A coil of wire is would on an iron core looped back on itself so that the core has two sets of closely wound identical
coaxial coils in series carrying currents in opposite direction, the self inductance of such a system is
(a) zero (b) very large (c) very small (d) difficult to determine

q2) A coil of wire forming an inductor of inductance L is shetched to double its length, the inductance of the coil will
(a) change to L/4 (b) not change at all (c) change to L/2 (d) change to L/8

Q3) A ac − circuit has L = 12.6 mH and C = 1.15 μF, the amount of resistance that should be inserted into the circuit in
series to reduce the resonant frequency by 0.01 is
(a) 2.96 W (b) 8.76 W (c) 29.6 W (d) 87.6 W

hi,

for 1st question answer is c.....this method is ususlly used in resistance boxes to reduce inductance

2)the inductance a coil of N turns and lenth l and of area of cross section A is given by

       L=m_rm_oN²A/l

as the coil is streched its area of cross section changes but volume remains same.

so, to calculate the new inductance eliminating A is necessary as it is unknown that by which amount area is decrease  

                 L=m_rm_oN²A/l                     m_r=relative permeability,m_o=absolute permeability

                             L=kAl/l²                          k=m_rm_oN²=constant

                      L=kv/l²                           v=volume

                     when lenght is doubled

                     L'=kv/(2l)²

                            L'=kv/4l²

                    L'=L/4