPPSC Polytechnic Lecturer 2021 (I) Q04 If 2 2 1 2 2 x y u sin x y − = + then u u x y ∂ ∂ + ∂ ∂ equal to English · PGT 2011 Q05 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 Q06 If 2 2 1 x y f sin x y − + = + then f f x x y ∂ ∂ + ∂ ∂ is equal to English · Rajasthan TGT 2011 UP PCS (Pre) -1994