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 An external of the functional [ ] () 3 + ∫ ' 2 y 0 I y(x) = e dx,y(0) = 0,y(2)=1, is- English · UPPSC Polytechnic Lecturer 2021 (I) Q03 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) Q04 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) Q05 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) Q06 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)