Q4
MCQ • 1M
Analytical & Spatial 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?
Q8
MCQ • 2M
Quantitative 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?
Q32
NAT • 1M
Strength of Materials & Elasticity
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
Structural Dynamics & Aeroelasticity
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
Aerospace Materials & Fatigue
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
Differential Equations
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
Numerical Methods
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
Basic Fluid Mechanics
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.
Q49
NAT • 2M
Static Stability & Control
A rigid bar AB is subjected to a uniformly distributed load of 100 N/m as shown in the figure. The bar is supported by rod CD, with A, C, and D as pin joints. The rod CD has axial stiffness of 40 N/mm. The vertical deflection at point D is __________ mm. (round off to nearest integer)
Q51
NAT • 2M
Space Dynamics & Orbital Mechanics
A single degree-of-freedom spring-mass-damper system has viscous damping ratio of 0.1. The mass is given an initial displacement of 10 cm without imparting any velocity. After exactly two complete cycles of oscillation (i.e., after time 2 dT , where dT is the period of the damped vibration) , the amplitud e of the displacement is ______ cm. (round off to two decimal place)
Q52
NAT • 2M
Space Dynamics & Orbital Mechanics
The shear flow distribution in a single cell, thin-walled beam under the action of an arbitrary shear load ys applied at the shear centre S is shown in the figure. The cell has horizontal symmetry with booms marked by 1 to 4 that carry direct stresses. The shear modulus G is the same for all the walls, and the area of the cell is 135000 mm2. With respect to the point O marked in the figure, the distance to the shear centre S is ______ mm. (round off to the nearest integer)
Q55
NAT • 2M
Inlets, Combustors & Nozzles
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
Inlets, Combustors & Nozzles
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).