Option 1 states that compared to the year 1950, the annual foodgrain production in India has risen to around four times by the year 2001. This statement is correct. Over the years, India has made significant progress in increasing its foodgrain production to meet the growing demands of its population.

Option 2 states that in the last three decades, the area under pulse cultivation has remained stagnant. This statement is also correct. Despite efforts to increase the production of pulses, the area under cultivation has not witnessed substantial growth.

Option 3 states that India is the largest producer of vegetables in the world. However, this statement is incorrect. While India is one of the largest producers of vegetables globally, it is not the largest.

Option 4 states that India is the second largest exporter of cashewnut in the world. This statement is not mentioned in the given question, so it is outside the scope of the question.

Therefore, the correct answer is option 1, which includes statements 1 and 2.