Regarding the 61st National Chess Championship:

1. GM Karthik Venkataraman triumphed in Gurgaon, earning ₹6 lakh.

2. IM Neelash Saha took silver but was edged out in a tiebreak against Ganguly.

The correct option is Both 1 and 2.

Let us analyze both statements regarding the 61st National Chess Championship:

1. Statement 1: GM Karthik Venkataraman won the 61st National Chess Championship held in Gurgaon (Gurugram), Haryana. He finished with 9 points out of 11 rounds to claim the title along with a cash prize of ₹6 lakh. Therefore, Statement 1 is correct.

2. Statement 2: International Master (IM) Neelash Saha also secured 9 points in the tournament. However, due to tiebreak scores (Buchholz system), GM Surya Shekhar Ganguly bagged the silver medal, while IM Neelash Saha took third place/bronze behind Ganguly. Thus, Neelash Saha was edged out in the tiebreak criteria against Ganguly, making Statement 2 correct.

Since both statements 1 and 2 are accurate, the correct answer is Both 1 and 2.