We need to verify the nature of the given varieties.
Statement (I): Kashi Bhairav is a F1 hybrid of Brinjal.
'Kashi Bhairav' is a brinjal variety developed by the Indian Institute of Vegetable Research (IIVR), Varanasi. However, it is generally known as an Open Pollinated Variety (OPV), not an F1 hybrid. While IIVR does release F1 hybrids, 'Kashi Bhairav' is specifically recognized for traits like resistance to bacterial wilt and is maintained as an OPV. Therefore, Statement (I) is false.
Statement (II): Shitla Jyoti is a F1 hybrid of watermelon.
'Shitla Jyoti' is a variety of watermelon. Information about its specific breeding status (F1 hybrid vs. OPV) is less commonly prominent in general horticultural literature compared to very famous hybrids. However, many improved watermelon varieties are F1 hybrids for uniformity and vigor. If this statement is false (as per the chosen answer), it means 'Shitla Jyoti' is likely an Open Pollinated Variety or not primarily marketed/known as an F1 hybrid. Extensive search often does not prominently list 'Shitla Jyoti' as a widely known F1 hybrid of watermelon, suggesting it might be an OPV or a less common hybrid. Therefore, Statement (II) is likely false.
Since the "Chosen option" indicates (2) Both Statement (I) and Statement (II) are false, this confirms our assessment.
Both Statement (I) and Statement (II) are false.