key : As we know that at t = 0 capacitor offers zero resistance and at t = infinity capacitors get fully charged and offers infinite resistance (in another term we assume break in circuit ).While inductor offers infinite resistance at t = 0 and zero resistance at t = infinite (in fully charged condition).So According to above concept we draw the circuit diagram at t = 0 and t = infinity as shown.so at t = 0Resistance of capacitor = 0, so potential difference = 0resistance of 10 \\Omega is out of circuit because current choose to follow the path having less resistance and capacitor has zero resistance at t=0. So current will follow this path only.So according to image (i), at t = 0Total resistance of circuit (R) = 20 + 20 = 40 \\Omega Total potential difference (V) = 20\\ V Current I = \\dfrac { V }{ R } ,Therefore I= \\dfrac { 20 }{ 40 } = 0.5\\ A At t = \\infty Resistance due to inductor is zero so potential difference across inductor at t = \\infty is zero.according to image (ii) solving circuit. Last two 10 \\Omega and 20 \\Omega resistances are in parallel, so its resultant resistance (R1) = \\dfrac { 20\ imes 10 }{ 20+10 } = \\dfrac { 20 }{ 3 } \\Omega \\quad First two resistances 10, 20 and resultant R1 are in series.So total resistance of circuit ( R_2 ) = 10+20 + \\dfrac { 20 }{ 3 } =\\dfrac { 110 }{ 3 } \\Omega \\quad Current at t = \\infty , I = \\dfrac { V }{ R2 } I = \\dfrac { 20 }{ \\dfrac { 110 }{ 3 } } \\quad =\\quad \\dfrac { 6 }{ 11 }\\ A. All options are true.