UGCNET Questions

Compound interest for 2 years at 10% per annum is computed using the amount formula A = P(1 + R/100) raised to the power of time. Here, A = 10,000 × (1 + 10/100)² = 10,000 × (1.1)². The value of (1.1)² is 1.21, so the amount becomes 10,000 × 1.21 = 12,100. The compound interest is the amount minus the principal, which is 12,100 − 10,000 = ₹2,100.

Option A:
Option A, ₹1,000, equals simple interest for one year at 10% but fails to account for the interest-on-interest effect in the second year. It underestimates the total interest earned over two years.

Option B:
Option B, ₹2,000, corresponds to simple interest over two years (10% each year on the principal only), but compound interest is slightly higher because the second year’s interest is also earned on the first year’s interest.

Option C:
Option C correctly derives the amount using the compound interest factor (1.1)² and subtracts the original principal. This procedure captures the compounding process and yields the slightly larger interest of ₹2,100.

Option D:
Option D, ₹2,200, overstates the effect of compounding and would require a higher effective rate or more time than actually given in the problem.

The given series multiplies each term by a constant factor to obtain the next one. Specifically, 9 ÷ 3 = 3, 27 ÷ 9 = 3 and 81 ÷ 27 = 3, so the common ratio is 3. To continue the pattern, we multiply 81 by 3 to obtain the next term. This gives 81 × 3 = 243, which preserves the geometric progression.

Option A:
Option A, 162, arises if someone incorrectly multiplies by 2 instead of 3, giving 81 × 2. However, this contradicts the established common ratio of 3 used in all previous steps.

Option B:
Option B, 200, does not correspond to any simple multiple of 81 consistent with the progression and seems unrelated to the pattern.

Option C:
Option C, 225, is 15² and may be chosen due to familiarity with square numbers, but it does not follow from multiplying 81 by the common ratio 3.

Option D:
Option D maintains the constant ratio of 3 between consecutive terms. By applying 81 × 3, we get 243, which is the only option that respects the geometric structure of the series.