Quantitative Ability
Directions: Answer Questions 13 and 14 based upon the following passage.
The Indian cricket team's selection board has to select 16 players in its team for an away tour to Australia and New Zealand. There are a total of 34 probables at the selection camp. The table below indicates the number of players available in different specialist categories and the corresponding number to be selected in the team. Each player belongs to one and only one category, and the categories are mutually exclusive and collectively exhaustive. Assume that within each specialist category the players have an equal chance of being selected.
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Directions: Answer Questions 13 and 14 based upon the following passage.
The Indian cricket team's selection board has to select 16 players in its team for an away tour to Australia and New Zealand. There are a total of 34 probables at the selection camp. The table below indicates the number of players available in different specialist categories and the corresponding number to be selected in the team. Each player belongs to one and only one category, and the categories are mutually exclusive and collectively exhaustive. Assume that within each specialist category the players have an equal chance of being selected.
| Specialist Category | Available | To be selected 'K' |
|---|---|---|
| Opening Batsman Middle-order (No.3 to 6) All-rounder Wicketkeeper Pace Bowler Spin Bowler | 6 10 4 4 5 5 | 2 ≤ K ≤ 3 5 ≤ K ≤ 7 1 ≤ K ≤ 2 1 ≤ K ≤ 2 3 ≤ K ≤ 4 2 ≤ K ≤ 3 |
| Q.13: | In how many ways can a team be chosen if all three Opening Batsman and both Wicketkeeper probables are chosen? | |||
| (A) 10C5 4C1 5C3 5C2 | (B) 24C11 | (C) 10C5 + 4C1 + 5C3 + 5C2 | (D) None | |
| Q.14: | In addition, what is the probability that all four Pace Bowler probables will be selected given that both All-rounders are selected? | |||
| (A) 0 | (B) 1/4 | (C) 4/34 | (D) None | |
| Q.15: | A hotel charges different prices for the same meal in two different locations. The demand function in each location is given by: P1 = 50 - 4Q1 in Location 1 P2 = 80 - 3Q2 in Location 2 The hotel's cost function is TC = 120 + 8Q, where Q = Q1 + Q2. Note that in general, the profit is maximized at Q* when (dTC/dQ) = (dP/dQ). The price and quantity at Locations 1 and 2 respectively for which the hotel's profit is maximized are: | |||
| (A) P1 = 29.2 P2 = 44 Q1 = 5.2 Q2 = 12 | (B) P1 = 44 P2 = 29.2 Q1 = 5.2 Q2 = 12 | |||
| (C) P1 = 44 P2 = 29.2 Q1 = 12 Q5.2 = 12 | (D) None | |||
| Q.16: | The present rate at which furnace oil (in '000 litres) is consumed monthly by a large engineering company is estimated as: Consumption rate = dQ/dt = 1560e0.012t where, 't' is in months. The ratio of consumption during the first ten months to the next ten months is: | |||
| (A) 0.89 | (B) 1.12 | (C) 1/2 | (D) None | |
| Q.17: | A carpenter employed on casual basis in a firm agrees to accept Rs.2000/= for the first week of his work. He negotiates for his pay to be raised by 1% every subsequent week. After serving for 10 weeks, he renegotiates his pay at Rs.2500/= for the next immediate week and a 2% raise every subsequent week. The total amount he would earn at the end of 30 weeks, and the average pay per week for the entire period of his work are: | |||
| (A) 33934.5 and 2262.3 | (B) 33528.6 and 2235.2 | (C) 33224.3 and 2163.5 | (D) None | |
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