Math Chapter Wise question with answer

Q01 The condition that ∂ ∂ d f f – = 0 dx y' y for the functional [ ] () ∫ 2 1 x I y(x) = f x,y,y' dx to have a station... English · UPPSC Polytechnic Lecturer 2021 (I) Q02 The extremal of the functional () ∫ 1 2 0 V[y(x)] = y' +12xy dx,y(0) = 0, y(1)=1, represents- English · UPPSC Polytechnic Lecturer 2021 (I) Q03 If F(x,y,y') is independent of x, then Euler's equation for the functional () ∫ 2 1 x F x,y,y' dx reduces to- English · UPPSC GDC 2021 UPPSC Polytechnic Lecturer 2021 (I) Q04 The Euler equation for the functional () () z ∫∫ 2 2 D x y I z x,y = + z dxdy satisfy- English · UPPSC Polytechnic Lecturer 2021 (I) Q05 The extremals of the functional ∫ 2 1 θ 2 2 '2 θ r + r dθ where () dr r = r θ,r' =, dθ is given by- English · UPPSC Polytechnic Lecturer 2021 (I) Q06 The extremals of the functional () ∫ π 2 2 2 5 0 I = y'' – y + x dx, () () y 0 = 0,y' 0 = 1 π 1 y' = 4 2 is- English · UPPSC Polytechnic Lecturer 2021 (I)