1. In compound interest, if the interest rates for the first, second, and third years are \(r_1\%\), \(r_2\%\), and \(2r_3\%\) respectively, then the amount after 3 years on a principal of ₹\(P\) will be: \[ P\left(1 + \cfrac{r_1}{100}\right)\left(1 + \cfrac{r_2}{100}\right)\left(1 + \cfrac{r_3}{100}\right) \]

2. If the principal is \(p\) rupees and the annual compound interest rates for the first, second, and third years are \(r_1\%\), \(r_2\%\), and \(r_3\%\) respectively, then what will be the total compound amount after 3 years?

3. Sudip Babu deposited ₹7,800 in the bank at compound interest. If the compound interest rates for the first, second, third, and fourth years are 5%, 4%, 10%, and 12% respectively, then what will be the compound principal after 4 years?

(a) ₹ 10,493.68 (b) ₹ 10,000 (c) ₹ 14,936 (d) none of the above

4. If the annual interest rates for ₹8000 in the first and second years are 9% and 10% respectively, then the amount after 2 years including interest will be –

(a) ₹ 9295 (b) ₹9952 (c) ₹ 9259 (d) ₹ 9592

5. If the compound interest rates for the first, second, and third years are 6%, 4%, and 10% respectively, then how much total amount (principal + interest) will a person receive after investing ₹50,000 for 3 years?

6. If the mode and the combined mean of a statistical distribution are ₹12.30 and ₹18.48 respectively, then the median of the distribution will be —

(a) ₹ 16 (b) ₹ 17 (c) ₹ 16.42 (d) ₹ 17.42

7. If five positive, whole, consecutive proportional numbers have the first and third terms as 3 and 12 respectively, then what are the remaining numbers?

(a) 24 and 48 (b) 26 and 52 (c) 25 and 50 (d) 28 and 54

8. The perimeters of two similar triangles are 20 cm and 16 cm respectively. If the length of a side of the first triangle is 4 cm, then the length of the corresponding side of the second triangle will be ____ .

9. If the interest rates for the first, second, and third years are 5%, 8%, and 10%, respectively, then the compound principal at the end of 3 years on ₹16,000 would be—

(a) ₹ 16,958 (b) ₹ 19,958.40 (c) ₹ 17,958 (d) ₹ 18,958.40

10. If the interest rates for the first, second, and third years are 5%, 10%, and 15% respectively, what will be the compound interest on ₹5000 at the end of 3 years?

(a) ₹ 2000 (b) ₹1900 (c) ₹ 1700 (d) ₹ 1641.25