Q5
MCQ • 1M
Verbal & Numerical Aptitude
In a group of students, 10 students like Mathematics, 12 students like English, 4 students like both Mathematics and English, and 6 students like neither Mathematics nor English. The number of students in the group is ____
Q8
MCQ • 2M
Verbal & Numerical Aptitude
Consider the cube shown below with its 8 corners labelled a, b, c, d, e, f, g, and h. The figure is representative. All corners are to be colored such that any two corners that are connected by an edge must be of different colors. The minimum number of colors required to achieve this is ________
Q9
MCQ • 2M
Verbal & Numerical Aptitude
Four hills H1, H2, H3, and H4 are present in an area. The following observations are made about them: i. Neither H2 nor H3 is the easternmost hill. ii. Neither H2 nor H3 is the westernmost hill. iii. Neither the easternmost hill nor the westernmost hill is the southernmost hill. iv. Two hills are located to the west of H2. v. The southernmost hill has at least two hills to its east. The southernmost hill is ________.
Q31
NAT • 1M
Incompressible & Compressible Aerodynamics
An aircraft starts gliding in power-off condition at an altitude of 4 km. Given that the maximum lift to drag ratio of the aircraft is 15, the maximum glide range that the aircraft can cover, measured along the ground, is ________ km (rounded off to the nearest integer).
Q37
MCQ • 2M
Linear Algebra & Differential Equations
For the matrix A = [a b c d], if the relation a + b = c + d holds and a, b, c, d ≠ 0, then which one of the following statements about A is FALSE?
Q38
MCQ • 2M
Air-Breathing & Rocket Propulsion
In an ideal turbofan engine shown in the figure below, the compressor is driven by the high pressure turbine, and the fan is driven by the low pressure turbine. The stations 0, 2, 3, 4, 4.5, and 5 refer to free-stream, compressor inlet, compressor outlet, combustor exit, high pressure turbine exit, and low pressure turbine exit, respectively, and the subscript 't' refers to the total condition. Also, 𝜏r = Tt0 T0⁄ , 𝜏c = Tt3 Tt2⁄ and 𝜏𝜆 = Tt4 T0.⁄ The total temperature ratio of the high pressure turbine (Tt4.5 Tt4⁄ ) is given by ______.
Q39
MCQ • 2M
Air-Breathing & Rocket Propulsion
An ideal rocket has characteristic exhaust velocity of 1200 m/s, mass flow rate of 75 kg/s, thrust coefficient of 1.5, and nozzle throat area of 0.025 m2. The chamber pressure in kPa and the specific impulse due to gravity in seconds are ________, respectively. Assume that the acceleration due to gravity is 9.8 m/s2.
Q41
MCQ • 2M
Incompressible & Compressible Aerodynamics
Consider a launch vehicle of mass 10 tons being launched vertically. The vehicle has 8 tons of propellant, which burns completely at a constant rate over 50 s. If the engine specific impulse is 250 s, and the acceleration due to gravity at sea level is g0, the acceleration experienced by the vehicle at lift-off is ________.
Q42
MCQ • 2M
Structural Mechanics
The figure below shows a compressor stage with station numbers 1, 2, and 3 as indicated. If p0i, T0i, and Ci refer to the average values of total pressure, total temperature, and absolute flow speed, respectively, at the ith station, select the CORRECT option considering losses.
Q43
MCQ • 2M
Incompressible & Compressible Aerodynamics
An experimental study is planned to map out the low-Reynolds number incompressible steady two-dimensional aerodynamic characteristics of a promising novel airfoil. The operational parameters of the problem are the speed, density and viscosity of the freestream, the chord of the airfoil and its angle of attack. If the objective is to achieve this with the minimum number of test runs Nmin while taking 10 equally-spaced test values of each independent parameter of the problem in a suitable range, then Nmin is ________.
Q49
NAT • 2M
Linear Algebra & Differential Equations
Consider the differential equation with the initial conditions given below. If y(x) is the solution of the equation, the value of the slope, dy dx , at x = ln(2) is ________ (rounded off to three decimal places). d2y dx2 + 2 dy dx + y = 0 with y|x=0 = 0 and dy dx| x=0 = 1
Q52
NAT • 2M
Structural Mechanics
Isobutane (C4H10) is burnt completely in pure oxygen as per the reaction given below. Given that the standard heats of formation (in kcal/mole) of isobutane, carbon dioxide, and water vapour are -31.489, -94.052, and -60.150, respectively, the heat of reaction is ________ kcal (rounded off to 2 decimal places). C4H10 + 6.5 O2 → 4 CO2 + 5 H2O
Q53
NAT • 2M
Structural Mechanics
A furnace of 250 MW rating is used to melt and raise the temperature of aluminium from 25 oC to 900 oC. Aluminium has a solid-state specific heat, latent heat, and liquid-state specific heat of 0.9 kJ/kg-K, 390 kJ/kg, and 1.108 kJ/kg-K, respectively, and the furnace has 70% efficiency. The melting point of aluminium is 660 oC. The amount of aluminium that can be processed per hour is ________ kg (rounded off to 1 decimal place).
Q59
NAT • 2M
Structural Mechanics
A system comprising a bar, spring and mass is shown in the figure below. The bar, having negligible mass, is made of a material having Young's modulus E = 200 GPa, cross-sectional area A = 100 mm2, and length L = 100 mm. The spring stiffness k = 200 kN/mm and the mass M = 100 kg. The natural frequency of free vibration of the system is ________ rad/s (rounded off to the nearest integer).
Q61
NAT • 2M
Incompressible & Compressible Aerodynamics
A centrifugal compressor has a constant-width radial diffuser. The diameters at the diffuser inlet and outlet are 0.2 m and 0.3 m, respectively. The flow at the diffuser inlet and outlet is assumed to be steady and uniform. The average velocity at the diffuser inlet and outlet are (60 êr + 75 ê𝛉) m/s and (u êr + 50 ê𝛉) m/s, respectively. If the flow through the diffuser is treated as steady and incompressible, the value of u is ________ (rounded off to the nearest integer).