Usha and Mohak were partners in a firm. Usha withdrew a fixed amount at the end of every half-year for the year ended 31st March, 2024. Interest on drawings is charged at 9% p.a. Interest on Usha’s drawings will be charged for months.
Step 1: Usha withdrew a fixed amount at the end of every half-year. That means she withdrew twice in the year:
- First withdrawal at the end of September 2023
- Second withdrawal at the end of March 2024
Step 2: Interest on drawings is calculated for the period from date of withdrawal till the end of the financial year.
Step 3: Interest is charged as follows:
- For withdrawal on 30th September, interest = 6 months (Oct to Mar)
- For withdrawal on 31st March, interest = 0 months
Step 4: Average period = \( \frac{6 + 0}{2} = 3 \) months
Interest on drawings will be charged for 3 months.
A current-carrying coil is placed in an external uniform magnetic field. The coil is free to turn in the magnetic field. What is the net force acting on the coil? Obtain the orientation of the coil in stable equilibrium. Show that in this orientation the flux of the total field (field produced by the loop + external field) through the coil is maximum.
Three students, Neha, Rani, and Sam go to a market to purchase stationery items. Neha buys 4 pens, 3 notepads, and 2 erasers and pays ₹ 60. Rani buys 2 pens, 4 notepads, and 6 erasers for ₹ 90. Sam pays ₹ 70 for 6 pens, 2 notepads, and 3 erasers.
Based upon the above information, answer the following questions:
(i) Form the equations required to solve the problem of finding the price of each item, and express it in the matrix form \( A \mathbf{X} = B \).