Indian Institute of Technology Madras (IIT-M) 2010 B.Tech Aeronautical Engineering Aerospace engineering gate-2011 - Question Paper
20)0_AE
Du ration: Thre Hours Maximum Marks: 100
Read the following Instructions carefully.
1. This question paper contains 16 pages including blank pages for rough work. Please check all pages and report discrepancy, if any.
2. Write your registration number, your name and name of the examination centre at the specified locations on the right half of the Optical Response Sheet (ORS),
3. Using HB pencil, darken the appropriate bubble under each digit of your registration number and the letters corresponding to your paper code.
4. All questions in this paper are of objective type.
5. Questions must be answered on the ORS by darkening the appropriate bubble (marked A, B, C D) using HB pencil against the question number on the left hand side of the ORS. For each question darken the bubble of (be correct answer. In case you wish to change an answer, erase the old answer completely. More than one answer bubbled against a question will be treated as an incorrect response.
6. There axe a total of 63 questions carrying 100 marks.
SEAL
7. Questions Q. I - Q.25 will carry 1-mark each, and questions Q-26 - Q.55 will carry 2-marks each.
8. Questions Q.45 - Q.51 (2 pairs) are common data questions and question pairs (Q 52, Q.53) and (Q.54, Q.55) are linked answer questions. The answer to the second question of the linked answer questions depends on the answer to the first question of the pair. If the first question in the linked pair is wrongly answered or is un-attenjpied, then the answer to the second question in the pair will not be evaluated.
9. Questions Q.56 - Q.65 belong to General Aptitude (GA>. Questions Q.56 - Q.6G will cany 1-mark each, and questions Q 61 - Q.65 will carry 2-marks each. The GA questions will begin on a fresh page starting from page 11.
10. Un-attempted questions will carry zero marks.
11. Wrong answers will carry NEGATIVE marks. For Q.l - Q.25 and Q.56 - Q.60, % mark will be deducted for each wrong answer. For Q.26 - Q.51 and Q.61 - Q.65, Y mark will be deducted for each wrong answer. The question pairs (Q.52, Q.53), and <Q54, Q.55) are questions with linked answers. There will be negative marks only for wrong answer to the first question of the linked answer question pair i.e. for Q.52 and Q.54* fi mark will be deducted for each wrong answer. There is no negative marking for Q.53 and Q.55.
12. Calculator (without data connectivity) is allowed in the examination hall.
13. Charts* graph sheets or tables are NOT allowed in the examination hall,
14. Rough work can be done on the question paper itself. Additionally, blank pages are provided at the end of the question paper for rough work.
2010
Q.1
01
Q.2
Q.3
Q.4
Q-5 Q 6 Q-7
Q.8
Q9
a -b b a
operation V2 =
The linear second order partial differential equation 5--y + 3--f-2- + 9 = 0 is
(A) translation
(B) rotation
(C) magnification
(D) combination of translation, rotation, and magnification.
An aircraft is climbing at a constant speed in a straight line at a steep angle of climb. The load factor it sustains during the cJimb is:
(A) equal to 1.0 (B) greater than 1 0
(C) positive but less than 1.0 (D) dependant on the weight of the aircraft
In a general case of a homogeneous material under (bermo-mechanical loading the number of distinct components of the state of stress is
(A) 3 (B) 4 {) 5 (D) 6
dV - dV 2
dx2 dvdy dy
(A) Parabolic (B) Hyperbolic (C) Elliptic <D) None of the above
All other factors remaining constant, if the weight of an aircraft increases by 30% then the takeoff distance increases by approximately:
(A) 15% (B)30% (C) 70% (D) 105%
A vertical slender rod is suspended by a hinge at the top and hangs freely. It is heated until it attains a uniform temperature, T. Neglecting the effect of gravity, the rod has
(A) Stress but no strain (B) Strain but no stress
(C) Both stress and strain (D) Neither stress nor strain
An aircraft stalls at a speed of 40 m/s in straight and level flight. The slowest speed at which this aircraft can execute a level turn at a bank angle of 60 degrees is:
(A) 28.3 m/s (ti) 40.0 m/s (C) 56.6 m/s (D) 80.0 m/s
The eigen-values of a real symmetric matrix are always
(A) positive (B) imaginary
<C) real (D) complex conjugate pairs
- Q.25 carry one mark each.
Tsentropic efficiency 7rfof a subsonic diffuser is defined as
(Note: a represents the ambient, 2 represents the exit of the diffuser and s represents an isentropic process)
t _7" T + T P P P P
(A) DZ1 " (B) (C) 02j (D) J
tk-t. t + t PK-Pm P-P,2
Two position vectors are indicated by Vi = ] 'land V-=J *[. If a2+b2-1, then the
U UJ
V] amounts to obtaining the position vector Vz from V\ by
Q. 10 The concentration x of a certain chemical species ai lime t in a chemical reaction is described by ihe
differential equation + kx = 0. with jc(j=0} = a,,. Given that e is the base of the natural dt
logarithms, the concentration x at / =
(A) falls to the value 0 5a0 (B) rises to the value 2x
Ml . .u i *0 <D> nscs 10 lhe value
(C) falls to the value
c
r dx
Qll The definite integral J r
-j
(A) does not exist (B) is equal to 2 (C) is equal to 0 (D) is equal to-2 Q J2 The absolute ceiling of an aircraft is the allitude above which it:
(A) can never reach
(B) cannot sustain Jevel flight at a consiant speed
(C) can perform accelerated flight as well as straight and level flight at a constant speed
(D) can perform straight and level flight at a constant speed only
Q. 13 A thin rectangular plate made of isotropic material which satisfies the octahedral Von Mises/ Distortion energy) failure criterion has yield strength of 200 MPa under uniaxial tension. As shown in the figure, if it is loaded with uniform tension of 150 MPa along the j-direciion, the maximum uniform tensile stress that can be applied along the y-dircction before the plate starts yielding is about
tJi. = 150 MPa
(A) 227 MPa (B) 77 MPa (C) 87 MPa <D) 114 MPa
Q. 14 Consider an incompressible 2-D Couette flow of water between two walls spaced Jm apart. The lower wall is kept stationary. What is the shear stress acting on the lower wall if the upper wall is
moving at a consiant speed of 2 m/s? = 7xl0'*N,s/in2)
i ! 2 m/s
(A) 3.5xI0'*N/m: (B) 7x10 N/m2 (C> l0.5xl0 JN/m' (D) 14xl0N/m2
Q. 15 The angular momentum, about the centre of mass of the earth, of an artificial satellite in a highly elliptical orbit is :
(A) a maximum when ihe satellite is farthest from the earth
(B) a constant
(C) proportional to the speed of the satellite
(D) proportional to the square of the speed of the satellite
Q. 16 A column of length I and flexural rigidity /. has one end fixed and the other end hinged. The critical buckling load for the column is
IT El it* El nzEl TtEl
(A) (B) . (C) 7 (D) -
(0.5/) (0.70 I! (21)
Q.17 A horizontal cantilevered steel beam of rectangular cross-section having width b and depth d is vibrating in the vertical plane. The natural frequency of bending vibration is highest when
2 b
(A) b=i Q>d=iO (B) l> = 20, d = 5 (C) b = 5, d = 20 (D) b = 25,d = 4 Q.18 Consider an incompressible 2-D viscous flow over a curved surface. Let the pressure distribution
on the surface be p(s) = 2 + sin~- + N/ni3< where s is the distance along the curved surface from the leading edge. The flow separates at
(A) 5 = (2/3)tt m (B)j = (3/2)m (C) s = (tt/2) m <D) s=n m Q.19 For a multi-stage axial compressor with conslant diameter hub
(A) Blade height decreases in the flow direction
(B) Blade height increases in the flow direction
(C) Blade height remains conslant
(D) Blade height first increases and then decreases in the flow direction
Q.20 In a 2-D, steady, fully developed, laminar boundary layer over a flat plate, if x is (he slream-wise coordinate, y is the wall normal coordinate and u is the stream-wise velocity component, which of the following is tnje:
_ 3u _ du dw Su _ du du
Q.21 How does the specific thrust, at constant turbine inlet temperature, produced by a turbofan engine change with an increase in compressor pressure ratio?
(A) Increases (B) Decreases
(C) First increases and then decreases (D) First decreases and then increases
Q.22 If 0 is the potential function for an incompressible irrotational flow, and u and v are the Cartesian velocity components, then which one of the following combinations is correct?
3d dtp 3d
(A) u=- > v = - (B) = -- , * = -
dr dx oy ox
(C) =
ay ay ox oy
Q.23 Among the choices given below, the Specific Impulse is maximum for a
(A) Cryogenic Rocket (B) Solid Rocket
(C) Liquid Rocket (D) Ramjet
Q.24 For a flow across an oblique shock which of the following statements is true?
(A) Component of velocity normal to shock decreases while tangential component increases.
(B) Component of velocity normal to shock increases while tangential component decreases.
(C) Component of velocity normal to shock is unchanged while tangential component decreases.
(D) Component of velocity normal to shock decreases while tangential component is unchanged,
Q.25 The maximum operating flow rate through a centrifugal compressor at a given RPM is limited by
(A) Impeller stall (B) Surge
(C) Choking of diffuser throat (D) Inlet flow distortion
Q.26 - Q.55 carry two marks each.
Q.26 A spacecraft of mass 100 kg, moving at an instantaneous speed of 1.8x10* m/s, picks up interstellar dust at the rate of 3.2 x 10"* kg/s. Assuming that the dust was initially at rest, the instantaneous rate of retardation of the spacecraft is:
(A) 7.9 x 10 m/s2 (B) 2.3 x 10"3 m/s: zero <D) 5,8 x 10"* m/s1
Q.27 Following stress state is proposed for a 2-D problem with no body forces: <7 = 3x*y + 4y2. ~ y* -f 14n't t - -3xyz - 7x1. It satisfies
(A) Equilibrium equations but not compatibility equation
(B) Compatibility equation but not equilibrium equations
(C) Neither equilibrium equations nor compatibility equation
(D) Both equilibrium equations and compatibility equation
Q.28 A uniform cross-section rigid rod of mass m and length I, is hinged at its upper end and suspended like a pendulum. Its natural frequency for small oscillations is
(B) Jf (C) (D,
Q 29 The thin rectangular plate shown in the figure is loaded with uniform shear, xD, along all edges and uniform uniaxial tension in the y-direction. The appropriate Airys stress function to solve for stresses is given by
 |
|
ffmnm |
|
(A) ~T0xy - - / ) (C) -r_rv + a,y (B) |
(D) rxv-KTy + <y (*'-/) |
Q 30 A propeller powered aircraft. trimmed to attain maximum range and flying in a straight line, travels a distance R from its take-off point when it has consumed a weight of fuel equal to 20% of its take-off weight. ]f the aircraft continues to fly and consumes a total weight of fuel equal to 50% of its take-off weight, the distance between ii and its take-off point becomes:
(A) 2.5 R
(B) 3 I R
(C) 2.1 R
(D) 3.9 R
Q. 31 The gi ven th in wal I section of u n iform thick ness. s. i s symmetric about *-axi s. Moment of i ncrt i a i s
gi ven to be / =th3. Shear ccn ter for t h is section i s I ocated at 12
(A) x - h 8
(B) * =--h
28
(c
(D) x = -ft 35
Q.32 Dunng an under-damped oscillation of a single degree of freedom system, in the limc-displacement plot the third peak is of magnitude 100 and the tenth peak is of magnitude 10. The damping ratio is approximately:
(A) 0.052
(B) 0.023
(C) 0.366
(D) 0.159
is
Q.33 Given that the Laplace transform of y(/) = (2cos2f-sin 2t) is Y(s) = Laplace transform of yt(f) = r{2cos 2t -sin 2i) is
the
(.* + 1)- +4 2(s-l)
2{s~2)
(s-i)'+4
2<J + 2)
{a + 1)j+4
2(.v + 2) (s + 3)1 + 4
(C)
(A)
(B)
(D)
(5-l)2+4
Q.34 In a certain region a hill is described by the shapez(x, y) = ~x* + y ~ *y ~3y, where the axes x
A A >.
and y are in the horizontal plane and axis ; points vertically upward. If i > j and k are unit vectors along j, y and respectively. then at the point x = 5, y = 10 the unit vector in the direction of the steepest slope of the hill will be:
(A) i
(C) k
(B) j
(D) i + j + k
Q.35 An aircraft is cruising at an altitude of 9 km. The free-stream static pressure and density at this altitude are 3.08 x 104 N/m: and 0.467kg/mA respectively. A Pilot tube mounted on the wing senses a pressure of 3.31 x 104 N/m' Ignoring compressibility effects, the cruising speed of the aircraft is approximately
(A) 50 m/s (B) 100 m/s (C) 150 m/s (D) 200 m/s
Q-36 The irim curves of an aircraft are of the fgrmC = (0.05 0.2)-0 1C, where the elevator deflection angle, $r, is in radians. The static margin of the aircraft is :
(A) 0.5 (B) 0.2 (0 0.1 (D) 0.05
Q37 The function /(x, v) = a' + v~ xv3y has an extremumat (he point
(A) (1,2) (B) (3,0) (C)(2.2) (D) (U)
Q 38 Consider the flow of air (p = 1.23 kg/m*) over a wing of chord length 0.5 m and span 3 m. Let the
free stream velocity be U = 100 m/sand the average circulation around the wing beT = 10 m2/s per unit span. The lift force acting on the wing is
(A) 615 N (B) 1845 N (C) 3690 N (D) 4920 N
Q.39 The stagnation pressure and stagnation temperature inside the combustion chamber of a liquid rocket engine are 1.5 MPa and 250U K respectively. The burned gases have y - 1.2 and R = 692,83 J/kgK The rocket has a converging - diverging nozzle with a throat area of 0.025 m* and the flow at the exit of the nozzle is supersonic. If the flow through the nozzle is isentropic, what is the mass flow rate of the gases out of the nozzle?
(A) 18.5 kg/s {B) 31,2 kg/s (C) 29.7 kg/s (D) 19.4kg/s
Q.40 In finding a root of the equation: x2 - 6x -h 5 = 0 the Newton-Raphson method achieves an order of convergence equal to:
(A) 1.0 (B) L67 (C) 2.0 (D) 2.5
Q.41 Consider a 1-D adiabatic, inviscid* compressible flow of air (/f = 287 J/Kg-K, cr ~7i8 J/Kg-K )
through a duct of constant cross-sectional areaA = ljn". If the volumetric flow rate is Q = 680 m?/s and stagnation temperature is 7J> = 580.05 K , then the air temperature inside (he duct is
(A) 300 K (B) 350 K (C) 400 K <D) 450 K.
Q.42 A two stage chemical rocket, having the same specific impulse (/) of 300 s for both the stages is designed in such a way that the payload ratio and the structural ratio are some for both the stages. The second stage of the rocket has following mass distribution :
Propellani Mass = 10208 kg Structural Mass - J134 kg Payload Mass = 1700 kg gr =9.8 m/s2
If the rockei is fired from rest and it flies in a zero gravity field and a drag free environment, the final velocity attained by the payload is
(A) 9729.3 m/s (B) 897.3 m/s (C) 9360.2 nVs (D) 8973.2 m/s
Q.43 A missile with a Ramjet engine is flying in air. The temperature at the inlet and the outlet of the combustor are 1200 K and 2500 K respectively. The heating value of tlie fuel i.v 43 MJ/kg and the burner efficiency is 90%. Considering the working fluid to be air (Cr = 1005 1/kgK. and y = 1.4). the rh
fuel/air ratio (/ = ) for this engine is equal to;
(A) 0.032 (B) 0.036 (Cl 0.042 <D) 0.026
_ _
Q 44 The irim curves of an aircraft are of the formC = (0.05 0.2<5r)-0.ICt where the elevator
deflection angle, 6t, is in radians. The change in elevator deflection needed to increase the lift coefficient from 0.4 to 0.9 is :
(A) -0.5 radians (B) -0.25 radians (C) 0.25 radians (D) 0.5 radians Q.45 If e is the base of the natural logarithms then the equation of the langent from the origin to the curve
\-e is
(A)y = x (B) y = ffx (C)y = - (D) y = ex
Q.46 Consider a potential flow over a finite wing with the following circulation distribution
|
23* | / I m /s 4 |
 |
r(3>)=iooj]-
If the free stream velocity is 100 m/s, the induced angle of attack is (A) 0.125 radians (B) -0,125 radians
(D) 0-125-fl f I radians
(C) 0.125J1-I I radians
Q.47 The inlet stagnation temperature for a single stage axial compressor is 300 K. and the stage efficiency is 0.80. Following conditions exist at the mean radius of the rotor blade:
Blade speed = 300 m/s Axial flow velocity = 160 m/s Inlet blade angle 0j ~ 44ft Outlet blade angle fa = 14
CV= 1005 J/kgK and y= 1.4
What is the stagnation pressure ratio (Prs) for this compressor?
(D) 1.23
(A) 1.41 (B) 1.37 (C) 1.51
Common Data Questions Common Data for Questions 48 and 49;
Consider a simply supported beam of length L, carrying a bracket welded at its center. The bracket carries a vertical load, R as shown in the figure. Dimensions of bracket are a=0.1. The beam has a square cross section of dimension h x h.
Q.48 Bending moment diagram is given by
Q.49 Maximum value of shear stress is
(A) 0.67 p/h2 (B) 1.33 P/h1 (C) 1.5 P/h1 (D) 0.9 P/h2
Common Data for Questions 50 and 51:
Consider a potential flow over a spinning cylinder. The stream function is given as
v = (V_r sin 0)(1 ~ r) + In r' 2ft R
where
Free stream velocity, V. = 25 m/s Cylinder radius, R = I m Circulation, T = SOn m2/s
Q-50 The radial and azimuthal velocities on the cylinder surface at B = 7t! 2 are
(A) Vr = 0 m/s, Vff - -75 m/s (B) V, = 0 m/s, V9 = 75 m/s (C) Vf =0 m/s, V0 =-25 m/s (D) Vf =0 m/s, Vfl = 25 m/s
Q 51 The stagnation points are located at
(A) 210 and 330* (B) 240 and 300 (C) 30* and 150 (D) 60 and 120
Statement for Linked Answer Questions 52 and 53:
An aircraft with an IDEALTurbojet engine is flying at 200 m/s at an altitude where (he ambient pressure is equal to 0.8 bar. The stagnation pressure and temperature at the inlet of the turbine are 6 bar and 1400 K respectively. The change in specific enthalpy across the compressor is 335 ki/kg. Assume the fuel flow ra(e to be very small in comparison to the air flow rate and consider Cp= 1117 J/kgK and y = 1.3.
Q.52 What is the stagnation pressure at the inlet of the nozzle?
(A) 2.8 bar (B) 5.7 bar (C) 2.1 bar {D) 6.3 bar
Q.53 What is the specific thnjst produced by this engine under the given conditions?
(A) 586 Ns/kg (B) 745 Ns/kg (C) 686 Ns/kg (D) 500 Ns/kg
Statement for Linked Answer Questions 54 and 55:
An aircraft is in straight and level flight at a constant speed v. It is disturbed by a symmetric vertical gust, resulting in a phugoid oscillation of time period T.
Q.54 Assuming that g is the acceleration due to gravity, r is given approximately by:
V V J?7TV
(A)--(B) <C) -p (D) VZ7n
*8 8 yi2xg ' g
Q.55 If v = 200 m/s ihcn the wavelength of the phugoid oscillations, assuming =9,81 nVs", is, approximately:
(A) 1.28 x 104 m (B) 1.30 x 105 m <C) 1.81 x I04m (Dj918m
General Aptitude (GA) Questions Q.56 - Q.60 carry one mark each.
Q.56 Which of the following options is the closest in meaning to the word below;
Circuitous
(A) cyclic
(B) indirect
(C) confusing
(D) crooked
Q.57 The question below consists of a pair of related words followed by four pairs of words. Select the pair that best expresses the relation in the original pair.
Unemployed : Worker
(A) fallow : land
(B) unaware : sleeper
(C) wit: jester
(D) renovated : house
Q.58 Choose the most appropriate word from the options given behw to complete the following sentence:
If we manage to_our natural resources, we would leave a better planet for
our children.
(A) uphold
(B) restrain
(C) cherish
(D) conserve
Q.59 Choose the most appropriate word from the options given below to complete the following sentence:
His rather casual remarks on politics_his lack of seriousness about the subject.
(A) masked
(B) belied
(C) betrayed
(D) suppressed
Q.60 25 persons are in a room. 15 of them play hockcy. 17 of them play football and 10 of them play both hockey and football. Then the number of persons playing neither hockey nor football is:
(A) 2 (B) 17 (C) 13 (D) 3
Q.61 - Q.65 carry two marks each.
Q 61 Modem warfare ha5 changed from large scale clashes of armies to suppression of civilian populations. Chemical agents that do their work silently appear to be suited to such warfare; and regretfully, there exist people in military establishments who think that chemical agents are useful tools for their cause.
Which of the following statements best sums up the meaning of the aJx>ve passage:
(A) Modem warfare has resulted in civil strife.
(B) Chemical agents are useful in modem warfare.
(C) Use of chemical agents in warfare would be undesirable.
(D) People in military establishments like to use chemical agents in war.
_AE
If 137 + 276 = 435 how much is 731 + 6727
Q. 02 Q.G3
Q.64
Q.65
(A) 534 (B) 1403 (C}1623 (D) 1513
5 skilled workers can build a wall in 20 days; 8 semi-skilled workers can build a wall in 25 days; 10 unskilled workers can build a wall in 30 days. If a (earn has 2 skilled, 6 semi-skilled and 5 unskilled workers, bow long will it take to build (he wall?
(A) 20 days (B) 18 days (C) 16 days (D) 15 days
Given digits 2. 2. 3. 3, 3, 4, 4, 4. 4 how many distinct 4 digit numbers greater than 3000 can be formed?
<A)50 (B) 51 (C)52 (D) 54
Hari (H), Gita (G), Irfan fl) and Saira (S) are siblings (i.e brothers and sisters). All were bom on 1M January, The age difference between any two successive siblings (that is bom one after another) is less than 3 years. Given the following facts:
L Haris age + Gitas age > Irfans age + Sairas age.
ii. The age difference between Gita and Saira is 1 year- However, Gita is not the oldest and Saira is not the youngest.
iii. There are no twins.
In what order were they bom (oldest first)?
(A)HSIG (B)SGH1 (Q IGSH <D) IHSG
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