Yes, there are certain instances in the story that show an intersection of time and space. Firstly, the first two levels of Grand Central Station were located in the present time while the third level existed in the 1890s. Secondly, Charley and his wife, Louisa, live in the present time yet he rushes to get old currency to buy two tickets to go to the Galesburg of 1894. Further, the old architecture of the platform at the third level is different from the modern platforms of the first two levels. Besides, the archaic manner of dressing by the people, and the newspaper, The World, dated June 11, 1984 also overlaps with Charley’s real time world and existence. Lastly, the letter that was mailed to Charley’s grandfather on 18th July, 1894 highlights the intersection of time and space as the sender (Charley’s friend Sam) and receiver (Charley himself) belong to the present time.
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 \( A \mathbf{X} = B \).
Simar, Tanvi, and Umara were partners in a firm sharing profits and losses in the ratio of 5 : 6 : 9. On 31st March, 2024, their Balance Sheet was as follows:
Liabilities | Amount (₹) | Assets | Amount (₹) |
Capitals: | Fixed Assets | 25,00,000 | |
Simar | 13,00,000 | Stock | 10,00,000 |
Tanvi | 12,00,000 | Debtors | 8,00,000 |
Umara | 14,00,000 | Cash | 7,00,000 |
General Reserve | 7,00,000 | Profit and Loss A/c | 2,00,000 |
Trade Payables | 6,00,000 | ||
Total | 52,00,000 | Total | 52,00,000 |
Umara died on 30th June, 2024. The partnership deed provided for the following on the death of a partner:
A coil of 60 turns and area \( 1.5 \times 10^{-3} \, \text{m}^2 \) carrying a current of 2 A lies in a vertical plane. It experiences a torque of 0.12 Nm when placed in a uniform horizontal magnetic field. The torque acting on the coil changes to 0.05 Nm after the coil is rotated about its diameter by 90°. Find the magnitude of the magnetic field.
The sequence of nitrogenous bases in a segment of a coding strand of DNA is
5' – AATGCTAGGCAC – 3'. Choose the option that shows the correct sequence of nitrogenous bases in the mRNA transcribed by the DNA.