Q1
MCQ[1 Mark]
“He often _____ the numbers. False claims are not going to help. Honesty _____ trust”, said the manager. Choose the option with the correct order of words to fill the blanks.
Type:
General Aptitude
10 QuestionsQ2
MCQ[1 Mark]
In the sequence of tiles shown below, the missing tile indicated by the question mark should be
Q3
MCQ[1 Mark]
A school has 100 students distributed among 1st to 10th standards. Based on this, which one of the following statements is always correct?
Q4
MCQ[1 Mark]
How many 3-digit numbers can be formed using three distinct single digit prime numbers?
Q5
MCQ[1 Mark]
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 ____
Q6
MCQ[2 Marks]
Charity : P :: Retaliation : Q Choose the appropriate pair of words P and Q that fit the analogy.
Q7
MCQ[2 Marks]
A paper shown in Panel I is folded along the dashed lines (- - -) to construct a cube. The shaded regions shown in Panel I appear on the outer surface of the cube. Referring to cubes shown in Panel II, which one of the options is correct?
Q8
MCQ[2 Marks]
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[2 Marks]
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 ________.
Q10
MCQ[2 Marks]
As shown in the figure, circle 𝐶1 with center 𝑂1 and radius 𝑟1 touches the square 𝑉𝑊𝑋𝑌 at points 𝑃 and 𝑄 while circle 𝐶2 with center 𝑂2 and radius 𝑟2 touches the square 𝑉𝑊𝑋𝑌 at points 𝑅 and 𝑆. The two circles touch each other at 𝑇. Given 𝑟1 = 1 cm and ̅̅̅̅ ̅̅̅̅̅ = 4 cm, 𝑟2 = _____ cm. 𝑉𝑌 = 𝑉𝑊
Engineering Mathematics
9 QuestionsQ11
MCQ[1 Mark]
Consider the contour 𝐶 shown in the figure below. For the vector 𝐹⃗ = (𝑥 + 2𝑦)𝑒̂𝑥 + (2𝑥 + 4𝑦)𝑒̂𝑦 , the integral ∮𝐶 𝐹⃗ ⋅ 𝑑𝑙⃗ =________. Here 𝑑𝑙⃗ represents an infinitesimal length along the contour 𝐶.
Q12
MCQ[1 Mark]
The Fourier series representation of a square wave is shown in the figure below. The fluctuations seen near x = ±1 are named after which one of the following scientists?
Q13
MCQ[1 Mark]
The following equation with respect to 𝜑(𝑥, 𝑡), where 𝑎 is a non-zero constant, represents ________. 𝜕𝜑 𝜕𝜑 +𝑎 =0 𝜕𝑡 𝜕𝑥
Q14
MSQ[1 Mark]
An 𝑛 × 𝑛 square matrix 𝐴 satisfies 𝐴𝑇 = 𝐴−1. The determinant of this matrix may take which of the following value(s)?
Q15
NAT[1 Mark]
If a matrix can be written as 𝐴 = 𝑢𝑣 𝑇 , where both 𝑢 and 𝑣 are 𝑛-dimensional real- valued non-zero column vectors, then the rank of the matrix 𝐴 is ________ (answer in integer).
Q16
MCQ[2 Marks]
𝑎 𝑏 For the matrix 𝐴 = [ ], if the relation 𝑎 + 𝑏 = 𝑐 + 𝑑 holds and 𝑎, 𝑏, 𝑐, 𝑑 ≠ 0, 𝑐 𝑑 then which one of the following statements about 𝐴 is FALSE?
Q17
NAT[2 Marks]
Consider the differential equation with the initial conditions given below. If 𝑦(𝑥) 𝑑𝑦 is the solution of the equation, the value of the slope, , at 𝑥 = ln(2) is 𝑑𝑥 ________ (rounded off to three decimal places). 𝑑2 𝑦 𝑑𝑦 𝑑𝑦 2 +2 + 𝑦 = 0 with 𝑦|𝑥=0 = 0 and | =1 𝑑𝑥 𝑑𝑥 𝑑𝑥 𝑥=0
Q18
NAT[2 Marks]
An object of mass 1 kg is launched with an initial speed of 𝑣𝑜 into a large tank filled with a viscous liquid. The liquid exerts a resistive force (drag) of the form 𝐷 = 𝛼𝑣 on any object that is moving inside it, where 𝑣 is the instantaneous speed of the object and 𝛼 = 1 kg/s. If the effect of gravity is ignored, the time taken by the object to slow down to the speed 𝑣𝑜 /2 is ________ s (rounded off to 2 decimal places). Assume that the tank is sufficiently large for the above deceleration to happen inside the tank.
Q19
NAT[2 Marks]
The minimum value of the function 𝑓(𝑥) = |𝑥| + |2𝑥 + 3| for real 𝑥 is ________ (rounded off to 1 decimal place).
Aerodynamics
17 QuestionsQ20
MCQ[1 Mark]
In fluid dynamics, d’Alembert’s paradox refers to which one of the following?
Q21
MCQ[1 Mark]
The velocity potential function (𝜑) given below represents which one of the following? 𝜑 = 5𝑥 − 12𝑦
Q22
MCQ[1 Mark]
The fundamental purpose of the Kutta condition in the thin airfoil theory is ________.
Q23
MCQ[1 Mark]
In the figure shown below, the flow at the nozzle exit is ________.
Q24
MSQ[1 Mark]
Shown below are qualitative illustrations of the lift curve for an airfoil when two different control surfaces are in their respective retracted and deployed configurations. Which of the following is/are TRUE?
Q25
MSQ[1 Mark]
Which of the following statements is/are TRUE regarding critical and drag divergence Mach numbers of a wing?
Q26
MSQ[1 Mark]
A flow is steady, inviscid and one-dimensional, with no shaft work or body forces. Which of the following is/are possible under the given conditions?
Q27
NAT[1 Mark]
The vortex shedding frequency behind a landing gear model is found to be 50 Hz when tested in a wind tunnel operating at 5 m/s. If the actual landing gear size is 10 times that of the model, and it is designed to operate at 50 m/s, then the expected vortex shedding frequency behind it is ________ Hz (rounded off to the nearest integer).
Q28
NAT[1 Mark]
An elliptic wing has a span of 6 m and a planform area of 6 m2. When generating a lift coefficient of 0.6, the induced drag it incurs is ________ × 10−3 (rounded off to 1 decimal place).
Q29
MCQ[2 Marks]
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 ________.
Q30
MSQ[2 Marks]
Consider the flow over an oval modeled using the elementary potential flows as shown below. 𝑈 represents uniform flow velocity and 𝛤 represents circulation around an irrotational line vortex. Which of the following statements is/are TRUE for this model?
Q31
MSQ[2 Marks]
What is/are the use(s) of the single horseshoe vortex model of finite wing aerodynamic theory?
Q32
NAT[2 Marks]
For an airfoil section the pitching moment coefficient is determined about a reference point that is 0.3 times the chord behind the leading edge. It varies with the lift coefficient as shown in the table below. The distance of the aerodynamic center from the leading edge of the airfoil as a fraction of the chord is ________ (rounded off to one decimal place). 𝑐𝑙 0.2 0.4 0.6 0.8 𝑐𝑚 – 0.02 0 0.02 0.04
Q33
NAT[2 Marks]
Consider a finite wing of aspect ratio 10 with span effectiveness factor 0.95. Its airfoil section has a lift slope of 0.106 per degree and a zero-lift angle of attack of –1.5°. The lift coefficient of the wing at an angle of attack of 3.5° is ________ (rounded off to 2 decimal places).
Q34
NAT[2 Marks]
Thin airfoil theory predicts the zero-lift angle of attack 𝛼𝐿=0 of NACA 2412 airfoil as −2.1°. The corresponding prediction of 𝛼𝐿=0 for NACA 5410 airfoil is ________ degrees (rounded off to 1 decimal place).
Q35
NAT[2 Marks]
Consider a centered Prandtl-Meyer expansion fan at a 𝜃 = 4° corner in a Mach 1.78 air flow, as shown in the figure below. The angle ψ (see figure) made by the ending wave of the fan with respect to the incoming stream is ________ degrees (rounded off to 1 decimal place). An excerpt from the table of Prandtl-Meyer function for air is provided below. M ν [deg] M ν [deg] M ν [deg] 1.72 18.40 1.82 21.30 1.92 24.15 1.74 18.98 1.84 21.88 1.94 24.71 1.76 19.56 1.86 22.45 1.96 25.27 1.78 20.15 1.88 23.02 1.98 25.83 1.80 20.73 1.90 23.59 2.00 26.38
Q36
NAT[2 Marks]
A Mach 1.5 air flow enters a round duct of length 20 cm and diameter 3 cm. If the flow exits with Mach number 1.1, the average Fanning friction factor 𝑓 of the duct is ________ × 10−3 (rounded off to 1 decimal place). An excerpt from the Fanno flow table for air is given below. M 1.1 1.2 1.3 1.4 1.5 1.6 𝟒𝒇𝑳∗ × 𝟏𝟎𝟒 99.35 336.4 648.3 997.4 1361 1724 𝑫
Flight Mechanics
3 QuestionsQ37
MSQ[1 Mark]
Which of the following statements is/are TRUE about the stability of an aircraft?
Q38
NAT[1 Mark]
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).
Q39
NAT[2 Marks]
𝑊𝐴 and 𝑊𝐵 are the respective maximum take-off weights of an aircraft for two ambient air conditions given below. Condition A: 𝑝 = 1 bar, 𝑇 = 50 o C; Condition B: 𝑝 = 0.66 bar, 𝑇 = −30 o C If all other parameters relevant for take-off are kept the same in these two conditions, the ratio 𝑊𝐵 /𝑊𝐴 is ________ (rounded off to 3 decimal places).
Structures
9 QuestionsQ40
MCQ[1 Mark]
The number of independent elastic constants that a fully anisotropic linear elastic material can have is ______.
Q41
MCQ[1 Mark]
A cantilever beam with an unsymmetric cross-section is subjected to a transverse shear force (P) at its free end. P acts at the shear center of the beam cross-section. Which one of the following statements is TRUE about the deformation of this beam?
Q42
MSQ[1 Mark]
The state of stress at a point in a 2-D body, in the x-y Cartesian coordinate system, is represented in matrix form as [σ]. The transformation matrix [Q] rotates the coordinate system to a new x'-y' Cartesian coordinate system. Select the CORRECT option(s) that represent(s) the state of stress in the new coordinate system.
Q43
NAT[1 Mark]
The response 𝑥(𝑡) of a freely vibrating single degree of freedom underdamped system is given below. In the equation, 𝐴 and 𝜙 are constants. The damping ratio of the system is ________ (rounded off to 3 decimal places). 𝑥(𝑡) = 𝐴e−5𝑡 sin(10𝑡 + 𝜙)
Q44
MCQ[2 Marks]
Consider a unit square body as shown in the figure below. The body is subjected to the deformation field u = –ay and v = ax, where ‘a’ is a constant. Due to the application of this deformation field, the body undergoes _______ in the x-y plane.
Q45
MSQ[2 Marks]
The deformation of an open-section bar subjected to pure torsion can be solved by choosing an appropriate Prandtl stress function. Which of the following statements is/are true about the Prandtl stress function?
Q46
NAT[2 Marks]
A thin-walled circular tube is made of a material whose magnitude of the ultimate strength, both in tension and compression, is 200 MPa. The mean radius of the tube is 0.2 m and the wall thickness is 0.004 m. Based on the maximum stress criteria, the maximum torque that the tube can sustain is ________ kN-m (round off to the nearest integer).
Q47
NAT[2 Marks]
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).
Q48
NAT[2 Marks]
A stepped cantilever beam, made of a material having Young’s modulus E = 200 GPa, is shown in the figure below. The length and the moment of inertia of the beam from point A to B are L1 = 100 mm and I1 = 100 mm4, respectively. The length and the moment of inertia of the beam from point B to C are L2 = 100 mm and I2 = 700 mm4, respectively. A shear force P = 30 N is applied at point A of the beam. The magnitude of the deflection of the beam at point A is ________ mm (rounded off to 1 decimal place).
Propulsion
15 QuestionsQ49
MCQ[1 Mark]
Which one of the following makes an ideal air-standard Stirling cycle?
Q50
MCQ[1 Mark]
The figure below depicts two ideal gas turbine cycles, cycle 1-2-3-4-1 and cycle 1-2-3'-4'-1, on a T-s diagram. Which one the following statements is FALSE?
Q51
MSQ[1 Mark]
For a given air-standard power, the propulsive efficiency of a turbofan engine is more than that of a turbojet engine. Which of the following is/are the reason(s) for this?
Q52
MSQ[1 Mark]
The figure below shows the blading of the rotors of two different axial turbomachines under their typical operating conditions, labelled as Configuration I and Configuration II. Which of the following statements is/are TRUE?
Q53
MSQ[1 Mark]
A multi-stage axial compressor can be operated at two points, A and B, both of which lie on the same speed line, as shown in the figure below. If 𝜂 is the isentropic efficiency of the compressor, select the statements that is/are TRUE.
Q54
MCQ[2 Marks]
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 ______.
Q55
MCQ[2 Marks]
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.
Q56
MCQ[2 Marks]
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 ________.
Q57
MCQ[2 Marks]
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 𝑖 th station, select the CORRECT option considering losses.
Q58
MSQ[2 Marks]
Which of the following process(es) is/are involved in the compression of air in an ideal ramjet engine?
Q59
MSQ[2 Marks]
The figure below shows the velocity triangles at the inlet and outlet of the rotor of a low hub-to-tip ratio axial compressor at the mid-span of the blade. The absolute and relative velocities of the flow are denoted by C and W, respectively. The subscripts 1 and 2 refer to the locations before and after the rotor, respectively. The blade velocity is denoted by U. Select the CORRECT statement(s) for this device.
Q60
NAT[2 Marks]
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
Q61
NAT[2 Marks]
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).
Q62
NAT[2 Marks]
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).
Q63
NAT[2 Marks]
A gas mixture at a pressure of 800 kPa and a density of 5 kg/m3 enters a turbine stage. The temperature of the gas at the nozzle exit and the stage exit are 790 K and 750 K, respectively. Assume the specific heats are constant for the gas mixture in the range of temperatures considered. The specific heat at constant pressure is 0.72 kJ/kg-K and the ratio of specific heats is 1.33. The value of the degree of reaction of the turbine stage is ________ (rounded off to 2 decimal places).
Space Dynamics
2 QuestionsQ64
MCQ[2 Marks]
An earth satellite has the instantaneous position vector 𝑟⃗ and velocity vector 𝑣⃗ as given below. Here 𝑝̂ and 𝑞̂ denote the unit vectors along the 𝑥 and 𝑦 axes of the perifocal frame, respectively. Assume that the value of gravitational parameter is 398600 km3/s2. Which one of the following trajectories does the satellite follow? 𝑟⃗ = (8000𝑝̂ + 9000𝑞̂) km and 𝑣⃗ = (−6𝑝̂ + 6𝑞̂) km/s
Q65
NAT[2 Marks]
An earth satellite moves in an elliptical orbit with a perigee altitude of 300 km and an apogee altitude of 3000 km. Assume that the radius of the earth is 6378 km. The eccentricity of the orbit is __________ (rounded off to three decimal places).