Describe the term Kalpanaswaram.
Kalpanaswaram is an improvisational aspect of Carnatic music where the performer spontaneously creates sequences of swaras (musical notes) adhering to the rules of the raga and tala. It is typically performed after the main composition (kriti) to showcase the musician's creativity, knowledge, and mastery over melody and rhythm.
Key features of Kalpanaswaram include:
Kalpanaswaram is a vital and exciting feature of Carnatic concerts, offering an opportunity for creative exploration within strict classical frameworks.
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 \( A \mathbf{X} = B \).