GATE XE 2026: Engineering Sciences
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Engineering Sciences (XE)
General Aptitude (GA)
Q.1 – Q.5 Carry ONE mark Each
Q.1 Suresh said, “I did it yesterday.”
Which one of the following options is the correct form of this sentence in indirect
speech?
(A) Suresh said that I did it yesterday.
(B) Suresh says I did it yesterday.
(C) Suresh says that he did it the day before.
(D) Suresh said that he had done it the day before.
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Engineering Sciences (XE)
Q.2 To continue the sequence of tiles shown, the tile indicated by the question mark
should be
(A)
(B)
(C)
(D)
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Engineering Sciences (XE)
Q.3 Consider an art gallery whose walkways are shown as lines in the diagram. A
black dot represents a junction of two walkways. A guard may be placed at a
junction to watch over the walkways that join at that junction. The minimum
number of guards needed to watch all the walkways is ________.
(A) 2
(B) 3
(C) 4
(D) 5
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Engineering Sciences (XE)
Q.4 The 2nd of June is a Thursday in a certain year. Which day of the week is the
3rd of July in that year?
(A) Thursday
(B) Friday
(C) Saturday
(D) Sunday
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Engineering Sciences (XE)
Q.5 A coin with heads facing up is shown as and a coin with tails facing up is
shown as .
Six coins are placed in the Starting Arrangement, as shown in the figure below.
A “step” is defined as interchanging a pair of adjacent coins without flipping
them. The minimum number of steps needed to go from the Starting Arrangement
to the Final Arrangement, as shown in the figure, is ________.
(A) 3
(B) 6
(C) 9
(D) 12
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Engineering Sciences (XE)
Q.6 – Q.10 Carry TWO marks Each
Q.6 Exacerbate : Mitigate :: ___________
Choose the option with the correct pair of words to fill the blank.
(A) Aggravate : Alleviate
(B) Alleviate : Precipitate
(C) Aggravate : Precipitate
(D) Emancipate : Exonerate
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Engineering Sciences (XE)
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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Engineering Sciences (XE)
Q.8 In a population, patients who have high cholesterol also have high blood-pressure
(BP). Some patients with high BP also have diabetes. There are no patients who
have both high cholesterol and diabetes. Furthermore,
1. the total number of patients with at least one of these conditions is 75,
2. the number of patients with high cholesterol is 10,
3. the number of patients with high BP is 45, and
4. the number of patients with only high BP and no other conditions is 20.
Then the number of patients who have both diabetes and high BP is _______
(A) 0
(B) 15
(C) 20
(D) 10
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Engineering Sciences (XE)
Q.9 Four people P, Q, R, and S, of different ages, make the following observations.
P – I am younger than S.
Q – I am neither the youngest nor the oldest.
R – P is older than me.
Based on these observations, the youngest person is ______.
(A) P
(B) Q
(C) R
(D) S
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Engineering Sciences (XE)
Q.10 Circles C1 , C2 , and C3 , with centers O1, O2, and O3 , and radii r1 , r2 , and r3 ,
respectively, touch each other as shown in the following figure. Given r1 = 2 cm,
r2 = 1 cm and the angle ∠O1 O3 O2 is 90°, r3 = _____ cm.
(A) 1
(−3 + √17 )
2
(B) 1
(3 + √17 )
2
(C) 1
(−2 + √17 )
2
(D) 1
(−3 + 2√17 )
2
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Engineering Mathematics (XE-A)
Q.11 – Q.17 Carry ONE mark Each
Q.11 For the complex function
f(z) = f(x + iy) = x 3 − 4xy 2 + i(4x 2 y − 2y 3 ),
consider the following two statements
P: f is not analytic at (0, 0).
Q: f does not satisfy the Cauchy-Riemann equations along the x-axis.
Then, which one of the following statements is true?
(A) P is false and Q is true
(B) P is true and Q is false
(C) Both P and Q are true, and Q implies P
(D) Both P and Q are true, but Q does not imply P
Q.12 Let C be the circle (x − 1)2 + y 2 = 25 oriented counterclockwise. Then, the value
of the line integral
2
∮ [(x 5 − 3y)dx + (−2x + e y )dy]
C
is
(A) 10π
(B) 15π
(C) 20π
(D) 25π
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Engineering Mathematics (XE-A)
Q.13 Let W(x) denote the Wronskian of two linearly independent solutions y1 (x) and
y2 (x) of the differential equation
d2 y dy
(x − 1) 2
+ 2 + xe x y = 0, x > 1.
dx dx
If W(2) = 2, then the value of W(5) is
(A) 1
8
(B) 1
5
(C) 5
(D) 8
Q.14 Which of the following statements is/are true?
(A) Y = 1 + 1.8X and X = 1 − 0.5Y are estimated as lines of regression of Y on X and
X on Y, respectively.
(B) Y = 1 + 1.3X and X = 2 + 1.1Y are estimated as lines of regression of Y on X and
X on Y, respectively.
(C) Y = 1 + 1.6X and X = 3 + 0.5Y are estimated as lines of regression of Y on X and
X on Y, respectively.
(D) Y = 1 + X and X = Y are estimated as lines of regression of Y on X and X on Y,
respectively, and the correlation between X and Y is ±1.
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Engineering Mathematics (XE-A)
Q.15 1 √2 0
Consider the matrix A = [√2 0 0]. Then, which of the following statements
0 0 1
is/are true?
(A) All the eigenvalues of A are real numbers
(B) 1
The eigenvalues of A−1 are 1, 2 , −1
(C) The determinant of A is 3
(D) The matrix A − 2I is invertible, where I denotes the identity matrix of order 3 × 3
Q.16 Let L be the lamina of the form x 2 + 4y 2 ≤ 64, 0 ≤ y ≤ 4, with density
ρ(x, y) = |x|y. Then, the mass of L (in integer) is __________
Q.17 Let X be a random variable having probability density function (pdf)
e
e −x , 0 < x < 1,
2(e − 1)
fX (x) = 1
, 1 < x < 2,
2
{ 0, elsewhere.
Then, the value of the expectation of X, E[X] (rounded off up to two decimal places)
is __________
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Engineering Mathematics (XE-A)
Q.18 – Q.21 Carry TWO marks Each
Q.18 Match each entry of List-1 with a suitable entry in List-2 and choose the correct
option.
List-1 List-2
The sum of the series ∑∞
1 I 3
P n=1 (n+2)(n+1) is equal to
2
3 x II 1
Q lim ( 2 ∫0 sin(t) dt) is equal to
x
x→0
1
the III
a0
R Let + ∑∞
n=1(an cos nx + bn sin nx) be
2 2
Fourier series expansion of the function
1 1 1
f(x) = sin x − cos x + sin 2x , x ∈ [0, 2π].
2 2 √2
Then, ∑∞ (a
n=0 n
2
+ bn
2
) is equal to
(A) P ⟶ I, Q ⟶ III, R ⟶ II
(B) P ⟶ III, Q ⟶ II, R ⟶ I
(C) P ⟶ III, Q ⟶ I, R ⟶ II
(D) P ⟶ II, Q ⟶ I, R ⟶ III
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Engineering Mathematics (XE-A)
Q.19 Consider the following partial differential equation (PDE)
∂ 2u 2
∂ 2u ∂u ∂u
(y − 1) 2
− (x − 3) 2
+ y2 + x2 + (x − y)u = 0.
∂x ∂y ∂x ∂y
Then, which of the following statements is/are true?
(A) In the region {(x, y) ∈ ℝ2 : y > 1, x > 3}, the PDE is hyperbolic
(B) In the region {(x, y) ∈ ℝ2 : y > 1, x < 3}, the PDE is elliptic
(C) In the region {(x, y) ∈ ℝ2 : y < 1, x > 3}, the PDE is elliptic
(D) In the region {(x, y) ∈ ℝ2 : y < 1, x < 3}, the PDE is hyperbolic
Q.20 l11 0 0 1 u12 u13
Let [l21 l22 0 ] [0 1 u23 ] be the LU decomposition of the matrix
l31 l32 −10 0 0 1
1 1 1
A = [4 3 −1]. Then, the value of a (in integer) is __________
3 5 a
Q.21 The initial value problem
du
= u2 + t 2 , t ≥ 0,
dt
with u(0) = 1,
is solved by using the explicit Euler method with step size ℎ = 0.2. Then, the
value of u(0.4) (rounded off upto two decimal places) is __________
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Fluid Mechanics (XE-B)
Q.22 – Q.30 Carry ONE mark Each
Q.22 For a laminar, incompressible, and fully-developed flow through a circular pipe, the
ratio of the maximum velocity to the average velocity of the flow is
(A) 1.5
(B) 2
(C) 3
(D) 4
Q.23 Air flows with a freestream velocity U over four different bodies having same frontal
area facing the flow direction, as shown in the figure. Which one of the following
bodies has the lowest pressure (form) drag force for Reynolds number, Re ≥ 104?
(A) Body P
(B) Body Q
(C) Body R
(D) Body S
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Fluid Mechanics (XE-B)
Q.24 Consider a steady, and incompressible flow over a body with characteristic
length L. The boundary layer thickness at a distance x from the leading edge is δ.
Which one of the following assumptions is correct for deriving the Prandtl boundary
layer equations?
(A) δ≈L
(B) δ>L
(C) δ≫L
(D) δ≪L
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Fluid Mechanics (XE-B)
Q.25 Three different siphons steadily discharge water at velocities VI, VII, and VIII, as shown
in the figure. The tubes of the siphons are of same diameter. If the frictional losses
are neglected, which one of the following options is correct?
In the figure, g is acceleration due to gravity; a, b, and h are different heights.
(A) VI > VIII > VII
(B) VI > VII > VIII
(C) VI = VII = VIII
(D) VII > VIII > VI
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Fluid Mechanics (XE-B)
Q.26 Consider the following statements:
Assertion (a)
Surface tension acts along the interface of two fluids.
Reason (r)
The pressure of the fluid inside a bubble is higher than that of the fluid outside the
bubble.
Which one of the following options is correct?
(A) Both (a) and (r) are true, and (r) is the correct explanation of (a).
(B) Both (a) and (r) are true, however (r) is not the correct explanation of (a).
(C) (a) is true, but (r) is false.
(D) (a) is false, but (r) is true.
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Fluid Mechanics (XE-B)
Q.27 The basic dimensions, i.e., mass, length, and time are represented by M, L, and T,
respectively. The correct dimension of dynamic viscosity is
(A) MLT −2
(B) M0 L2 T −1
(C) ML−1 T −1
(D) M0 L−2 T 2
Q.28 The velocity components in x- and y-directions of a two-dimensional, incompressible
flow field are u(x, y) = 2x 2 + y 3 and v(x, y) = x 3 − 2xy + f(x, y), respectively.
Here, f(x, y) is a polynomial function and g(x) is a polynomial function of x only.
Which one of the following options for f(x, y) is correct?
(A) f(x, y) = −xy 2 + g(x)
(B) f(x, y) = −2x + g(x)
(C) f(x, y) = −2xy + g(x)
(D) f(x, y) = −2x 2 y + g(x)
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Fluid Mechanics (XE-B)
Q.29 Which of the following statements about streamlines, pathlines, and streaklines is/are
correct?
(A) A streamline is a curve that is everywhere tangent to the instantaneous local velocity
vector.
(B) Two streamlines can intersect at a point in a flow.
(C) A pathline is the locus of fluid particles passing sequentially through a particular
point.
(D) For steady flow, streamlines, pathlines, and streaklines are the same.
Q.30 A piezometer and a Pitot tube are tapped into a horizontal water
pipe, as shown in the figure, where ℎ1 = 4 cm, ℎ2 = 6 cm and ℎ3 = 5 cm. Consider
the flow to be steady, laminar, and incompressible. Assume the density of water as
1000 kg.m−3 and acceleration due to gravity as 10 m.s−2. The water velocity
V (in m.s−1) at the center of the pipe is ________. (rounded off to one decimal place)
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Fluid Mechanics (XE-B)
Q.31 – Q.43 Carry TWO marks Each
Q.31 A steady, laminar, and incompressible flow between a pair of infinite parallel plates
is driven by a constant pressure gradient (−dp/dx). The plates are separated by a
distance 2ℎ, as shown in the figure. The fully-developed velocity profile of the
flow is
dp ℎ2 y2
u(y) = − (1 − 2 ) ,
dx 2μ ℎ
where μ is the dynamic viscosity.
The values of y, for which the local flow velocity is equal to the average flow
velocity, are
(A) ℎ
±
2
(B) ℎ
±
√2
(C) ℎ
±
3
(D) ℎ
±
√3
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Fluid Mechanics (XE-B)
Q.32 An incompressible fluid flows between a pair of infinite plates separated by a
distance L. The top plate is moving with a constant velocity U, whereas the bottom
plate is stationary, as shown in the figure. The difference of the stream functions
(ψT − ψB ) at the two plates for a laminar and fully-developed flow is equal to
(A) UL
2
(B) UL
(C) 2UL
(D) 4UL
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Fluid Mechanics (XE-B)
Q.33 Consider two different cases of water flowing through a smooth pipe of 50 cm
diameter. The mass flow rates for the two cases are (i) 0.25 kg.s−1, and (ii) 0.8 kg.s−1.
Assume the density and dynamic viscosity of water as 1000 kg.m−3 and 10−3 Pa.s,
respectively. Which one of the following options is correct?
(A) The flow is laminar for both (i), and (ii).
(B) The flow is laminar for (i), and turbulent for (ii).
(C) The flow is turbulent for (i), and laminar for (ii).
(D) The flow is turbulent for both (i), and (ii).
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Fluid Mechanics (XE-B)
y
Q.34 A two-dimensional source flow (with stream function, ψ1 = m tan−1 x ) is placed
at the origin in a uniform flow (with stream function, ψ2 = Uy). Here, the strength
of the source is m and the freestream velocity is U. The velocity components u and
v of the combined flow in x- and y-directions, respectively, are
(A) mx my
u=U+ 2 ; v=
x +y 2 x 2 +y 2
(B) mx my
u= ; v=U+
x 2 +y 2 x 2 +y 2
(C) mx my
u=U+ 2 ; v=−
x +y 2 x 2 +y 2
(D) mx my
u= ; v=U−
x 2 +y 2 x 2 +y 2
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Fluid Mechanics (XE-B)
Q.35 Consider a steady, laminar, and incompressible flow over a flat plate, as shown in
the figure. With freestream velocity U∞ and kinematic viscosity ν1 , the boundary
layer thickness at a distance x1 from the leading edge is δ1 . If the kinematic
viscosity of the fluid is increased by a factor of four (ν2 = 4ν1 ), the boundary layer
thickness (δ2 ) at x1 with same U∞ will be equal to
U y
( x)
x
(A) δ1
2
(B) δ1
(C) 2δ1
(D) 4δ1
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Fluid Mechanics (XE-B)
Q.36 A vertical jet of diameter d1 strikes a horizontal plate with a velocity U, as shown
in the figure. The plate has a hole of diameter d2 (< d1 ) concentric to the flow
through which a portion of fluid passes with the same velocity U. The remaining
fluid moves radially outward along the plate. If F is the force acting vertically
upward to hold the horizontal plate at its initial place, which of the following
statements is/are true?
(A) Radially outward flow has no effect on F.
(B) F decreases as d2 decreases keeping other parameters unchanged.
(C) F increases as U increases keeping other parameters unchanged.
(D) F remains constant as d1 increases keeping other parameters unchanged.
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Fluid Mechanics (XE-B)
Q.37 The velocity of a fluid particle in a flow is given as:
⃗ = (a − x)î + (b + y)ĵ + (c + z)k̂
V
where a, b, c are constants, and î, ĵ, k̂ are unit vectors in x-, y-, z-directions,
respectively.
Which of the following statements is/are correct?
(A) The flow is steady for any value of a, b, and c.
(B) At a point (2, 3, 6), the velocity component in x-direction is higher than the velocity
components in y- and z-directions for a = 2, b = 6, and c = 2.
(C) The point (2, 3, 6) is a stagnation point for a = 2, b = −3, and c = −6.
(D) The acceleration of the flow along the x-direction is not constant for any value of
a, b, and c.
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Fluid Mechanics (XE-B)
Q.38 A gas is pressurized in a vertical frictionless piston-cylinder device, as shown in the
figure. The piston has a mass of 4 kg and a cross-sectional area of 40 cm2. A metallic
block of 13 kg is placed on the piston. The atmospheric pressure (pa ) is 1 bar.
Assume acceleration due to gravity as 10 m.s−2. The pressure inside the cylinder,
pi (in bar) is __________. (rounded off to three decimal places)
Q.39 A ship is designed to sail at a speed of 8 m.s−1. A designer makes a 1/10 scaled
model to test the ship in a water tunnel. The model and the ship satisfy the dynamic
similarity. The speed (in m.s−1) of the model is _________. (rounded off to two
decimal places)
Q.40 A rectangular block (density = 600 kg.m−3) with base area of 0.06 m2 and height
15 cm is partially submerged in water (density = 1000 kg.m−3), as shown in the
figure. Assume acceleration due to gravity as 10 m.s−2. The submerged depth,
ℎ (in m) of the block in the water is _________. (rounded off to two decimal places)
Q.41 For a steady, laminar, and incompressible flow over a flat plate, the local skin
0.664
friction coefficient is given as Cf = , where Rex is the local Reynolds number.
√Rex
The density and kinematic viscosity of the fluid are 1.2 kg.m−3 and 1.5×10−5 m2.s−1,
respectively. If the freestream velocity is 3 m.s−1, then the local shear stress
(in N.m−2) at x = 0.05 m is __________. (rounded off to three decimal places)
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Fluid Mechanics (XE-B)
Q.42 The axial velocity profile of a laminar, incompressible, and fully-developed flow in
1 dp
a circular pipe of radius R is given as vz = (r 2 − R2 ), where µ, p, z, and r
4μ dz
are dynamic viscosity, pressure, axial coordinate, and radial coordinate,
respectively. If the magnitude of shear stress at the pipe wall is given as
R dp
|τw | = , then the value of K is __________. (answer in integer)
K dz
Q.43 Air flows through a pipe of diameter D with an average velocity of 3 m.s−1.
The Darcy friction factor of the pipe is 0.02. Assume acceleration due to gravity as
10 m.s−2. If the head loss per meter is 0.05, the diameter (in m) of the
pipe is __________. (rounded off to two decimal places)
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Materials Science (XE-C)
Q.44 – Q.52 Carry ONE mark Each
Q.44 The band gap of a material is Eg and the energy of an incident photon is Ep. Optical
absorption will occur in this material if,
(A) Eg < Ep
(B) Eg > Ep
(C) Electron-electron recombination occurs
(D) Electron-hole recombination occurs
Q.45 Discoloration and loss of mechanical strength of plastic chairs exposed to sunlight
for several days is due to
(A) Hydrophilic degradation
(B) Oxidative degradation
(C) Photo-degradation
(D) Thermal degradation
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Materials Science (XE-C)
Q.46 Which one of the following polymer processing techniques involves shaping a
heated sheet?
(A) Thermoforming
(B) Injection molding
(C) Blow molding
(D) Extrusion
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Materials Science (XE-C)
Q.47 The plot shows three different paths (1, 2, and 3) connecting the initial equilibrium
state X to the final equilibrium state Y in a thermodynamic process. Which of the
following statements is/are correct?
(A) The change in internal energy is the same for all three paths.
(B) The work done is the same for all three paths.
(C) The heat exchange will differ depending on the path taken.
(D) The first law of Thermodynamics is violated if work differs along the paths.
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Materials Science (XE-C)
Q.48 Which of the following is/are polarization mechanisms in dielectric solids?
(A) Mechanical polarization
(B) Ionic polarization
(C) Electronic polarization
(D) Thermal polarization
Q.49 Which of these methods is/are used for the synthesis of ceramic powders?
(A) Sol-gel
(B) Hydromechanical
(C) Thermomechanical
(D) Hydrothermal
Q.50 The degrees of freedom of a system with 2 components and 2 phases in equilibrium
is _________ (answer in integer).
Q.51 The interplanar spacing of (ℎ k l) planes is 4.5 nm in a given crystal. For the
(3ℎ 3k 3l) planes, the interplanar spacing, in nm, is _________ (rounded off to one
decimal place).
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Materials Science (XE-C)
Q.52 The equilibrium vacancy concentration in aluminum at 900 K is 1.1 × 10 4. The
enthalpy of formation of vacancies, in kJ.mol1 , is _________ (rounded off to one
decimal place).
Given: Universal gas constant = 8.314 J.K1.mol1
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Materials Science (XE-C)
Q.53 – Q.65 Carry TWO marks Each
Q.53 Three phases, α, β and L are shown in the binary phase diagram below. Identify the
correct G – X (Gibbs free energy vs Composition) plot corresponding to
temperature T0.
(A)
(B)
(C)
(D)
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Materials Science (XE-C)
a
Q.54 In a cubic crystal, the Burgers vector for a mixed dislocation line is 2 [110]. The
dislocation line lies along the [011] direction. The slip plane of the dislocation is
(A) (11̅1)
(B) (111)
(C) (01̅1)
(D) (11̅0)
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Materials Science (XE-C)
Q.55 Match the Thermodynamic laws in Column I with the description given in
Column II
Column I Column II
P Zeroth law 1 Entropy of a perfect crystal at 0 K is zero
Q First law 2 Introduces Entropy
R Second law 3 Defines thermal equilibrium
S Third law 4 Defines internal energy
(A) P 3; Q 4; R 2; S 1
(B) P 1; Q 2; R 4; S 3
(C) P 1; Q 4; R 3; S 2
(D) P 3; Q 1; R 2; S 4
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Materials Science (XE-C)
Q.56 Match the material property in Column I with the measurement technique in
Column II.
Column I Column II
P Electrical conductivity 1 UV-Vis spectroscopy
Q Band gap energy 2 4-Probe method
R Young’s modulus 3 Differential scanning calorimetry
S Heat of fusion 4 Acoustic measurement
(A) P 2; Q 1; R 4; S 3
(B) P 1; Q 2; R 4; S 3
(C) P 2; Q 3; R 4; S 1
(D) P 1; Q 4; R 2; S 3
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Materials Science (XE-C)
Q.57 Which one of the following statements regarding point defects in ionic solids is
correct?
(A) Frenkel defects are dominant in those ionic solids where there is a considerable size
difference between the cation and anion.
(B) Schottky defects are dominant in those ionic solids where there is a considerable
size difference between the cation and anion.
(C) Schottky defects are the dominant defects in all ionic solids.
(D) Similar density of both Frenkel and Schottky defects is present in all ionic solids.
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Materials Science (XE-C)
Q.58 Consider 3 crystals (all having FCC lattice) labelled as P, Q and R as described
below:
Crystal P: Cu crystal with 4 Cu atoms per unit cell
Crystal Q: NaCl crystal with 4 Na+ ions and 4 Cl ions per unit cell
Crystal R: Diamond crystal with 8 C atoms per unit cell
Which of the following options is/are correct?
(A) Only crystal P is a close packed structure.
(B) Only crystal Q is a close packed structure.
(C) Crystal R has the smallest packing factor.
(D) All the crystals P, Q and R are close packed structures.
Q.59 Which of the following statements is/are applicable to Fick’s second law:
(A) Concentration changes with time
(B) Steady state condition prevails
(C) Diffusion is time dependent
(D) Concentration profile is linear
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Materials Science (XE-C)
Q.60 According to quantum free electron theory, which of the following statements is/are
correct regarding the behavior of valence electrons in a metal?
(A) Valence electrons are localized to individual atoms.
(B) Valence electrons are delocalized within the crystal.
(C) Energy distribution of valence electrons follows Fermi-Dirac statistics.
(D) Energy distribution of valence electrons follows Maxwell-Boltzmann statistics.
Q.61 Fe has a density of 7.87 g.cm3, atomic mass of 55.84 g.mol1 and net magnetic
moment per atom of 2.22 Bohr magnetons (µB). The saturation magnetization of Fe,
in A.m1, is _________ ×105 (rounded off to one decimal place).
Given: µB = 9.27×1024 A.m2, Avogadro number = 6.023×1023 mol1
Q.62 At the peak (also denoted as UTS) of an engineering stress vs. engineering strain
curve for ductile metal, the engineering strain is 0.2. The corresponding
true stress (σ) vs. true strain (ε) relationship follows the equation: σ = Kε n , where
K and n are constants.
The engineering stress at the peak, in MPa, is _________ (rounded off to one
decimal place).
Given: K = 200 MPa
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Materials Science (XE-C)
Q.63 A 1 cm3 Si cube is doped with As with a concentration of 1 atom per 109 Si atoms.
The resistance of the doped Si cube, in Ohms, is _________ (rounded off to one
decimal place).
Given:
Atomic concentration of Si = 5×1022 cm3
Intrinsic concentration of electrons in Si = 1×1010 cm3
Electron mobility in Si = 1350 cm2.V1.s1
Hole mobility in Si = 450 cm2.V1.s1
Electronic charge = 1.6×1019 C
Q.64 A circular disk-shaped ceramic green body has a relative density of 50%. On
sintering, both the height and the diameter of the disk shrink by 20%. The sintered
disk’s relative density, in %, is _________ (rounded off to one decimal place).
Q.65 The standard electrode potential of Cu2+ | Cu is +0.34 V and Zn2+ | Zn is −0.76 V.
For the Zn | Zn2+ || Cu2+ | Cu cell, the EMF, in Volts, is _________ (rounded off to
two decimal places).
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Solid Mechanics (XE-D)
Q.66 – Q.74 Carry ONE mark Each
Q.66 Two axial members, namely OP and OQ, are pin joined at O as shown in the figure.
A force F acts at point P along the positive x direction and a force √3F acts at point
Q along the positive y direction.
The resultant of the applied forces makes an angle (anticlockwise from the
positive x-axis).
The value of is ______.
(A) 30°
(B) 45°
(C) 60°
(D) 75°
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Solid Mechanics (XE-D)
Q.67 Two smooth drums each weighing W and radius, r are connected by a stiff rope of
length, h as shown in the figure. Force F is applied using a massless lever (RS) of
length, l. The friction between the drums and the lever (RS) is negligible. The
system is in static equilibrium.
Which one of the following represents the CORRECT free body diagram of the
lever (RS)?
Figures are not to scale. N1, N2, and N3 in the options are reaction forces and Ff is
the frictional force.
(A)
(B)
(C)
(D)
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Solid Mechanics (XE-D)
Q.68 Identify the zero-force member in the truss structure as shown in the figure.
Figure is not to scale
(A) ST
(B) SR
(C) SP
(D) SQ
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Solid Mechanics (XE-D)
Q.69 A rigid block of mass m on a horizontal surface is connected to three springs each
having spring constant k as shown in the figure.
Which one of the following is the CORRECT natural frequency of the system?
(A)
3k
√
4m
(B)
2k
√
3m
(C)
3k
√
2m
(D)
3k
√
m
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Solid Mechanics (XE-D) Q.70 Which among the following options is/are CORRECT unit(s) of stress? (A) Nm2 (B) Pa (C) Nm (D) N/m2 Organizing Institute: IIT Guwahati Page 48 of 124
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Solid Mechanics (XE-D)
Q.71 A car is moving on a horizontal surface in a straight line with a constant velocity of
3 m/s. A ball is thrown vertically upwards at time t = 0 from the top of the moving
car with a velocity of 20 m/s. The acceleration due to gravity is 10 m/s2.
At what value(s) of time t in second(s), the ball is at a height of 15 m from the top
of the moving car?
(A) 1
(B) 2
(C) 3
(D) 4
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Solid Mechanics (XE-D)
Q.72 A cart of weight (W) 5 kN, stands on an inclined smooth surface at an angle (θ) of
45° as shown in the figure. The cart is maintained in equilibrium by a horizontal
force F acting at point S.
The value of F is ______ kN (in integer).
Figure is not to scale
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Solid Mechanics (XE-D)
Q.73 A 2D state of stress at a point in a body is given by σxx = −40 MPa,
σyy = 100 MPa and τxy = 50 MPa.
The radius of the Mohr’s circle for the given state of stress is ______MPa
(rounded off to two decimal places).
Q.74 11 4
Sum of the principal stresses of a 2D stress state [ ] is ______ (in integer).
4 5
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Solid Mechanics (XE-D)
Q.75 – Q.87 Carry TWO marks Each
Q.75 The force (F) acting on the block, as shown in the figure is 2 N. The stiffness of the
spring (k) is 100 N/m.
Assume that the block is in static equilibrium and its mass is negligible.
If the static deflection of the spring (∆) is 0.01 m, which one of the following is the
corresponding angle (θ) in radians?
(A) π
3
(B) π
4
(C) π
5
(D) π
6
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Solid Mechanics (XE-D)
Q.76 Which one of the following options is the CORRECT absolute value of the bending
moment at R in the frame as shown in the figure?
Figure is not to scale
(A) 0
(B) Fl
(C) 2Fl
(D) 3Fl
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Solid Mechanics (XE-D)
Q.77 One column with square cross section of side r and another column with rectangular
cross section of breadth p and width q (< p) are made from the same material. Both
the columns have one end fixed, and the other end is free. They are subjected to
axial loads along the centroidal axis.
Consider the area of cross sections of both the columns to be the same. The
minimum critical Euler buckling loads of the columns with rectangular and square
cross-sections are Frect and Fsq , respectively.
Frect
Then is ______.
Fsq
(A) p
q
(B) q
p
(C) r
q
(D) r2
pq
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Solid Mechanics (XE-D)
Q.78 Two prismatic rods of identical lengths are designed for the same strain energy
density when subjected to the same axial load. One of the rods is made of steel
(Young’s modulus = 210 GPa) and another is made of aluminum (Young’s modulus
= 70 GPa).
If the diameter of the aluminum rod is 70 mm, then which one of the following
options corresponds to the diameter of the steel rod in mm?
(A) 53.19
(B) 70
(C) 210
(D) 29.13
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Solid Mechanics (XE-D)
Q.79 A spring of stiffness k is connected to the center of a homogeneous right circular
cylinder of radius r placed on a horizontal surface as shown in the figure. The
cylinder is assumed to be rolling without slipping.
Considering small amplitude of oscillation, which one of the following options is
the CORRECT natural frequency of the system?
(A)
k
√
2m
(B)
3k
√
2m
(C)
k
√
m
(D)
2k
√
3m
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Solid Mechanics (XE-D)
Q.80 A 2D stress state of pure shear is shown in the figure.
Which one of the following options is equivalent to the given stress state?
Figures are not to scale.
(A)
(B)
(C)
(D)
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Solid Mechanics (XE-D)
Q.81 The point Q of a thin rigid equilateral triangular plate PQR is constrained to move
in a horizontal channel. Point P of the same plate is constrained to move in the
vertical channel as shown in the figure. The length of the side PQ is 4 m.
π
At the instant when the angle θ = 3 rad and the velocity of point Q in the positive
x direction is 20 m/s, which one of the following options is the magnitude of the
angular velocity vector of the line SR on the plate in rad/s?
Figure is not to scale
(A) 5
(B) 10
(C) 20
(D) 25
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Solid Mechanics (XE-D)
Q.82 A motorized pulley of diameter 200 mm is used to transfer a block of mass 100 kg
from platform 1 to platform 2 using a ramp kept at an inclination of 30° as shown
in the figure. The coefficient of static friction between the block and the ramp is
0.2. The acceleration due to gravity is 10 m/s2.
Assume the rope to be parallel to the ramp surface.
The minimum torque required by the motor to transport the block uphill is ____ Nm
(rounded off to two decimal places).
Figure is not to scale
Q.83 The bending moment diagram for a simply supported beam is piecewise linear as
shown in the figure. The bending moment M(x) at x = 0.5 m is 5 Nm. The beam has
a rectangular cross-section with an area of 1 m2.
The absolute value of the maximum shear stress on the cross-section at x = 0.75 m
is ______ N/m2 (in integer).
Figure is not to scale
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Solid Mechanics (XE-D)
Q.84 A thin walled cylindrical container of diameter 2 m and wall thickness of 2.5 cm is
made of steel whose Young’s modulus is 200 GPa and yield stress is 450 MPa.
Using von Mises criteria, the maximum permissible pressure is ______MPa
(rounded off to the nearest integer).
Q.85 A solid axial bar made of steel with Young’s modulus, 200 GPa and Poisson’s ratio,
0.3, is subjected to uniaxial stress of 50 MPa.
The absolute value of the maximum shear strain on the outer surface of the bar is
______× 10−4 (rounded off to two decimal places).
Q.86 EFGH (solid lines) is the initial configuration and E′F′G′H′ (dashed lines) is the
deformed configuration of an object as shown in the figure. E′ coincides with E and
F′ coincides with F.
The average normal strain along the line segment OP is ______ (rounded off to
three decimal places).
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Solid Mechanics (XE-D)
Q.87 A simply supported beam of length l = 2 m is subjected to a concentrated moment
M = 150 kNm at a distance l/2 from the left end as shown in the figure. The
elastic-strain energy U of the beam is given by the following expression:
M2 l
U = 48 EI
The section modulus of the beam is EI = 25 × 105 Nm2 .
The absolute value of the slope of the beam at a distance l/2 from the left end is
______(rounded off to three decimal places).
Figure is not to scale
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Thermodynamics (XE-E)
Q.88 – Q.96 Carry ONE mark Each
Q.88 Consider any substance whose mass specific heat capacity at constant pressure and
mass specific heat capacity at constant volume are cP and cV , respectively. If the
gas constant is R, which ONE of the following relations is CORRECT for the
substance at all conditions?
(A) cP cV
(B) cP cV R
(C) cP cV
(D) cP cV
Q.89 Consider a mixture of ideal gases, nitrogen (N2) and carbon-dioxide (CO2), at 25 ℃
and 101 kPa. The molar mass of N2 is 28 kg/kmol and molar mass of CO2 is
44 kg/kmol. If the molar mass of the mixture is 34 kg/kmol, which ONE of the
following mixture compositions is possible?
(A) 62.5% N2 and 37.5% CO2 by mass
(B) 62.5% N2 and 37.5% CO2 by volume
(C) 37.5% N2 and 62.5% CO2 by mass
(D) 37.5% N2 and 62.5% CO2 by volume
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Thermodynamics (XE-E)
Q.90 In a mixing chamber hot water enters at a temperature of 80 ℃ with a flowrate of
0.5 kg/s. From another entry, cold water enters the chamber at 20 ℃. The desired
temperature after mixing at the exit of the chamber is 40 ℃. There is no water
leakage and the mixing happens at adiabatic conditions. Assume the specific heat
capacity of water is 4.2 kJ/kg-K. For a steady state operation, the mass flow rate (in
kg/s) of the cold-water stream is
(A) 2.0
(B) 1.5
(C) 1.0
(D) 0.5
Q.91 Which ONE of the following statements is CORRECT?
For an ideal gas, specific enthalpy ( h ) is a function of both temperature and
(A)
pressure.
(B) Internal energy ( U ), entropy ( S ), and enthalpy ( H ) are path functions.
(C) Heat transferred ( Q ) and work done ( W ) are state (point) functions.
(D) Temperature ( T ), pressure ( P ), and specific volume ( v ) are intensive properties.
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Thermodynamics (XE-E)
Q.92 A mixture of carbon-dioxide (CO2), nitrogen (N2) and oxygen (O2) are introduced
in a rigid and impermeable tank containing only liquid water (H2O). Assume that
the components are non-reacting and un-dissociated. The system is kept isolated till
an equilibrium is achieved, where only two phases are present. The degrees-of-
freedom of the equilibrium mixture, as obtained from the phase rule, is
(A) 1
(B) 2
(C) 3
(D) 4
Q.93 A stream of moist air at 101 kPa and 25 ℃ undergoes a constant pressure process
such that its dry bulb temperature increases and specific humidity decreases. For
this process, which of the following statements is/are always CORRECT?
(A) Wet bulb temperature increases.
(B) Dew point temperature decreases.
(C) Relative humidity decreases.
(D) Adiabatic saturation temperature increases.
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Thermodynamics (XE-E)
Q.94 Which of the following is/are example(s) of a pure substance at 25 ℃ and 101 kPa?
(A) Gaseous oxygen
(B) Mixture of liquid water and water vapor
(C) Mixture of liquid water and gaseous oxygen
(D) Homogenous mixture of gaseous oxygen and water vapor
Q.95 A house looses heat at a rate of 150 MJ per hour. The temperature outside the house
is 3 ℃. The minimum power (in kW) required to maintain the temperature inside
the house at 25 ℃ using a heat pump is ________________ (rounded off to two
decimal places).
Q.96 Consider an ideal Otto-cycle with cold-air-standard assumptions to be applicable.
The temperature of the working fluid at the start and the end of the compression
process is 300 K and 750 K, respectively. For the working fluid take the ratio of the
specific heat capacities as 1.4. The thermal efficiency (in %) of the cycle is
________________ (rounded off to two decimal places).
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Thermodynamics (XE-E)
Q.97 – Q.109 Carry TWO marks Each
Q.97 Consider a real gas, which obeys the following equation-of-state:
RT C
v C1 2 ,
P Pv
where v is the mass specific volume, P is the pressure, T is the temperature and
R is the gas constant. C1 and C2 are constants. If s is the mass specific entropy,
s
the quantity for the gas is given by
v T
R
(A)
v
R 2T
(B)
Pv 2
R
(C)
v C1
C1C2
(D)
Tv
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Thermodynamics (XE-E)
Q.98 M kg of a liquid at a temperature T1 is mixed with M kg of the same liquid at
another temperature T2 in an isolated tank at constant pressure. The mass specific
heat capacity at constant pressure of the liquid is cP , which is a constant. The total
entropy change in the process is
T T
(A) McP ln 1 2
2 TT
1 2
T T
(B) 2McP ln 1 2
TT
1 2
T T
(C) McP ln 1 2
TT
1 2
T T
(D) 2McP ln 1 2
2 TT
1 2
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Thermodynamics (XE-E)
A fluid undergoes a process where its pressure ( P ), temperature ( T ) and volume
Q.99 ( V ) changes from ( P1 , T1 , V1 ) to ( P2 , T2 , V2 ). During the process, volume
expansivity ( ) and isothermal compressibility ( T ) remains constant. Given that
1 V 1 V V2
and T , the ratio is
V T P V P T V1
(T2 T1 )
(A)
T ( P2 P1 )
(B) (T2 T1 )T (P2 P1 )
exp (T2 T1 )
(C)
exp T ( P2 P1 )
(D) (T2 T1 ) T ( P2 P1 )
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Thermodynamics (XE-E)
Q.100 Consider an ideal Rankine cycle with fixed conditions at the turbine inlet. If the
condenser pressure is lowered, which of the following statements is/are
CORRECT?
(A) Pump work input remains the same.
(B) Moisture content at turbine exit decreases.
(C) Heat rejected in the condenser decreases.
(D) Turbine work output increases.
Q.101 An adiabatic rigid and impermeable tank of volume 10 m3 contains air at 800 kPa
and 70 ℃. The air is allowed to leave the tank until the pressure is one-fourth of
its original value. During the process, the air in the tank is maintained at 70 ℃
using an electrical heater. Assume that the air behaves as an ideal gas having gas
constant and ratio of specific heat capacities as 287 J/kg-K and 1.4, respectively.
The total electrical energy (in MJ) supplied by the heater is _____________
(rounded off to two decimal places).
Q.102 Two kg of a gas is compressed in a process. Pressure (P) and mass specific volume
(v) of the gas during the process follows: Pv1.2 constant. The temperature of the
gas before and after compression is 300 K and 600 K, respectively. Assume that
the gas behaves as an ideal gas with gas constant and ratio of specific heat
capacities equal to 287 J/kg-K and 1.4, respectively. The heat rejected (in kJ)
during the process is ________________(rounded off to two decimal places).
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Thermodynamics (XE-E)
Q.103 Consider a single component fluid at saturation conditions having the following
properties.
Latent heat of vaporization, h fg 39.6 103 kJ/kmol
vg Psat vg
Compressibility factor for the vapor phase, z g 0.95
videal RuT
Psat is the saturation pressure
T is the temperature
v g is the molar specific volume of the vapor phase
Assume that v fg vg , where v fg is the difference in the molar specific volume of
the vapor and the liquid phases
Universal gas constant, Ru 8.314 kJ/kmol-K
d ln P
Using the Clapeyron equation, the quantity (in K) is ________
d 1 T saturation
(rounded off to two decimal places).
Q.104 h h
It is given that: c p and (v Tv) . Here h is the mass specific
T P P T
1 v
enthalpy, v is the mass specific volume, is the volume expansivity,
v T P
and c p is the mass specific heat capacity at constant pressure. T and P represent
the temperature and the pressure, respectively. The inversion temperature is the
T
temperature at which the Joule-Thomson coefficient, JT , goes to zero.
P h
Consider a fluid with properties: v 1.03 m3/kg, cP 1 kJ/kg-K, and
4.39 103 1/K;
The inversion temperature (in K) for the fluid is ________ (rounded off to two
decimal places).
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Thermodynamics (XE-E)
Q.105 A stream of moist air enters an adiabatic saturator at 45 ℃ and 101 kPa and leaves
as a saturated mixture at 30 ℃. Make-up water to the saturator is supplied at
30 ℃. The amount of make-up water (in grams per kg of dry air) supplied is
________________(rounded off to two decimal places).
Use the following data:
Specific heat capacity of water is 4.2 kJ/kg-K
Specific heat capacity of air at constant pressure is 1 kJ/kg-K
Saturated water properties:
At 30 ℃: specific enthalpy of saturated water vapor is 2556 kJ/kg-K, specific
enthalpy of saturated liquid water is 125.7 kJ/kg-K, and saturation pressure is
4.25 kPa
At 45 ℃: specific enthalpy of saturated water vapor is 2582 kJ/kg-K, specific
enthalpy of saturated liquid water is 188.4 kJ/kg-K, and saturation pressure is
9.60 kPa
Q.106 A rigid spherical solid ball at 1000 ℃ is cooled slowly to 200 ℃ in a surrounding
air at 25 ℃. The density, specific heat capacity, and diameter of the ball are
8000 kg/m3, 500 J/kg-K, and 10 mm; respectively. Assuming that the cooling
process is quasi-equilibrium, the entropy generated (in J/K) in the process is
________________(rounded off to two decimal places).
Q.107 Consider an ideal Diesel-cycle with cold-air-standard assumptions to be
applicable. The compression ratio is 20 and the cut-off ratio is 1.8. At the end of
the compression process, the working fluid is at 1120 K and 6.6 MPa. The ratio of
the specific heat capacities is 1.4 for the working fluid. The temperature (in K) at
the end of the expansion process is ________________(rounded off to two decimal
places).
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Thermodynamics (XE-E)
Q.108 A mixture of helium (He) and nitrogen (N2) expands in a turbine from 800 kPa to
100 kPa. The mixture composition is 40% He and 60% N2 by mass. The turbine
inlet temperature is 1000 K. The temperature (in K) at the turbine exit is
________________(rounded off to two decimal places).
Assume:
The process is isentropic. Kinetic and potential energy changes in the process are
negligible. He and N2 behaves as ideal gases. Specific heat capacities are constant.
Use the following data:
Ratio of specific heat capacities for He and N2 are 1.67 and 1.4, respectively.
Specific heat capacities at constant pressure for He and N2 are 5.19 kJ/kg-K and
1.04 kJ/kg-K, respectively.
Q.109 A rigid and impermeable tank has only moist air with a specific humidity of
0.025 kgwater-vapor/kgdry-air at 30 ℃ and 101 kPa. The air is heated to 90 ℃. Assume
moist air to behave as an ideal gas. The relative humidity (in %) of the heated air
is ________________(rounded off to two decimal places).
Saturation pressure of water at 30 ℃ is 4.25 kPa and at 90 ℃ is 70.18 kPa.
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Polymer Science and Engineering (XE-F)
Q.110 – Q.118 Carry ONE mark Each
Q.110 Which one of the following polymerization methods is used for the synthesis of
butyl rubber?
(A) Ring opening polymerization
(B) Condensation polymerization
(C) Cationic polymerization
(D) Anionic polymerization
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Polymer Science and Engineering (XE-F)
Q.111 The stress-strain profiles in the figure were obtained following longitudinal tensile
loading for a brittle polymer, glass fibre, and a composite lamina consisting of
unidirectional continuous glass fibres and the polymer matrix. Assume that the
matrix is free of voids, there is perfect bonding between glass fibres and the matrix,
and there are no residual stresses in the composite lamina.
P
Stress
Q
R
Strain
Identify the correct stress-strain profile for the polymer matrix, glass fibre, and their
composite lamina from the above figure.
(A) P – Matrix ; Q – Glass fibre ; R – Composite
(B) P – Glass fibre ; Q – Composite ; R – Matrix
(C) P – Glass fibre ; Q – Matrix ; R – Composite
(D) P – Composite ; Q – Glass fibre ; R – Matrix
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Polymer Science and Engineering (XE-F)
Q.112 Norrish-Smith effect or Trommsdorff effect during free radical bulk polymerization
at high conversion is characterized by_________________.
(A) increase in rate of polymerization with time due to increase in viscosity
(B) decrease in rate of polymerization with time due to increase in viscosity
(C) decrease in rate of polymerization with time due to reduction in viscosity
(D) increase in rate of polymerization with time due to reduction in viscosity
Q.113 For a polydisperse polymer, the viscosity-average molecular weight (M̅v) becomes
equal to the weight-average molecular weight (M̅w), when the Mark–Houwink
constant a is ___________________.
(A) 0.1
(B) 0.5
(C) 0.7
(D) 1.0
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Polymer Science and Engineering (XE-F) Q.114 Which one of the following is NOT a rotational rheometer? (A) Cone and plate rheometer (B) Parallel plate rheometer (C) Capillary rheometer (D) Cylindrical Couette rheometer Organizing Institute: IIT Guwahati Page 76 of 124
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Polymer Science and Engineering (XE-F)
Q.115 Select the correct option to match the Product with the most appropriate
Processing technique from the table given below:
Product Processing technique
P Fibre-reinforced pressure vessel I Rotomoulding
Q Overhead water tank II Thermoforming
R Blister package for medicine III Filament winding
S Plastic carry bag IV Blown film extrusion
(A) P–III ; Q–II ; R–I ; S–IV
(B) P–IV ; Q–III ; R–II ; S–I
(C) P–II ; Q–I ; R–III ; S–IV
(D) P–III ; Q–I ; R–II ; S–IV
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Polymer Science and Engineering (XE-F)
Q.116 Which of the following is/are the most appropriate compatibilizer(s) for the
polypropylene/Nylon 66 blend?
(A) Maleic anhydride grafted polystyrene
(B) Maleic anhydride grafted polypropylene
(C) Polypropylene-b-polystyrene
(D) Glycidyl methacrylate grafted polypropylene
Q.117 Which of the following polymers is/are prone to hydrolytic degradation?
(A) Poly(ethylene terephthalate)
(B) Polypropylene
(C) Poly(lactic acid)
(D) Polycaprolactone
Q.118 An insulating polymer is used as a dielectric medium between two capacitor plates.
The dielectric constant of the polymer is 5.0 and the permittivity of vacuum is
8.85 × 10–12 F/m. The permittivity of the polymer is _____________ × 10–12 F/m
(rounded off to two decimal places).
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Polymer Science and Engineering (XE-F)
Q.119 – Q.131 Carry TWO marks Each
Q.119 Select the correct option to match the Polymer to its Major polymeric constituent
from the table given below:
Polymer Major polymeric constituent
P Natural rubber I Polyisobutylene
Q Gutta percha II Polychloroprene
R Neoprene III trans-1,4-polyisoprene
S Butyl rubber IV cis-1,4-polyisoprene
(A) P–IV ; Q–III ; R–I ; S–II
(B) P–IV ; Q–III ; R–II ; S–I
(C) P–II ; Q–IV ; R–I ; S–III
(D) P–II ; Q–IV ; R–III ; S–I
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Polymer Science and Engineering (XE-F) Q.120 Resol is produced by reaction of ___________________. (A) phenol with an excess of formaldehyde in presence of a base catalyst (B) formaldehyde with an excess of phenol in presence of a base catalyst (C) phenol with an excess of formaldehyde in presence of an acid catalyst (D) an equimolar mixture of phenol and formaldehyde at neutral pH Organizing Institute: IIT Guwahati Page 80 of 124
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Polymer Science and Engineering (XE-F)
Q.121 Select the correct option to match the Polymer to its most suitable Monomer(s)
from the table given below:
Polymer Monomer(s)
O CH3
P Poly(p-phenylene I Cl C Cl + HO C OH
sulfide) CH3
Q Poly(ether sulfone) II Na2S + Cl Cl
R Poly(ether ether III O
ketone) F C F + HO OH
S Polycarbonate IV O
HO S Cl
O
(A) P–II ; Q–IV ; R–III ; S–I
(B) P–II ; Q–IV ; R–I ; S–III
(C) P–IV ; Q–III ; R–II ; S–I
(D) P–IV ; Q–I ; R–III ; S–II
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Polymer Science and Engineering (XE-F)
Q.122 Select the correct option to match the Compound/Additive to its most suitable
Function from the table given below:
Compound/Additive Function
P Azocarbonamide I Flame retardant
Q 2-(2-hydroxyphenyl)-benzotriazole II Coupling agent
R (3-Aminopropyl)triethoxysilane III Blowing agent
S Ammonium polyphosphate IV UV-absorber
(A) P–IV ; Q–III ; R–II ; S–I
(B) P–III ; Q–IV ; R–II ; S–I
(C) P–I ; Q–III ; R–II ; S–IV
(D) P–III ; Q–IV ; R–I ; S–II
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Polymer Science and Engineering (XE-F)
Q.123 The variation of steady shear viscosity (η ) of a polymer melt with shear rate (γ̇ ) is
shown in the figure, where γ̇s is the upper limit of the applied shear rate.
Which one of the following figures, labeled P, Q, R and S, shows the most
appropriate variation of shear stress (τ) with shear rate for the same polymer melt?
(A) P
(B) Q
(C) R
(D) S
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Polymer Science and Engineering (XE-F)
Q.124 Select the correct option to match the Initiator(s) with the Method of
polymerization from the table given below:
Initiator(s) Method of polymerization
P BF3/H2O I Anionic polymerization
Q n-C4H9Li II Cationic polymerization
R FeCl2/K2S2O8 III Coordination addition
polymerization
S Metallocene/methylaluminoxane IV Free radical addition
polymerization
(A) P–II ; Q–III ; R–IV ; S–I
(B) P–IV ; Q–I ; R–II ; S–III
(C) P–III ; Q–II ; R–IV ; S–I
(D) P–II ; Q–I ; R–IV ; S–III
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Polymer Science and Engineering (XE-F)
Q.125 Select the correct option to match the Characterization technique with the
Information that is obtained using these techniques.
Characterization technique Information
P Differential scanning I Spherulite size
calorimetry
Q Infrared spectroscopy II Loss modulus
R Dynamic mechanical thermal III Functional groups
analysis
S Optical microscopy IV Enthalpy of crystallization
(A) P–IV ; Q–III ; R–I ; S–II
(B) P–III ; Q–IV ; R–I ; S–II
(C) P–IV ; Q–III ; R–II ; S–I
(D) P–III ; Q–IV ; R–II ; S–I
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Polymer Science and Engineering (XE-F)
Q.126 Which of the following options is/are used to plasticize poly(vinyl chloride) (PVC)?
(A) Addition of vinyl acetate comonomer during the synthesis of PVC
(B) Chlorination of PVC
(C) Addition of di-iso-octyl phthalate during processing of PVC
(D) Addition of dicumyl peroxide during processing of PVC
Q.127 A certain amount of plasticizer with a glass transition temperature (Tg) of –50 °C
was added to a polymer to reduce its Tg from 70 °C to 30 °C. Using the Fox equation,
the weight fraction of the plasticizer used is ________________ (rounded off to two
decimal places).
Q.128 A rectangular plastic specimen with a cross-sectional area of 240 mm2 is subjected
to tension with a force of 15000 N resulting in elastic deformation. If the Young’s
modulus of the specimen is 34.55 MPa, the value of strain is ________________
(rounded off to two decimal places).
Q.129 Equimolar mixture of terephthalic acid and butylene glycol was taken to synthesize
a polyester. The reaction was stopped at 99.6% conversion of the acid monomer.
The weight-average molecular weight (M̅w) of the synthesized polyester is
________________ g/mol (rounded off to the nearest integer).
Q.130 A viscoelastic polymer is subjected to a constant strain of 0.3. The behaviour of the
polymer follows Maxwell model of linear viscoelasticity. Elastic modulus of the
polymer is 5 MPa and the relaxation time is 200 days. The stress in the polymer
after 100 days from the initial application of the strain is ________________ MPa
(rounded off to two decimal places).
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Polymer Science and Engineering (XE-F)
Q.131 A single-screw extruder is operated at 12 rpm under open discharge condition (i.e.,
without a die).
The screw has a diameter of 10 cm, a distance of 2.5 cm between the adjacent
flights, a gap of 0.25 cm between the screw and the inner wall of the barrel, and a
helix angle (i.e., angle between the flights and the plane perpendicular to the screw
axis) of 8°.
If the flow of the molten polymer in the metering zone through the extruder is
assumed isothermal, Newtonian and incompressible, the volumetric flow rate of the
polymer melt is ________________ cm3/min (rounded off to the nearest integer).
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Food Technology (XE-G) Q.132 – Q.140 Carry ONE mark Each Q.132 Ergotism is caused by ingestion of grains infected with (A) Clostridium perfringens (B) Rhizopus stolonifer (C) Lactococcus lactis (D) Claviceps purpurea Organizing Institute: IIT Guwahati Page 88 of 124
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Food Technology (XE-G)
Q.133 Match the bacteria in Column I with their respective characteristic features in
Column II.
Column I Column II
(1) Gram-positive, round-shaped and
(P) E. coli
non-spore formers
(2) Gram-negative, rod-shaped and
(Q) B. subtilis
non-spore formers
(3) Gram-positive, rod-shaped and
(R) S. aureus
spore formers
(4) Gram-positive, rod-shaped and
(S) L. monocytogenes
non-spore formers
(A) P-1; Q-4; R-2; S-3
(B) P-2; Q-1; R-3; S-4
(C) P-2; Q-3; R-1; S-4
(D) P-2; Q-4; R-1; S-3
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Food Technology (XE-G) Q.134 Carmine, a food colorant, is derived from (A) Curcuma longa (B) Dactylopius coccus (C) Beta vulgaris (D) Monascus purpureus Q.135 Which one of the following carbohydrates is NOT a storage polysaccharide? (A) Starch (B) Glycogen (C) Chitin (D) Dextran Organizing Institute: IIT Guwahati Page 90 of 124
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Food Technology (XE-G)
Q.136 Which one of the following statements is true for a high-pressure homogenizer?
(A) Homogenization takes place only due to uniform mixing of solid and liquid
(B) Solid particles in the suspension are disintegrated due to the high shear rate
exerted by the liquid
(C) High pressure steam is injected to dissolve the solids
(D) Solid particles in the suspension are compressed into a cake under high pressure
Q.137 Coconut oil contains a small fraction of unsaturated fatty acids, but still has a low
melting point due to the presence of
(A) large amounts of long chain saturated fatty acids
(B) mostly medium chain saturated fatty acids such as lauric acid
(C) few hydrogen bonds per fatty acid chain
(D) higher cholesterol content
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Food Technology (XE-G)
Q.138 Which of the following amines, produced as a result of protein degradation, is/are
foul smelling?
(A) Histamine
(B) Cadaverine
(C) Tyramine
(D) Putrescine
Q.139 Water is flowing at 100 litres/min through a pipe with a diameter of 5 cm. Assume
the coefficient of viscosity of water to be 0.001 Pa.s and the density to be
1000 kg/m3. The Reynolds number for this flow is _______
(Round off to nearest integer)
Q.140 A wet solid, fed to a dryer at a rate of 5 kg/s, is dried using hot air. In this process
its moisture content is reduced from 25% to 15%. The rate of moisture removal
is _______ kg/s. (Round off to two decimal places)
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Food Technology (XE-G)
Q.141 – Q.153 Carry TWO marks Each
Q.141 Match the toxins in Column I with their respective sources in Column II.
Column I Column II
P. Aflatoxin 1. Fusarium verticilloides
Q. Nisin 2. Enterohemorrhagic E. coli
R. Fumonisin 3. Lactococcus lactis
S. Shiga-like toxin 4. Aspergillus flavus
(A) P-1; Q-2; R-3; S-4
(B) P-4; Q-1; R-2; S-3
(C) P-4; Q-3; R-1; S-2
(D) P-1; Q-3; R-2; S-4
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Food Technology (XE-G)
Q.142 Match the vitamins in Column I with their respective coenzyme forms listed in
Column II.
Column I Column II
P. Vitamin B1 1. Tetrahydrofolate
Q. Vitamin B2 2. Methylcobalamin
R. Pantothenic acid 3. Thiamine pyrophosphate
S. Vitamin B12 4. Flavin adenine dinucleotide
T. Folic acid 5. Coenzyme A
(A) P-3; Q-4; R-5; S-2; T-1
(B) P-4; Q-3; R-1; S-5; T-2
(C) P-1; Q-5; R-4; S-2; T-3
(D) P-5; Q-2; R-4; S-3; T-1
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Food Technology (XE-G)
Q.143 Which one of the following proteins brings about the coagulation of milk in the
stomach of calves?
(A) Rennin
(B) Alpha-lactalbumin
(C) Beta-lactoglobulin
(D) Lactoferrin
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Food Technology (XE-G)
Q.144 Match the class of additives used for food preservation listed in Column I with
their specific examples in Column II.
Column I Column II
P. Antioxidants 1. Rice bran wax
Q. Anti-foaming agent 2. Tricalcium phosphate
R. Anti-caking agent 3. Mineral oil
S. Glazing agent 4. Butylated hydroxy anisole (BHA)
(A) P-3; Q-4; R-2; S-1
(B) P-4; Q-3; R-1; S-2
(C) P-4; Q-3; R-2; S-1
(D) P-2; Q-3; R-1; S-4
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Food Technology (XE-G)
Q.145 Match the food items listed in Column I with their respective flavoring agents in
Column II.
Column I Column II
P. Cloves 1. Diacetyl
Q. Butter 2. Limonene
R. Orange 3. Eugenol
S. Lemon 4. Diallyl disulfide
T. Garlic 5. Citral
(A) P-1; Q-3; R-2; S-4; T-5
(B) P-3; Q-2; R-1; S-5; T-4
(C) P-4; Q-2; R-5; S-1; T-3
(D) P-3; Q-1; R-2; S-5; T-4
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Food Technology (XE-G)
Q.146 Vegetable oils resist oxidation and maintain their quality for a long period due to
the presence of
(A) tocopherols
(B) hydrolytic enzyme such as lipases
(C) microorganisms such as molds and yeast
(D) carbohydrates
Q.147 For a given temperature difference between the top and bottom surfaces of a flat
metal plate, Fourier’s law of heat conduction implies that
(A) temperature gradient increases with increase in heat transfer area
(B) heat flux is proportional to the thermal conductivity of the metal
(C) heat flux increases with increase in thickness of the metal plate
(D) temperature gradient decreases with increase in thickness of the metal plate
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Food Technology (XE-G) Q.148 Xylooligosaccharides can be produced by (A) hydrolytic degradation of xylan by hydrochloric acid (B) hydrolysis of starch (C) enzymatic hydrolysis of lactose (D) enzymatic hydrolysis of xylan containing lignocellulosic material Q.149 In a α-helix, the R-groups on the amino acid residues (A) are found on the outside of the helix (B) participate in the backbone H-bonding that stabilize the helix (C) allow formation of right-handed helices (D) allow formation of left-handed helices Organizing Institute: IIT Guwahati Page 99 of 124
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Food Technology (XE-G)
Q.150 During constant pressure cake filtration, for an incompressible cake deposited
uniformly over a constant filter surface area,
(A) the cake resistance remains constant
(B) the cake resistance increases in proportion to the cake thickness
(C) the filtration rate remains constant
(D) the filtration rate decreases with time
Q.151 Hot oil is being cooled in a countercurrent, double-pipe heat exchanger from
410 K to 340 K by chilled water entering at 290 K and exiting the exchanger at
330 K. The Log Mean Temperature Difference (LMTD) for this heat transfer
is ________K. (Round off to one decimal place)
Q.152 A cold-storage room has a double-layered wall. The inner layer is 10 cm thick,
made of fiber insulation board (k = 0.048 W m-1 K-1), and the outer layer is 15 cm
thick, made of concrete (k = 0.762 W m-1 K-1). The surface temperature of the
wall inside the cold room is 260 K and the ambient temperature outside is 300 K.
The steady state heat flux into the cold room is ____________ W/m2.
(Round off to two decimal places)
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Food Technology (XE-G)
Q.153 A tubular centrifuge separates 5 micron particles of density 1500 kg/m3 from a
slurry. The slurry is fed at a volumetric flow rate of 0.5 m3/s. The equivalent
clarification area of the centrifuge is _______m2. (Answer in integer)
Assume g = 10 m/s2 and for water, density = 1000 kg/m3,
coefficient of viscosity (µ) = 10-3 Pa-s
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Atmospheric and Oceanic Sciences (XE-H)
Q.154 – Q.162 Carry ONE mark Each
Q.154 Which of the following is TRUE for the ‘summer solstice’ in the Northern
Hemisphere?
(A) Longest night of the year
(B) Equal duration of daylight and night
(C) Longest duration of daylight of the year
(D) Shortest duration of daylight of the year
Q.155 Which of the following options are parts of the atmospheric boundary layer?
(A) Benthic boundary layer, Internal boundary layer
(B) Mixed layer, Entrainment layer
(C) Mixed layer, Internal boundary layer
(D) Mixed layer, Benthic boundary layer
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Atmospheric and Oceanic Sciences (XE-H)
What is the approximate value of annual-mean pH of seawater at the surface in the
Q.156
northern Indian Ocean?
(A) 4.5
(B) 5.0
(C) 8.0
(D) 11.0
Q.157 Which of the following weather systems has the shortest duration of lifecycle?
Tropical Cyclones
(A)
Thunderstorms
(B)
Western Disturbance
(C)
Winter Monsoon
(D)
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Atmospheric and Oceanic Sciences (XE-H)
Q.158 Which of the following statements based on the given figure is / are TRUE with
respect to the upwelling process in the ocean?
(A) Wind is northerly.
(B) Wind is southerly.
(C) Event occurs in the southern hemisphere.
(D) Event occurs in the northern hemisphere.
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Atmospheric and Oceanic Sciences (XE-H)
Q.159 In a stable atmosphere, the change in pressure (in kilo Pascal) at a height of 100 m
from the mean sea level is _____. (rounded off to three decimal places)
[Density of air is 1.029 kg m−3 and acceleration due to gravity is 9.81 m s −2 ]
Q.160 If 20 wave crests pass a fixed point in an interval of 5 minutes, then the frequency
of the wave (in Hertz) is _______. (rounded off to three decimal places)
Q.161 The required magnitude of heat transfer to reduce the temperature of
10 kg of dry air by 5 ℃ is ____________ kilo Joules. (rounded off to one decimal
place)
[Specific heat capacity of dry air is 1004 J kg−1 K −1]
Q.162 The mass (in kg) of dry air in a room, measuring 10 m × 7 m × 3 m, is ______.
(rounded off to two decimal places)
[Density of dry air is 1.029× 10−3 g cm−3]
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Atmospheric and Oceanic Sciences (XE-H)
Q.163 – Q.175 Carry TWO marks Each
Q.163 In a two-layered fluid system, temperature and salinity values are given for cases
P, Q and R. Which of the following options indicates that the process of ‘salt
fingering’ is likely to occur?
(A) Only P
(B) Only Q
(C) Q and R
(D) P and R
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Atmospheric and Oceanic Sciences (XE-H)
Q.164 A body radiates heat at a rate of 5 cal m−2 s −1, when its temperature is 227 ℃.
Which of the following is the correct value of the heat (in cal m−2 s −1) radiated
by the same body at a temperature of 727 ℃?
(A) 25
(B) 80
(C) 150
(D) 625
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Atmospheric and Oceanic Sciences (XE-H)
Q.165 From the given cases (P, Q, R and S), which represents the annual mean profile of
dissolved oxygen in the Bay of Bengal?
(A) P
(B) Q
(C) R
(D) S
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Atmospheric and Oceanic Sciences (XE-H)
The given figure illustrates a subtropical gyre in the Southern Indian Ocean.
Q.166
Identify the currents in the correct sequence of P, Q, R and S, respectively from the
following options.
South Equatorial Current, West Australian Current, Madagascar Current and South
(A)
Indian Ocean Current
South Equatorial Current, Madagascar Current, West Australian Current and South
(B)
Indian Ocean Current
South Equatorial Current, Madagascar Current, South Indian Ocean Current and
(C)
West Australian Current
South Equatorial Current, South Indian Ocean Current, Madagascar Current and
(D)
West Australian Current
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Atmospheric and Oceanic Sciences (XE-H)
Q.167 Which of the following is/are generally associated within a cyclonic eddy in the
northern Indian Ocean?
(A) Upwelling
(B) Positive sea level anomaly
(C) Negative sea level anomaly
(D) Downwelling
Which of the following combinations of forces is/are balanced in a cyclostrophic
Q.168
motion?
Pressure Gradient, Coriolis, and Centrifugal
(A)
Pressure Gradient and Centrifugal
(B)
Centrifugal and Coriolis
(C)
Pressure Gradient and Coriolis
(D)
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Atmospheric and Oceanic Sciences (XE-H)
Which of the following statements is/are correct for the Equatorial Indian Ocean
Q.169
during a positive Indian Ocean Dipole event?
(A) Strong surface westerly winds
(B) Weak surface westerly winds
(C) Positive Sea Surface Temperature anomaly in the western region
(D) Negative Sea Surface Temperature anomaly in the western region
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Atmospheric and Oceanic Sciences (XE-H)
Q.170 The temperature of a dry air parcel is 20 ℃ at a height of 150 m with atmospheric
pressure of 1000 hPa. If the air parcel rises adiabatically to a height of 2 km where
atmospheric pressure is 800 hPa, then the temperature (in ℃) of the air parcel at
that height will be __________. (rounded off to three decimal places)
[Gas constant and specific heat capacity for the dry air are 287 J kg−1 K −1 and
1004 J kg−1 K −1 , respectively.]
Q.171 For an incompressible fluid, the velocity components (u, v, and w) are given as:
u(x, y, z) = 2x + y + 2z
v(x, y, z) = ax + by + cz
w(x, y, z) = −6z
The value of b is ______________. (Answer in integer)
Q.172 A steady westerly wind is blowing over the ocean surface at a latitude of 30°N and
exerting a wind stress of 0.8 N m−2 .
The magnitude of net volume transport (in m2 s −1) per unit width is ______.
(rounded off to three decimal places)
[Density of seawater is 1025 kg m−3, angular velocity of the Earth is
7.29 × 10−5 s −1 .]
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Atmospheric and Oceanic Sciences (XE-H)
Q.173 In a free atmosphere without friction, if the pressure increases by
one kilo Pascal eastward across a distance of 200 km, the magnitude of geostrophic
flow (in m s −1) is _____. (rounded off to two decimal places)
[Density of air is 1.029 kg m−3and the Coriolis parameter is 10−4 s −1.]
Q.174 Using the dispersion relation for deep water small amplitude wave, the wavelength
(in m) for a 20 second gravity wave is ______. (Answer in integer)
[Take acceleration due to gravity as 9.81 m s −2 ]
Q.175 A two-layered fluid system in an estuarine environment has a total water depth of
10 m. The difference in densities between the two layers is 15 kg m−3 and thickness
of the less dense upper layer is 3 m.
If complete mixing occurs in 3 hours, then intensity (in W m−2) of mixing process
is _________. (rounded off to three decimal places)
[Acceleration due to gravity is 9.81 m s −2]
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Energy Science (XE-I)
Q.176 – Q.184 Carry ONE mark Each
Q.176 The luminous efficacy of an electric light bulb is measured in which one of the
following units?
(A) lumen W–1
(B) lumen W–1 h–1
(C) lumen m–2
(D) candela W–1
Q.177 Which one of the following biomass treatment processes occurs in an oxygen
limited condition approximately between 450 ℃ and 600 ℃, and produces biochar
and bio-oil as primary products?
(A) Gasification
(B) Pyrolysis
(C) Anaerobic Digestion
(D) Steam Reforming
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Energy Science (XE-I)
Q.178 For a fixed thermal output, which one of the following is the major advantage
offered by a concentrated collector over a flat plate collector?
(A) Utilization of diffuse solar radiation
(B) Reduction of capital cost of the system
(C) Operation at higher temperature
(D) Reduction in aperture area of the collector
Q.179 A part of the blowdown energy losses in a boiler can be recovered by which one of
the following ways?
(A) Completely avoiding the blowdown
(B) Recycling the blowdown to the steam drum
(C) Flashing the blowdown to generate low-pressure steam
(D) Mixing the blowdown with the boiler feedwater
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Energy Science (XE-I)
Q.180 Which of the following is/are greenhouse gas(es), as identified by the
Intergovernmental Panel on Climate Change (IPCC)?
(A) Nitrogen dioxide (NO2)
(B) Nitrous oxide (N2O)
(C) Sulphur hexafluoride (SF6)
(D) Carbon monoxide (CO)
Q.181 Which of the following is/are step(s) followed in energy audit?
(A) Walkthrough
(B) Collection of past energy consumption data
(C) Evaluation of energy conservation measures
(D) Preparation of historic profit and loss statement
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Energy Science (XE-I)
Q.182 An energy conservation project requires an initial investment of ₹ 50,000 with an
expected annual operation and maintenance cost of ₹ 5,000. This project is expected
to reduce the monthly energy cost by ₹ 1,250. The simple payback period (in years)
is_________________. (Answer in integer)
Q.183 The open circuit voltage, short circuit current, and the fill factor of a solar
photovoltaic module are 45 V, 9 A, and 0.8, respectively. The maximum output
power (in Watt) of the solar photovoltaic module is_______________________.
(Answer in integer)
Q.184 Energy is extracted from a fully charged supercapacitor bank and the voltage of this
system drops to 25 % of its initial value. The energy extracted with respect to initial
energy (in %, rounded off to two decimal places) is_______________.
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Energy Science (XE-I)
Q.185 – Q.197 Carry TWO marks Each
Q.185 A grid-connected induction generator is used to generate electricity from a wind
turbine. Which one of the following statements is true while the generator is feeding
power to the grid?
(A) The slip of the induction generator is zero
(B) The slip of the induction generator is one
(C) The slip of the induction generator is less than zero
(D) The slip of the induction generator is greater than one
Q.186 A hydro turbine works under a head of 20 m and has a maximum volume flow rate
of 4 m3 s–1 and a speed of 750 rpm. Determine the speed (in rpm) in order to operate
the same turbine at approximately the same efficiency under a head of 5 m.
(A) 375.0
(B) 187.5
(C) 750.0
(D) 524.5
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Energy Science (XE-I)
Q.187 Which one of the following defines the angle made by the line joining the centers
of the sun and the earth with its projection on the equatorial plane?
(A) Declination
(B) Latitude
(C) Azimuth angle
(D) Zenith angle
Q.188 Which one of the following is the major environmental problem associated with the
production of coal-bed methane?
(A) Contamination of water
(B) Emission of Carbon dioxide
(C) Generation of Nitrogen oxides
(D) Generation of Sulphur oxides
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Energy Science (XE-I)
Q.189 A radioactive isotope sample has a decay constant λ = 2.31 × 10−4 year–1. Initially
the sample contains 8000 × 1015 atoms. The sample decays to 25% of its initial
value. The number of years it takes to decay to this stage is closest to
______________
(A) 3000
(B) 6000
(C) 900
(D) 2600
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Energy Science (XE-I)
Q.190 A fuel with composition by mass is given as 78 % carbon (C), 16 % hydrogen (H2),
3.2 % sulphur (S), 1.6 % oxygen (O2), and ash. The fuel is fired in a boiler with
excess air for the complete combustion and no carbon monoxide (CO) is detected
in the flue gases. The dry flue gas contains 0.2 % sulphur dioxide (SO2) by volume.
Which one of the following options is closest to the amount of excess air provided
(in % by mass)?
Assume molar masses (g mol–1) of C, H2, S, and O2 are 12, 2, 32, and 32,
respectively, and the volumetric ratio of nitrogen (N2) and oxygen (O2) in the air as
3.76:1.
(A) 14.8
(B) 7.4
(C) 22.2
(D) 3.1
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Energy Science (XE-I)
Q.191 Which of the following statements is/are FALSE concerning a wind turbine
generation system?
(A) The rotor power coefficient, Cp , of a multi-blade turbine is a monotonically
increasing function of tip-speed ratio
(B) Maximum power point tracking algorithms are typically employed in wind turbine
generators for enhancing energy yield
(C) The theoretical maximum value of rotor power coefficient, Cp , is 0.65
(D) Speed control of wind turbine generator is carried out to ensure rotor speed varies
in response to wind speed
Q.192 Which of the following options is/are true regarding the behaviour of a typical solar
photovoltaic cell?
(A) Ideal current source
(B) Current limited voltage source
(C) Voltage limited current source
(D) Ideal power source
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Energy Science (XE-I)
Q.193 A 75 kWh electric vehicle battery pack made of lithium-ion batteries has 4,800
individual cells in a series-parallel combination, with 120 cells in series. The
nominal voltage of the individual cell is 3.7 V. The capacity in Ah (rounded off to
two decimal places) of the individual cell is__________________________.
Q.194 A nonlinear load connected to a sinusoidal voltage source (of peak value Vm and
50 Hz frequency) draws a quasi-square wave shaped current (of maximum value
Im ) as shown in the figure below. The power factor of the nonlinear load (rounded
off to two decimal places) is__________________________________.
Q.195 A resident has ₹ 50,000 to purchase a 5-star rated air conditioner with a life of
10 years. The annual energy cost savings (in ₹) needed to recover this investment
in 6 years assuming a discount rate of 10 % per annum is_____________________.
(Answer in integer)
Q.196 A country’s annual crude oil production in the year 2024 was 150 million tons and
that in 2022 was 141 million tons. The proven crude oil resources in 2024 of the
country are 12,000 million tons. Consider an exponential growth rate model with a
growth rate as compound annual growth rate during 2022-2024. The crude oil
reserve will last for _____________ years. (rounded off to nearest integer)
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Energy Science (XE-I)
Q.197 The useful heat gain in Watt (rounded off to one decimal place) of a solar flat plate
collector using Hottel-Whillier-Bliss equation is_________________________.
Assume:
Collector heat removal factor = 0.85
Absorber plate area = 1.5 m2
Absorbed solar flux by the absorber plate = 600 Wm–2
Overall loss coefficient = 4 Wm–2K–1
Water inlet temperature = 60 ℃
Ambient temperature = 25 ℃
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Answer Key for Engineering Sciences (XE)
Q. No. Session Question Type Section Key/Range Marks
1 1 MCQ GA D 1
2 1 MCQ GA C 1
3 1 MCQ GA B 1
4 1 MCQ GA D 1
5 1 MCQ GA C 1
6 1 MCQ GA A 2
7 1 MCQ GA B 2
8 1 MCQ GA B 2
9 1 MCQ GA C 2
10 1 MCQ GA A 2
11 1 MCQ XE-A C 1
12 1 MCQ XE-A D 1
13 1 MCQ XE-A A 1
14 1 MSQ XE-A C;D 1
15 1 MSQ XE-A A;B 1
16 1 NAT XE-A 256 to 256 1
17 1 NAT XE-A 0.90 to 1.10 1
18 1 MCQ XE-A C 2
19 1 MSQ XE-A A;C 2
20 1 NAT XE-A 3 to 3 2
21 1 NAT XE-A 1.45 to 1.55 2
22 1 MCQ XE-B B 1
23 1 MCQ XE-B D 1
24 1 MCQ XE-B D 1
25 1 MCQ XE-B C 1
26 1 MCQ XE-B B 1
27 1 MCQ XE-B C 1
28 1 MCQ XE-B C 1
29 1 MSQ XE-B A;D 1
30 1 NAT XE-B 0.9 to 1.1 1
31 1 MCQ XE-B D 2
32 1 MCQ XE-B A 2
33 1 MCQ XE-B A 2
34 1 MCQ XE-B A 2
35 1 MCQ XE-B C 2
36 1 MSQ XE-B A;C 2
37 1 MSQ XE-B A;C;D 2
38 1 NAT XE-B 1.410 to 1.430 2
39 1 NAT XE-B 2.30 to 2.60 2
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Q. No. Session Question Type Section Key/Range Marks
40 1 NAT XE-B 0.08 to 0.10 2
41 1 NAT XE-B 0.030 to 0.040 2
42 1 NAT XE-B 2 to 2 2
43 1 NAT XE-B 0.17 to 0.19 2
44 1 MCQ XE-C A 1
45 1 MCQ XE-C C 1
46 1 MCQ XE-C A 1
47 1 MSQ XE-C A;C 1
48 1 MSQ XE-C B;C 1
49 1 MSQ XE-C A;D 1
50 1 NAT XE-C 2 to 2 1
51 1 NAT XE-C 1.4 to 1.6 1
52 1 NAT XE-C 64.5 to 70.0 1
53 1 MCQ XE-C A 2
54 1 MCQ XE-C A 2
55 1 MCQ XE-C A 2
56 1 MCQ XE-C A 2
57 1 MCQ XE-C A 2
58 1 MSQ XE-C A;C 2
59 1 MSQ XE-C A;C 2
60 1 MSQ XE-C B;C 2
61 1 NAT XE-C 16.0 to 19.0 2
62 1 NAT XE-C 118.0 to 126.0 2
63 1 NAT XE-C 90.0 to 95.0 2
64 1 NAT XE-C 96.5 to 99.0 2
65 1 NAT XE-C 1.05 to 1.15 2
66 1 MCQ XE-D C 1
67 1 MCQ XE-D A 1
68 1 MCQ XE-D A 1
69 1 MCQ XE-D B 1
70 1 MSQ XE-D B;D 1
71 1 MSQ XE-D A;C 1
72 1 NAT XE-D 5 to 5 1
73 1 NAT XE-D 85.90 to 86.10 1
74 1 NAT XE-D 16 to 16 1
75 1 MCQ XE-D D 2
76 1 MCQ XE-D B 2
77 1 MCQ XE-D B 2
78 1 MCQ XE-D A 2
79 1 MCQ XE-D D 2
80 1 MCQ XE-D B 2
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Q. No. Session Question Type Section Key/Range Marks
81 1 MCQ XE-D B 2
82 1 NAT XE-D 66.90 to 67.50 2
83 1 NAT XE-D 15 to 15 2
84 1 NAT XE-D 13 to 13 2
85 1 NAT XE-D 3.00 to 3.50 2
86 1 NAT XE-D -0.029 to -0.021 2
87 1 NAT XE-D 0.004 to 0.006 2
88 1 MCQ XE-E C 1
89 1 MCQ XE-E B 1
90 1 MCQ XE-E C 1
91 1 MCQ XE-E D 1
92 1 MCQ XE-E D 1
93 1 MSQ XE-E B;C 1
94 1 MSQ XE-E A;B 1
95 1 NAT XE-E 3.70 to 4.20 1
96 1 NAT XE-E 57.00 to 63.00 1
97 1 MCQ XE-E C 2
98 1 MCQ XE-E D 2
99 1 MCQ XE-E C 2
100 1 MSQ XE-E C;D 2
101 1 NAT XE-E 5.50 to 6.50 2
102 1 NAT XE-E 408.00 to 453.00 2
103 1 NAT XE-E 5000.00 to 5030.00 2
104 1 NAT XE-E 226.50 to 229.00 2
105 1 NAT XE-E 6.30 to 6.60 2
106 1 NAT XE-E 3.30 to 3.70 2
107 1 NAT XE-E 740.00 to 800.00 2
108 1 NAT XE-E 440.00 to 480.00 2
109 1 NAT XE-E 6.50 to 6.80 2
110 1 MCQ XE-F C 1
111 1 MCQ XE-F B 1
112 1 MCQ XE-F A 1
113 1 MCQ XE-F D 1
114 1 MCQ XE-F C 1
115 1 MCQ XE-F D 1
116 1 MSQ XE-F B;D 1
117 1 MSQ XE-F A;C;D 1
118 1 NAT XE-F 44.20 to 44.30 1
119 1 MCQ XE-F B 2
120 1 MCQ XE-F A 2
121 1 MCQ XE-F A 2
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Q. No. Session Question Type Section Key/Range Marks
122 1 MCQ XE-F B 2
123 1 MCQ XE-F B 2
124 1 MCQ XE-F D 2
125 1 MCQ XE-F C 2
126 1 MSQ XE-F A;C 2
127 1 NAT XE-F 0.15 to 0.30 2
128 1 NAT XE-F 1.70 to 1.90 2
129 1 NAT XE-F 54850 to 54950 2
130 1 NAT XE-F 0.90 to 0.95 2
131 1 NAT XE-F 110 to 120 2
132 1 MCQ XE-G D 1
133 1 MCQ XE-G C 1
134 1 MCQ XE-G B 1
135 1 MCQ XE-G C 1
136 1 MCQ XE-G B 1
137 1 MCQ XE-G B 1
138 1 MSQ XE-G B;D 1
139 1 NAT XE-G 42000 to 43000 1
140 1 NAT XE-G 0.55 to 0.65 1
141 1 MCQ XE-G C 2
142 1 MCQ XE-G A 2
143 1 MCQ XE-G A 2
144 1 MCQ XE-G C 2
145 1 MCQ XE-G D 2
146 1 MCQ XE-G A 2
147 1 MSQ XE-G B;D 2
148 1 MSQ XE-G A;D 2
149 1 MSQ XE-G A;C;D 2
150 1 MSQ XE-G B;D 2
151 1 NAT XE-G 62.0 to 65.0 2
152 1 NAT XE-G 16.00 to 19.00 2
153 1 NAT XE-G 71000 to 73000 2
154 1 MCQ XE-H C 1
155 1 MCQ XE-H B 1
156 1 MCQ XE-H C 1
157 1 MCQ XE-H B 1
158 1 MSQ XE-H A;D 1
159 1 NAT XE-H 1.000 to 1.020 1
160 1 NAT XE-H 0.060 to 0.070 1
161 1 NAT XE-H 50.0 to 51.0 1
162 1 NAT XE-H 216.00 to 216.20 2
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Q. No. Session Question Type Section Key/Range Marks
163 1 MCQ XE-H B 2
164 1 MCQ XE-H B 2
165 1 MCQ XE-H B 2
166 1 MCQ XE-H C 2
167 1 MSQ XE-H A;C 2
168 1 MSQ XE-H B 2
169 1 MSQ XE-H B;C 2
170 1 NAT XE-H 1.800 to 2.000 2
171 1 NAT XE-H 4 to 4 2
172 1 NAT XE-H 10.000 to 11.000 2
173 1 NAT XE-H 48.00 to 49.00 2
174 1 NAT XE-H 600 to 640 2
175 1 NAT XE-H 0.203 to 0.205 2
176 1 MCQ XE-I A 1
177 1 MCQ XE-I B 1
178 1 MCQ XE-I C 1
179 1 MCQ XE-I C 1
180 1 MSQ XE-I B;C 1
181 1 MSQ XE-I A;B;C 1
182 1 NAT XE-I 5 to 5 1
183 1 NAT XE-I 324 to 324 1
184 1 NAT XE-I 93.75 to 93.75 1
185 1 MCQ XE-I C 2
186 1 MCQ XE-I A 2
187 1 MCQ XE-I A 2
188 1 MCQ XE-I A 2
189 1 MCQ XE-I B 2
190 1 MCQ XE-I B 2
191 1 MSQ XE-I A;C 2
192 1 MSQ XE-I B;C 2
193 1 NAT XE-I 4.20 to 4.24 2
194 1 NAT XE-I 0.55 to 0.59 2
195 1 NAT XE-I 11000 to 11650 2
196 1 NAT XE-I 39 to 42 2
197 1 NAT XE-I 585.5 to 587.0 2
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Source: GATE. Question paper published by GATE.