EAMCET Engineering 2003 Solved Paper

Let the three resistances are R1,R2 and R3.
∴‌‌‌

R1

R2

=‌

1

2

⇒R1=k,R2=2k
In parallel,
‌

1

R

‌=‌

1

R1

+‌

1

R2

+‌

1

R3

‌

1

1

‌=‌

1

k

+‌

1

2k

+‌

1

R3

‌

1

R3

‌=1−‌

1

k

−‌

1

2k

‌=‌

2k−2−1

2k

=‌

2k−3

2k

R3‌=‌

2k

2k−3

If k=1, then R3 is found to be negative, which is impossible.
If k=2, then R1=2,R2=4,R3=4
R2=R3, not satisfying the condition of the question that all resistance are unequal.
If k=3, then R1=3,R2=6
R3‌=2Ω
∴‌‌‌ Largest resistance ‌‌=6Ω