For the following questions answer them individually
The length of the longest diagonal of a cube is $$7\sqrt{3}$$ cm. Find its volume (in $$cm^{3}$$).
The mean proportional of $$\left(a + b\right) \left(a - b\right)^{3}, \left(a + b\right)^{3} \left(a - b\right)$$
A group of college students had decided to complete a project in 10 days. As 2 students dropped out every day, the project got completed at the end of the 15th day. The number of students at the beginning of the project was:
4 men, working together, can finish a work in 18 days. How many more men are required to finish the same work in 12 days?
Having started from the same point and at the same time, two runners - P and Q - are running around a circular track of length 500 m in opposite directions with the speeds of 6 m/s and 10 m/s, respectively. If they exchange their speeds after meeting for the first time, who will reach the starting point first?
A cuboid with sides 4, 6 and 8 units is covered with paper. The paper is removed and a square is made from it. What is the side (in units) of the square?
S deposits a total of ₹50,000 in two accounts which give 8% and 12% simple interest annually, respectively. After one year, he gets a total ₹5,200. How much money does he deposit in the account with a 12% interest rate?
Study the given table and answer the question that follows.
The table represents the expenditure of a company (in thousand rupees) per annum over the given year.
What is the average amount of salary per year, which the company has to pay during these four years?
Tarun owned a plot of land having an area that was 10% more than the area of the plot owned by Basab, while the area of the plot of land owned by Nakul was 40% more than the area of the plot owned by Tarun. If the area of the plot owned by Nakul was 2695 square feet, what was the area (in square feet) of the plot owned by Basab?