GATE 2026 Question Paper Aerospace Engineering (AE)

FOR GATE EXAM PREPARATION

GATE 2026
Question Paper ·
Aerospace Engineering
(AE)
EXAM YEAR TYPE SUBJECT

GATE 2026 Question Paper Aerospace Engineering (AE)

Notes · Sample Papers · Previous Year Papers · Mock Tests

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General Aptitude (GA)
Q.1 – Q.5 Carry ONE mark Each

Q.1 “He often _____ the numbers. False claims are not going to help. Honesty _____
trust”, said the manager.
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Choose the option with the correct order of words to fill the blanks.

.co s e m
s em l a
g la ag
(A) a exaggerates; engenders

(B) excels; encourages

(C) aggravates; alleviates

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.co
(D) diminishes; eliminates

e m
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ag

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a

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Q.2 In the sequence of tiles shown below, the missing tile indicated by the question
mark should be

(A)

(B)

(C)

(D)

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Q.3 A school has 100 students distributed among 1st to 10th standards.

Based on this, which one of the following statements is always correct?

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.co s e m
(A)
s em
There are at least 10 students who belong to the same standard.
l a
g la ag
(B) a There is at least one student in each standard.

(C) There are at most 10 students in 10th standard.

(D) The total number of students from 1st to 5th standards is at least 50.

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s e
la
Q.4 How many 3-digit numbers can be formed using three distinct single digit prime
numbers?
ag

(A) 64

(B) 24
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12
s e
s e g l a
g la (D) 4 a
a

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Q.5 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

(D) 32

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Q.6 – Q.10 Carry TWO marks Each

Q.6 Charity : P :: Retaliation : Q

Choose the appropriate pair of words P and Q that fit the analogy.

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(A)
s em
P = Parsimonious; Q = Vengeful
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(B) a P = Altruistic; Q = Amicable

(C) P = Resentful; Q = Spiteful

(D) P = Magnanimous; Q = Vindictive

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s e
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a

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a

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Q.7 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.

(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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Q.8 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 ________

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m .co s e m
s e l a
g l a ag
a

m
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s e
(A) 8
g la
a
(B) 4

(C) 3

(D) 2
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g la a
a

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.co s e m
s em l a
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Q.9 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 ________.

(A) H1

(B) H2

(C) H3

(D) H4

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Q.10 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.

̅̅̅̅ = 𝑉𝑊
Given 𝑟1 = 1 cm and 𝑉𝑌 ̅̅̅̅̅ = 4 cm, 𝑟2 = _____ cm.

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a

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s e
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a

m
m 4 − 3√2
.co
(A)

m .co s e m
s e (B) 1 + 2√2
g l a
g la a
a (C) 7 − 4√2

(D) 5 + 3√2

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.co s e m
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Q.11 – Q.35 Carry ONE mark Each

Q.11 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.

(A) 0

(B) 2

(C) 4

(D) 6

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Q.12 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?

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s e
(A) Cauchy
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a
(B) Fourier

(C) Gibbs

(D) Laplace
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a

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Q.13 The following equation with respect to 𝜑(𝑥, 𝑡), where 𝑎 is a non-zero constant,
represents ________.

𝜕𝜑 𝜕𝜑
+𝑎 =0
𝜕𝑡 𝜕𝑥

(A) linear wave propagation

(B) transient heat conduction

(C) Newton’s law of cooling

(D) radiative transfer

Q.14 Which one of the following makes an ideal air-standard Stirling cycle?

(A) Two reversible isobars, and two reversible adiabatics

(B) Two reversible isotherms, and two reversible isobars

(C) Two reversible isotherms, and two reversible isochores

(D) Isentropic compression, constant volume heat addition, isentropic expansion, and
constant volume heat rejection

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Q.15 In fluid dynamics, d’Alembert’s paradox refers to which one of the following?

Deviation of drag from 𝐷 ∝ 𝑣 2 at very low speeds m
.co
(A)

o m m
c
Deviation .of drag from 𝐷 ∝ 𝑣 at high subsonic speeds
s e
em
2

a
(B)
s l
g la of zero drag by potential flow theory ag
(C)
a Prediction

(D) Presence of shocks in transonic flows

Q.16
m
The number of independent elastic constants that a fully anisotropic linear elastic

.co
material can have is ______.

e m
las
ag
(A) 36

(B) 21

(C) 10

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m .co
.co m
(D) 2

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s e g l a
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a

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Q.17 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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Q.18 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?

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a

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(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
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c. o(D) m.co
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The amount of heat added in the combustion process is greater for the cycle
s e
s e 1-2-3'-4'-1
g l a
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a

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Q.19 The velocity potential function (𝜑) given below represents which one of the
following?

𝜑 = 5𝑥 − 12𝑦

(A) Doublet

(B) Irrotational vortex

(C) Source

(D) Uniform flow

Q.20 The fundamental purpose of the Kutta condition in the thin airfoil theory is
________.

(A) to determine the total strength of the source distribution

(B) to determine the speed of the uniform flow

(C) to incorporate the essential effect of viscosity in the potential flow theory

(D) to incorporate the concept of induced drag in the inviscid theory

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Q.21 In the figure shown below, the flow at the nozzle exit is ________.

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(A) overexpanded

(B) underexpanded

(C) ideally expanded
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(D) subsonic
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Q.22 An 𝑛 × 𝑛 square matrix 𝐴 satisfies 𝐴𝑇 = 𝐴−1. The determinant of this matrix may
take which of the following value(s)?

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.co
(A)
e m
e m l as
las (B) −1
ag
ag
(C) 𝑛

(D) 0

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s em l a
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Q.23 Which of the following statements is/are TRUE about the stability of an aircraft?

(A) Static stability of an aircraft is sufficient to guarantee its dynamic stability

(B) Static stability of an aircraft is related only to its initial tendency to return towards
the equilibrium position from which it is disturbed

(C) An aircraft may be dynamically unstable even if it is statically stable

(D) Dynamic stability is related to the time history of aircraft motion after being
disturbed from its equilibrium position

Q.24 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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Q.25 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?

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s e l a
g l a ag
a

m
.co
(A) Figure P is for a flap

e m
(B) Figure P is for a slat
las
ag
(C) Figure Q is for a slat

(D) Figure Q is for a flap

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s e g l a
g la a
a

m .
.co s e m
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Q.26 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.

(A) [Q] [σ] [Q]T

(B) [Q] [σ] [Q]–1

(C) ([Q]–1)T [σ] [Q]T

(D) [Q]–1 [σ] [Q]

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Q.27 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?

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s e l a
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a

m
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s e
g la
a

(A) Configuration I corresponds to the rotor of a compressor and Configuration II
corresponds to the rotor of a turbine

m
.co
(B) Configuration I corresponds to the rotor of a turbine and Configuration II
m
.co
corresponds to the rotor of a compressor

m s em
s e g laalong the +𝜃
la
(C) The rotor blades of the turbomachine in Configuration I move
g direction a
a
(D) The rotor blades of the turbomachine in Configuration II move along the +𝜃
direction

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Q.28 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.

(A) 𝜂𝐴 > 𝜂𝐵

(B) 𝜂𝐵 > 𝜂𝐴

(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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Q.29 Which of the following statements is/are TRUE regarding critical and drag
divergence Mach numbers of a wing?

m
(A)
m
Critical Mach number is the minimum freestream Mach number for which sonic
.co
.co
condition is attained somewhere over the wing
m s e m
s e l a
a divergence Mach number is always higher than the critical Mach number ag
l
ag
(B) Drag

(C) Drag divergence Mach number is the local Mach number over the wing at which
the drag increases drastically

(D) Critical Mach number is independent of the angle of attack

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.co
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Q.30 a one-dimensional, with no shaft work or body forces.
A flow is steady, inviscid and
Which of the following is/are possible under the given conditions?

(A) Oblique shocks
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.co m
(B) Sound propagation

m s e
s e g l a
la a
(C) Rayleigh flow

ag
(D) Fanno flow

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.co s e m
s em l a
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Q.31 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).

Q.32 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).

Q.33 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)

Q.34 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).

Q.35 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).

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Q.36 – Q.65 Carry TWO marks Each

Q.36 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?
m
m
𝑟⃗ = (8000𝑝̂ + 9000𝑞̂) km and 𝑣⃗ = (−6𝑝̂ + 6𝑞̂) km/s
.co
m .co s e m
s e l a
g l a ag
a
(A) Circle

(B) Hyperbola

(C) Parabola
m
(D) Straight line
m .co
s e
g la
a
Q.37 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?

m
m 1 .co
.co
(A) [ ] is an eigenvector
1
e m
e m l as
las 𝜆 = 𝑎 + 𝑏 is an eigenvalue ag
g
(B)
a
(C) 𝜆 = 𝑑 − 𝑏 is an eigenvalue

(D) 𝜆 = 𝑑 + 𝑏 is an eigenvalue

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.co s e m
s em l a
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Q.38 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 ______.

(A) 𝜏𝑟
1− (𝜏 − 1)
𝜏𝜆 𝑐

(B) 𝜏𝑟
1+ (𝜏 + 1)
𝜏𝜆 𝑐

(C) 𝜏𝑟
1− (𝜏 + 1)
𝜏𝜆 𝑐

(D) 𝜏𝑟
1+ (𝜏 − 1)
𝜏𝜆 𝑐

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An ideal rocket has characteristic exhaust velocity of 1200 m/s, mass flow rate of
Q.39 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.

m
m .co
(A)
.co
3600 and 183.67
s e m
s em l a
(B)
g la and 190.51
4600 ag
a
(C) 3600 and 175.23

(D) 3500 and 183.67

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s e
g la
a

m
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m .co s e m
s e g l a
g la a
a

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Q.40 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.

(A) biaxial deformation

(B) pure shear

(C) pure bending

(D) rigid body rotation

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Q.41 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 ________.

m
m .co
m .co s e m
(A)
s e
𝑔0
l a
g l a ag
(B)
a 2𝑔 0

(C) 3𝑔0

(D) 4𝑔0

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s e
g la
a

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m .co s e m
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a

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Q.42 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.

(A) 𝑝01 < 𝑝02 , 𝑝02 > 𝑝03 ; 𝑇01 < 𝑇02 , 𝑇02 ≈ 𝑇03 ; 𝐶1 < 𝐶2 , 𝐶2 > 𝐶3

(B) 𝑝01 < 𝑝02 , 𝑝02 = 𝑝03 ; 𝑇01 < 𝑇02 , 𝑇02 ≈ 𝑇03 ; 𝐶1 < 𝐶2 , 𝐶2 = 𝐶3

(C) 𝑝01 < 𝑝02 , 𝑝02 > 𝑝03 ; 𝑇01 < 𝑇02 , 𝑇02 < 𝑇03 ; 𝐶1 > 𝐶2 , 𝐶2 > 𝐶3

(D) 𝑝01 < 𝑝02 , 𝑝02 < 𝑝03 ; 𝑇01 < 𝑇02 , 𝑇02 < 𝑇03 ; 𝐶1 = 𝐶2 = 𝐶3

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Q.43 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
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the problem in a suitable range, then 𝑁𝑚𝑖𝑛 is ________.
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l a ag
(A) ag10

(B) 100

(C) 10,000

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(D) 1,00,000

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Q.44 Which of the following process(es) is/are involved in the compression of air in an
ideal ramjet engine?

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oblique shock

e m l as
las (B) mechanical compression
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(C) normal shock

(D) subsonic diffusion

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Q.45 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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Q.46 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

m
device.

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(A) The axial velocity is constant across the rotor

(B) The flow coefficient is 0.6

(C) The blade loading coefficient is 0.6

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(D) If the acoustic velocity at the rotor inlet is 350 m/s, then the inlet relative

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number is 0.333
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Q.47 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?

(A) Increasing 𝑈 enlarges the oval

(B) Increasing 𝛤 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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Q.48 What is/are the use(s) of the single horseshoe vortex model of finite wing
aerodynamic theory?

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(A)
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It can approximate the wing pitching moment coefficient
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(B) It can approximate the wing induced drag coefficient

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(C) a It can approximate the effect of the wing on the induced drag coefficient of a
typical horizontal tail

(D) It can approximate the aerodynamic benefit/penalty of formation flight compared
to isolated flight

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Q.49 a with the initial conditions given below. If 𝑦(𝑥)
Consider the differential equation
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

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An object of mass 1 kg is launched with an initial speed of 𝑣𝑜 into a large tank
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filled with a viscous liquid. The liquid exerts a resistive force (drag) of the form
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la a
𝐷 = 𝛼𝑣 on any object that is moving inside it, where 𝑣 is the instantaneous speed

ag 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.

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Q.51 The minimum value of the function 𝑓(𝑥) = |𝑥| + |2𝑥 + 3| for real 𝑥 is ________
(rounded off to 1 decimal place).

Q.52 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

Q.53 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).

Q.54 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

Q.55 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).

Q.56 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).

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Q.57 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
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conditions, the ratio 𝑊𝐵 /𝑊𝐴 is ________ (rounded off to 3 decimal places).

o m m
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emboth in tension and compression, is 200 MPa. The mean radius of the glas
Q.58 A thin-walled circular tube is made of a material whose magnitude of the ultimate
s
a is 0.2 m and the wall thickness is 0.004 m. Based on the maximum stress a
strength,
lcriteria,
gtube
a off to thethenearest
maximum torque that the tube can sustain is ________ kN-m (round
integer).

Q.59 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

m
of free vibration of the system is ________ rad/s (rounded off to the nearest

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integer).

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Q.60 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).

Q.61 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).

Q.62 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).

Q.63 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).

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Q.64 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.
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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
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Q.65 A Mach 1.5 air flow enters a round duct of length 20 cm and diameter 3 cm. If the

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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
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1724

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𝑫
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