The correct answer is that both statements are correct.

Statement 1: The Peninsular region of India does not have a well-defined cold weather season. This is largely true. While the Peninsular plateau experiences cooler temperatures during winter compared to the summer months, the temperature differences are less pronounced than in the northern plains of India. The lack of significant snowfall and the relatively moderate temperature fluctuations result in a less defined cold weather season compared to the northern parts of the country.

Statement 2: By the end of December (that is, by 22 December), the Sun shines vertically over the Tropic of Capricorn in the Southern Hemisphere. This is correct. The December solstice occurs around December 21st or 22nd each year. This is the point at which the Sun reaches its southernmost declination and is directly overhead at the Tropic of Capricorn (23.5° South latitude). This marks the beginning of summer in the Southern Hemisphere and winter in the Northern Hemisphere. The Earth's axial tilt and revolution around the Sun cause this variation in the Sun's vertical position throughout the year.

Therefore, both statements accurately reflect geographical and astronomical realities.