physics-mechanics

Statement (1) is wrong
since Vs/Vp = Ns/Np, where Vs and Vp are the output and input voltages of the transformer respectively.
Ns and Np are the no. of turns in the secondary and primary coils respectively
When Vp =220 v and Vs = 6 v, then Ns/Np = 6/220
or Np = (220/6).Ns
when Vp = 220 v and Vs = 12 v, then Ns/Np' = 12/220
i.e. Np' = (220/12).Ns = (1/2)(220/6).Ns = Np/2
Therefore, the no of turns of the primary coil should be halved, not doubled.
Statement (2) is wrong.
Since the load is fixed, using power P = Vs^2/R, where R is the load resistance, doubling the secondary voltage from 6 v to 12 v will increase the power by 4 times (12^2/R against 6^2/R).
Since the transformer is 100% efficiency, the input power is also increased by 4 times. Since input power = Vp.Ip (Ip is the primary current), an increase of 4 times the input power indicates an increase of 4 times the primary current, as Vp is fixed at 220 v.
Statement(3) is correct.
When the ouptut voltage is at 6 v,
power = 6^/R watts = 36/R watts (R is the load resistance)
When the ouput power is at 12 v,
new power = 12^2/R watts = 144/R watts
hence, new power/original power = 144/36 = 4