Check the two claims against the meaning of the word gynoecious.
Gynoecious literally means female bearing, so a gynoecious bitter gourd line carries mostly female flowers with very few or no male flowers on the same plant. A male:female ratio of 25:1 would describe an ordinary monoecious bitter gourd, where male flowers vastly outnumber female flowers, which is the opposite of the gynoecious condition. This makes Statement (II) false.
On the historical side, IARI New Delhi is credited with releasing Pusa Hybrid-4 as the first hybrid of bitter gourd built on a gynoecious parent line, which supports Statement (I).
\[\boxed{\text{Statement (I) correct, Statement (II) incorrect}}\]