ASHCHARYA BANSAL

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Which one of the following statements regarding a Rankine cycle is FALSE? Cycle efficiency increases as boiler pressure decreases. Superheating the steam in the boiler increases the cycle efficiency. The pressure at the turbine outlet depends on the condenser temperature.  Cycle efficiency increases as condenser pressure decreases.

Steady, compressible flow of air takes place through an adiabatic converging-diverging nozzle, as shown in the figure. For a particular value of pressure difference across the nozzle, a stationary normal shock wave forms in the diverging section of the nozzle. If E and F denote the flow conditions just upstream and downstream of the normal shock, respectively, which of the following statement(s) is/are TRUE? Mach number at E is lower than the Mach number at F Density at E is lower than the density at F Specific entropy at E is lower than the specific entropy at F Static pressure at E is lower than the static pressure at F

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What is the effective annual interest rate if a nominal interest rate of 6% per annum is compounded semi-annually? 6.06% 6.07% 6.08% 6.09%

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The circumference of a jogging track is 735 m. Peter and Tom start walking from the same point at the same time in opposite direction. If they are walking at 6 km/hr and 8 km/hr respectively, after how much time they will meet? Option 3 minutes 12 minutes 15 minutes 4 minutes

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Part of tank filled by pipe A in one hour working alone = 1 / 12 Part of tank filled by pipe B in one hour working alone = 1 / 16 => Part of tank filled by pipe A and pipe B in one hour working together = (1 / 12) + (1 / 16) = 7 / 48 Therefore, time taken to completely fill the tank if both A and B work together = 48 / 7 hours

Part of tank filled by pipe A in one hour working alone = 1 / 10 Part of tank filled by pipe B in one hour working alone = 1 / 12 Part of tank emptied by pipe C in one hour working alone = 1 / 30 => Part of tank filled by pipes A,B and C in one hour working together = (1 / 10) + (1 / 12) – (1 / 30) = 3 / 20 Therefore, time taken to completely fill the tank if both A and B work together = 20 / 3 hours = 6 hours 40 minutes

Part of tank filled by pipe A in one hour working alone = 1 / 10 Part of tank emptied by pipe B in one hour working alone = 1 / 12 Part of tank emptied by pipe C in one hour working alone = 1 / 30 => Part of tank filled by pipes A, B and C in one hour working together = (1 / 10) – (1 / 12) – (1 / 30) = -1 / 60 Therefore, time taken to completely empty the tank if all pipes are opened simultaneously = 1 / 60 hours = 60 hours

Let the time taken by first pipe working alone be ‘t’ minutes. => Time taken by second pipe working alone = t + 10 minutes. Part of tank filled by pipe A in one hour working alone = 1 / t Part of tank filled by pipe B in one hour working alone = 1 / (t + 10) => Part of tank filled by pipe A and B in one hour working together = (1 / t) + (1 / t+10) = (2t + 10) / [t x (t + 10)] But we are given that it takes 12 minutes to completely fill the cistern if both pipes are working together. => (2t + 10) / [t x (t + 10)] = 1 / 12 => t x (t + 10) / (2t + 10) = 12 => t2 + 10t = 24t + 120 => t2 – 14t – 120 = 0 => (t – 20) (t + 6) = 0 => t = 20 minutes (Time cannot be negative) Therefore, time taken by second pipe working alone = 20 + 10 = 30 minutes

Let the capacity of tank be LCM (10, 30) = 30 units => Efficiency of pipe A = 30 / 10 = 3 units / hour => Efficiency of pipe B = 30 / 30 = 1 units / hour => Combined efficiency of pipes A and B = 4 units/hour Therefore, time taken to completely fill the tank if only A and B are opened = 30 / 4 = 7 hours 30 minutes => Time taken to completely fill the tank if all pipes are opened = 7 hours 30 minutes + 30 minutes = 8 hours => Combined efficiency of all pipes = 30 / 8 = 3.75 units / hour Now, efficiency of pipe C = Combined efficiency of all three pipes – Combined efficiency of pipes A and B Therefore, efficiency of pipe C = 4 – 3.75 = 0.25 units / hour Thus, time taken to empty the tank if only C is opened = 30 / 0.25 = 120 hours.

Let the capacity of the tank be LCM (36, 45, 30) = 180 units => Efficiency of pipe A = 180 / 36 = 5 units / second => Efficiency of pipe B = 180 / 45 = 4 units / second => Efficiency of pipe C = – 180 / 30 = – 6 units / second Now, for the first 7 seconds, A and B were open. => Combined efficiency of A and B = 5 + 4 = 9 units / second => Part of the tank filled in 7 seconds = 7 x 9 = 63 units => Part of tank empty = 180 – 63 = 117 units Now, all pipes are opened. => Combined efficiency of all pipes = 5 + 4 – 6 = 3 units / second Therefore, more time required = 117 / 3 = 39 seconds.

Let the capacity of the tank be LCM (20, 30) = 60 units => Efficiency of pipe A = 60 / 20 = 3 units / hour => Efficiency of pipe B = 60 / 30 = 2 units / hour => Combined efficiency of pipes A and B = 5 units / hour Let both A and B be opened for ‘n’ hours and then, B be closed and only A be opened for the remaining ’18 – n’ hours. => 5n + 3 x (18 – n) = 60 => 2n + 54 = 60 => 2n = 6 => n = 3 Therefore, B should be closed after 3 hours.\