Q4
MCQ • 1M
Verbal & Numerical Aptitude
In 2022, June Huh was awarded the Fields medal, which is the highest prize in Mathematics. When he was younger, he was also a poet. He did not win any medals in the International Mathematics Olympiads. He dropped out of college. Based only on the above information, which one of the following statements can be logically inferred with certainty?
Q6
MCQ • 2M
Verbal & Numerical Aptitude
Human beings are one among many creatures that inhabit an imagined world. In this imagined world, some creatures are cruel. If in this imagined world, it is given that the statement " Some human beings are not cruel creatures" is FALSE, then which of the following set of statement(s) can be logically inferred with certainty? (i) All human beings are cruel creatures. (ii) Some human beings are cruel creatures. (iii) Some creatures that are cruel are human beings. (iv) No human beings are cruel creatures.
Q8
MCQ • 2M
Verbal & Numerical Aptitude
The World Bank has declared that it does not plan to offer new financing to Sri Lanka, which is battling its worst economic crisis in decades, until the country has an adequate macroeconomic policy framework in place. In a statement, the World Bank said Sr i Lanka needed to adopt structural reforms that focus on economic stabilisation and tackle the root causes of its crisis. The latter has starved it of foreign exchange and led to shortages of food, fuel, and medicines. The bank is repurposing resources under existing loans to help alleviate shortages of essential items such as medicine, cooking gas, fertiliser, meals for children, and cash for vulnerable households. Based only on the above passage, which one of the following statements can be inferred with certainty?
Q17
MCQ • 1M
Incompressible & Compressible Aerodynamics
An ideal glider has drag characteristics given by 0D D D i C C C=+ , where 2 DLi C KC= is the induced drag coefficient, LC is the lift coefficient, and K is a constant. For maximum range of the glider, the ratio 0DD i CC is
Q32
NAT • 1M
Incompressible & Compressible Aerodynamics
An airplane weighing 40 kN is landing on a horizontal runway during which it is retarded by an arresting cable mechanism. The tension in the arresting cable at a given instant, as shown in the figure, is 100 kN. Assuming that the thrust from the engine continues to balance airplane drag, the magnitude of horizontal load factor is ________. (round off to one decimal place)
Q34
NAT • 1M
Incompressible & Compressible Aerodynamics
Airplane A and Airplane B are cruising at altitudes of 2 km and 4 km, respectively. The free stream density and static pressure at altitude 2 km are 1.01 kg/m3 and 79.50 kPa, respectively, and at altitude 4 km, they are 0.82 kg/m3 and 61.70 kPa, respectively. The differential pressure reading from the pitot-static tubes is 3 kPa for both the airplanes. Assuming incompressible flow, the ratio of cruise speeds of Airplane A to Airplane B is ______. (round off to two decimal places)
Q35
NAT • 1M
Air-Breathing & Rocket Propulsion
A supersonic vehicle powered by a ramjet engine is cruising at a speed of 1000 m/s. The ramjet engine burns hydrogen in a subsonic combustor to produce thrust. The heat of combustion for hydrogen is 120 MJ/kg. The overall efficiency of the engine o , defined as the ratio of propulsive power to the total heat release in the combustor, is 40%. Taking acceleration due to gravity 0 10g = m/s2, the specific impulse of the engine is _____________ seconds. (round off to the nearest integer).
Q38
MCQ • 2M
Incompressible & Compressible Aerodynamics
Two missiles A and B powered by solid rocket motors have identical specific impulse, liftoff mass of 5600 kg each, and burn durations of 30At = s and 70Bt = s, respectively. The propellant mass flow rates, Am and Bm , for missiles A and B, respectively, are given by 120 kg/s, 0 30 70 kg/s, 0 70 A B t t m m = = Neglecting gravity and aerodynamic forces, the relationship between the final velocities AV and BV of missiles A and B, respectively, is given by
Q39
MCQ • 2M
Incompressible & Compressible Aerodynamics
A perfect gas stored in a large reservoir exhausts into the atmosphere through a convergent duct. The reservoir pressure is P0 and temperature is T0. The jet emerges from the nozzle at choked conditions with average velocity u, Mach number M, pressure p, temperature T, and density . If the reservoir pressure is increased, then
Q41
MCQ • 2M
Incompressible & Compressible Aerodynamics
A scramjet engine features an intake, isolator, combustor, and a nozzle, as shown in the schematic. Station 3 indicates the combustor entry point. Assume stagnation enthalpy to be constant between Stations 1 and 3, and air to be a calorically perfect gas with specific heat ratio γ. Select the correct expression for Mach number M3 at the inlet to the combustor from the options given.
Q55
NAT • 2M
Structural Mechanics
The operating characteristics of a pump were measured to be 2 PCa = , where power coefficient 35P PC D= , is the flow coefficient, a is a constant, D is a length scale, is the rotation rate, is fluid density, and P is the power required. The flow coefficient is a dimensionless volume flow rate scaled with and D . Assuming that the flow rate remains the same, if the rotation rate is increased to 1.25 , the power changes to P . The value of is ________ . (round off to two decimal places)
Q57
NAT • 2M
Structural Mechanics
In a potential flow, a uniform stream of strength U directed along the x-axis and four line sources (2-dimensional) of strengths , , ,2 3 4 5 -- are placed along the x-axis at x = 0, 1, 2 and 3, respectively. The strength of an additional line source to be placed at 4x = such that a closed streamline encircles all five sources is _____. (round off to two decimal places).