Given,
\(k\) = 1.237 × 10-2 S m-1 , c = 0.001 M
Then, \(k\) = 1.237 × 10-4 S cm-1 , c ½ = 0.0316 M½
∴ \(\land_m=\frac{\kappa}{c}\)
= \(\frac{1.237\times 10^{-4} S cm^{-1}}{0.001 mol L^{-1}} \times \frac{1000 cm^3}{L}\)
=123.7 S cm2 mol-1
Given,
\(k\) = 11.85 × 10-2 S m-1 , c = 0.010M
Then, \(k\) = 11.85 × 10-4 S cm-1 , c ½ = 0.1 M½
\(\therefore \land_m = \frac{\kappa}{c}\)
\(= \frac{11.85\times 10^{-4}S cm^{-1}}{0.010 mol L^{-1}}\times \frac{1000 cm^3}{L}\)
\(= 118.5 S cm^2mol^{-1}\)
Given,
\(k\) = 23.15 × 10-2 S m-1 , c = 0.020 M
Then, \(k\) = 23.15 × 10-4 S cm-1 , c1/2 = 0.1414 M½
∴\(\land_m = \frac{\kappa}{c}\)
=\(\frac{23.15\times 10^{-4}Scm^{-1}}{0.020 mol L^{1}}\times\frac{1000cm^3}{L}\)
= 115.8 S cm2 mol-1
Given,
\(k\) = 55.53 × 10-2 S m-1 , c = 0.050 M
Then, \(k\) = 55.53 × 10-4 S cm-1 , c1/2 = 0.2236 M½
∴ \(\land_m = \frac{\kappa}{c}\)
= \(\frac{55.53 \times 10^{-4}Scm^{-1}}{0.050 mol L^{-1}}\times\frac{1000 cm^3}{L}\)
= 111.1 1 S cm2 mol-1
Given,
\(k\) = 106.74 × 10-2 S m-1 , c = 0.100 M
Then, \(k\) = 106.74 × 10-4 S cm-1 , c1/2 = 0.3162 M½
∴ \(\land_m = \frac{\kappa}{c}\)
= \(\frac{106.74 \times 10^{-4}Scm^{-1}}{0.100 mol \; L^{-1}}\times\frac{1000cm^3}{L}\)
= 106.74 S cm2 mol-1
Now, we have the following data:
c½/M½ | 0.0316 | 0.1 | 0.1414 | 0.2236 | 0.3162 |
\(\land_m(S cm^2\, mol^{-1})\) | 123.7 | 118.5 | 115.8 | 111.1 | 106.74 |
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:
Conductance is an expression of the ease with which electric current flows through materials like metals and nonmetals. In equations, an uppercase letter G symbolizes conductance. The standard unit of conductance is siemens (S), formerly known as mho.
Conductance in electricity is considered the opposite of resistance (R). Resistance is essentially the amount of friction a component presents to the flow of current.