βHe often _____ the numbers. False claims are not going to help. Honesty _____ trustβ, said the manager. Choose the option with the correct order of words to fill the blanks.
a.
exaggerates; engenders
Correct Answer
b.
excels; encourages
c.
aggravates; alleviates
d.
diminishes; eliminates
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Q2mcq
In the sequence of tiles shown below, the missing tile indicated by the question mark should be
a.
b.
Correct Answer
c.
d.
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Q3mcq
A school has 100 students distributed among 1 st to 10 th standards. Based on this, which one of the following statements is always correct?
a.
There are at least 10 students who belong to the same standard.
Correct Answer
b.
There is at least one student in each standard.
c.
There are at most 10 students in 10 th standard.
d.
The total number of students from 1 st to 5 th standards is at least 50.
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Q4mcq
How many 3-digit numbers can be formed using three distinct single digit prime numbers?
a.
64
b.
24
Correct Answer
c.
12
d.
4
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Q5mcq
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 ____
a.
18
b.
20
c.
24
Correct Answer
d.
32
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Q6mcq
Charity: P:: Retaliation: Q Choose the appropriate pair of words P and Q that fit the analogy.
a.
P = Parsimonious; Q = Vengeful
b.
P = Altruistic; Q = Amicable
c.
P = Resentful; Q = Spiteful
d.
P = Magnanimous; Q = Vindictive
Correct Answer
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Q7mcq
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?
a.
Only (i) can correspond to the unfolded cube in Panel I.
Correct Answer
b.
Only (ii) can correspond to the unfolded cube in Panel I.
c.
Both (i) and (ii) can correspond to the unfolded cube in Panel I.
d.
Neither (i) nor (ii) can correspond to the unfolded cube in Panel I.
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Q8mcq
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 ________
a.
8
b.
4
c.
3
d.
2
Correct Answer
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Q9mcq
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 iv. Two hills are located to the west of H2. v. The southernmost hill has at least two hills to its east.
hill. The southernmost hill is ________.
a.
H1
b.
H2
c.
H3
Correct Answer
d.
H4
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Q10mcq
As shown in the figure, circle $C$ 1 with center $O$ 1 and radius $r$ 1 touches the square $VWXY$ at points $P$ and $Q$ while circle $C$ 2 with center $O$ 2 and radius $r$ 2 touches the square $VWXY$ at points $R$ and $S.$ The two circles touch each other at $T.$
Μ Μ Μ Μ Μ = 4 cm, $r$ = _____ cm. Given $r$ = 1 cm and Μ Μ Μ Μ $VY$ = $VW$
2 1
a.
4 - $3\sqrt{2}$
b.
1 + $2\sqrt{2}$
c.
7 - $4\sqrt{2}$
Correct Answer
d.
5 + $3\sqrt{2}$
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Consider the contour $C$ shown in the figure below. For the vector $Fβ$ = $(x$ + $2y)eΜ$ + $(2x$ + $4y)eΜ$, the integral $\oint Fβ$ β $dlβ$ =________.
$x y C$ Here $dlβ$ represents an infinitesimal length along the contour $C.$
a.
0
b.
2
c.
4
d.
6
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The Fourier series representation of a square wave is shown in the figure below. The fluctuations seen near x = $\pm1$ are named after which one of the following scientists?
a.
Cauchy
b.
Fourier
c.
Gibbs
d.
Laplace
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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?
a.
The beam undergoes only torsion
b.
The beam undergoes only bending
c.
The beam undergoes both torsion and bending
d.
The beam undergoes neither torsion nor bending
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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?
a.
The thermal efficiency of the two cycles is the same
b.
The specific work of the two cycles is the same
c.
The processes 2-3 and 2-3' are isobaric
d.
The amount of heat added in the combustion process is greater for the cycle 1-2-3'-4'-1
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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?
a.
The mass flow rate is more for a turbofan engine
b.
The exit velocity is lower for a turbofan engine
c.
A turbofan engine operates at a lower altitude
d.
The fan of a turbofan engine consumes lesser power
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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?
a.
Figure P is for a flap
b.
Figure P is for a slat
c.
Figure Q is for a slat
d.
Figure Q is for a flap
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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 [Ο]. 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.
a.
[Q] [Ο] [Q] T
b.
[Q] [Ο] [Q] β1
c.
([Q] β1) T [Ο] [Q] T
d.
[Q] β1 [Ο] [Q]
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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?
a.
Configuration I corresponds to the rotor of a compressor and Configuration II corresponds to the rotor of a turbine
b.
Configuration I corresponds to the rotor of a turbine and Configuration II corresponds to the rotor of a compressor
c.
The rotor blades of the turbomachine in Configuration I move along the $+ΞΈ$ direction
d.
The rotor blades of the turbomachine in Configuration II move along the $+ΞΈ$ direction
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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 $Ξ·$ is the isentropic efficiency of the compressor, select the statements that is/are TRUE.
a.
$Ξ· A$ > $Ξ· B$
b.
$Ξ· B$ > $Ξ· A$
c.
In comparison to point B, point A is closer to the surge point
d.
In comparison to point A, point B is closer to the choke point
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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).
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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).
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The response $x(t)$ of a freely vibrating single degree of freedom underdamped system is given below. In the equation, $A$ and $Ο$ are constants. The damping ratio of the system is ________ (rounded off to 3 decimal places).
$x(t)$ = $Ae -5t sin(10t$ + $Ο)$
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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).
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An elliptic wing has a span of 6 m and a planform area of 6 m 2. When generating a lift coefficient of 0.6, the induced drag it incurs is ________ $\times$ 10 -3 (rounded off to 1 decimal place).
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An earth satellite has the instantaneous position vector $rβ$ and velocity vector $vβ$ as given below. Here $pΜ$ and $qΜ$ denote the unit vectors along the $x$ and $y$ axes of the perifocal frame, respectively. Assume that the value of gravitational parameter is 398600 km 3 /s 2. Which one of the following trajectories does the satellite follow?
$rβ$ = $(8000pΜ$ + $9000qΜ)$ km and $vβ$ = $(-6pΜ$ + $6qΜ)$ km/s
a.
Circle
b.
Hyperbola
c.
Parabola
d.
Straight line
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$a b$ For the matrix $A$ = [ ], if the relation $a$ + $b$ = $c$ + $d$ holds and $a, b, c, d =ΜΈ$ 0, $c d$ then which one of the following statements about $A$ is FALSE?
a.
1 [ ] is an eigenvector 1
b.
$Ξ»$ = $a$ + $b$ is an eigenvalue
c.
$Ξ»$ = $d$ - $b$ is an eigenvalue
d.
$Ξ»$ = $d$ + $b$ is an eigenvalue
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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 βtβ refers to the total condition. Also, $Ο$ = $T$ β $T$,
$r t0$ 0 $Ο c$ = $T t3$ β $T t2$ and $Ο Ξ»$ = $T t4$ β $T$ 0. The total temperature ratio of the high pressure turbine $(T t4.5$ β $T t4$) is given by ______.
a.
1- $r (Ο$ - 1) $c$ $Ο$ $Ο Ξ»$
b.
1+ $r (Ο$ + 1) $c$ $Ο$ $Ο Ξ»$
c.
1- $r (Ο$ + 1) $c$ $Ο$ $Ο Ξ»$
d.
1+ $r (Ο$ - 1) $c$ $Ο$ $Ο Ξ»$
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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 m 2. 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/s 2.
a.
3600 and 183.67
b.
4600 and 190.51
c.
3600 and 175.23
d.
3500 and 183.67
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Consider a unit square body as shown in the figure below. The body is subjected to the deformation field u = βay and v = ax, where βaβ is a constant. Due to the application of this deformation field, the body undergoes _______ in the x-y plane.
a.
biaxial deformation
b.
pure shear
c.
pure bending
d.
rigid body rotation
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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 $g$ 0, the acceleration experienced by the vehicle at lift-off is ________.
a.
$g$ 0
b.
$2g$ 0
c.
$3g$ 0
d.
$4g$ 0
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The figure below shows a compressor stage with station numbers 1, 2, and 3 as indicated. If $p 0i$, $T 0i$, and $C i$ 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.
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 $N min$ while taking 10 equally-spaced test values of each independent parameter of the problem in a suitable range, then $N min$ is ________.
a.
10
b.
100
c.
10,000
d.
1,00,000
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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?
a.
It satisfies the equilibrium equation
b.
It is zero on the lateral surfaces of the bar
c.
It satisfies the compatibility equation
d.
It does not satisfy the equilibrium equation
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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.
a.
The axial velocity is constant across the rotor
b.
The flow coefficient is 0.6
c.
The blade loading coefficient is 0.6
d.
If the acoustic velocity at the rotor inlet is 350 m/s, then the inlet relative Mach number is 0.333
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Consider the flow over an oval modeled using the elementary potential flows as shown below. $U$ represents uniform flow velocity and $Ξ$ represents circulation around an irrotational line vortex. Which of the following statements is/are TRUE for this model?
a.
Increasing $U$ enlarges the oval
b.
Increasing $Ξ$ enlarges the oval
c.
Interchanging the sense of the two vortices does not alter the oval
d.
Moving the vortices too far apart causes the oval to break up
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Consider the differential equation with the initial conditions given below. If $y(x)$ is the solution of the equation, the value of the slope,, at $x$ = ln(2) is ________ (rounded off to three decimal places).
$dy$
$dx$
$d$ 2 $y dy dy$
+2 + $y$ = 0 with $y| x=0$ = 0 and | =1
2 $dx dx dx$
$x=0$
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An object of mass 1 kg is launched with an initial speed of $v o$ into a large tank filled with a viscous liquid. The liquid exerts a resistive force (drag) of the form $D$ = $Ξ±v$ on any object that is moving inside it, where $v$ is the instantaneous speed of the object and $Ξ±$ = 1 kg/s. If the effect of gravity is ignored, the time taken by the object to slow down to the speed $v o$ /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.
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Isobutane (C 4 H 10) 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 β31.489, β94.052, and β60.150, respectively, the heat of reaction is ________ kcal (rounded off to 2 decimal places).
C 4 H 10 + 6.5 O 2 $\to$ 4 CO 2 + 5 H 2 O
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A furnace of 250 MW rating is used to melt and raise the temperature of aluminium from 25 o C to 900 o C. 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 o C. The amount of aluminium that can be processed per hour is ________ kg (rounded off to 1 decimal place).
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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).
$c l$ 0.2 0.4 0.6 0.8
$c m$ β 0.02 0 0.02 0.04
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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).
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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 β1.5Β°. The lift coefficient of the wing at an angle of attack of 3.5Β° is ________ (rounded off to 2 decimal places).
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$W A$ and $W B$ 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 $W B /W A$ is ________ (rounded off to 3 decimal places).
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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).
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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 Youngβs modulus E = 200 GPa, cross-sectional area A = 100 mm 2, 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).
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A stepped cantilever beam, made of a material having Youngβs 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 L 1 = 100 mm and I 1 = 100 mm 4, respectively. The length and the moment of inertia of the beam from point B to C are L 2 = 100 mm and I 2 = 700 mm 4, 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).
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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 $eΜ r$ + 75 $eΜ ΞΈ$) m/s and $(u eΜ r$ + 50 $eΜ ΞΈ$) 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).
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A gas mixture at a pressure of 800 kPa and a density of 5 kg/m 3 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).
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Thin airfoil theory predicts the zero-lift angle of attack $Ξ± L=0$ of NACA 2412 airfoil as -2.1Β°. The corresponding prediction of $Ξ± L=0$ for NACA 5410 airfoil is ________ degrees (rounded off to 1 decimal place).
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Consider a centered Prandtl-Meyer expansion fan at a $ΞΈ$ = 4Β° corner in a Mach 1.78 air flow, as shown in the figure below. The angle Ο (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
1.72
1.74
1.76
1.78
1.80
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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 ________ $\times$ 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
$4fL$ β
$\times 10 4$ 99.35 336.4 648.3 997.4 1361 1724
$D$
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