Which day is 10th October, 2027?

Correct Answer: (A) Sunday

Calculating odd days up to October 10, 2027: from 2001 to 2026 (26 years with 6 leap years and 20 ordinary years), total odd days are $6$$\times$ 2 + 20 $\times$ 1 = 32 $\equiv$ 4 \pmod 7. In 2027, odd days through October 10 are: Jan(3) + Feb(0) + Mar(3) + Apr(2) + May(3) + Jun(2) + Jul(3) + Aug(3) + Sep(2) + 10 days of Oct(3) = 24 $\equiv 3(\mathrm{m}\mathrm{o}\mathrm{d}7)$$\equiv$ 3 \pmod 7. Total odd days = $4 + 3 = 7$$\equiv$ 0 \pmod 7, which corresponds to Sunday.