Math Chapter Wise question with answer

Q01 Let f(x, y) = 2 2 2 x y x + y for (x, y) ≠ (0, 0) then English · Bihar (TRE 1.0) -2023 Q02 If V = (x2 + y2 + z2)–1/2, then ∂ ∂ ∂ ∂ ∂ ∂ V V V x + y + z x y z is equal to English · UP PGT 2021 Q03 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 Q04 If u = f (y/x), then the value of u u x y ∂ ∂ + ∂ ∂ is – English · UPPSC GIC 2021 Q05 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 Q06 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)