Math Chapter Wise question with answer

Q01 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) Q02 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) Q03 An extremals to the functional () () () ∫ b 2 a V y x = 1+ y' x dx English · UPPSC Polytechnic Lecturer 2021 (I) Q04 The number of extremals s for the functional 1 2 2 0 I[y()] (y y 2y y')d,y(0) 1,y(1) 2 = + − = ∫ x x x is: English · UKPSC Lecturer (Mains) 2020 Q05 How many extremals s are possible for the extremals () ∫ 2 1 2 0 d y I y x = + y dx,y(0) = 1, dx () () () y 1 = –1,... English · UPPSC Polytechnic Lecturer 2021 (I) Q06 The extremals of 1 2 2 0 I[y()] [y y' ]d, = + ∫ x x x y(0) 0,y(1) 1 = English · UKPSC Lecturer (Mains) 2020