Suresh said, โI did it yesterday.โ 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.
Correct Answer
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Q2mcq
To continue the sequence of tiles shown, the tile indicated by the question mark should be
a.
b.
c.
Correct Answer
d.
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Q3mcq
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
Correct Answer
c.
4
d.
5
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Q4mcq
The 2 nd of June is a Thursday in a certain year. Which day of the week is the 3 rd of July in that year?
a.
Thursday
b.
Friday
c.
Saturday
d.
Sunday
Correct Answer
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Q5mcq
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 โstepโ 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
Correct Answer
d.
12
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Q6mcq
Exacerbate: Mitigate:: ___________ Choose the option with the correct pair of words to fill the blank.
a.
Aggravate: Alleviate
Correct Answer
b.
Alleviate: Precipitate
c.
Aggravate: Precipitate
d.
Emancipate: Exonerate
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Q7mcq
A paper shown in Panel I is folded along the dashed lines (- - -) to construct a cube. The shaded regions shown in Panel I appear on the outer surface of the cube. Referring to cubes shown in Panel II, which one of the options is correct?
a.
Only (i) can correspond to the unfolded cube in Panel I.
b.
Only (ii) can correspond to the unfolded cube in Panel I.
Correct Answer
c.
Both (i) and (ii) can correspond to the unfolded cube in Panel I.
d.
Neither (i) nor (ii) can correspond to the unfolded cube in Panel I.
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Q8mcq
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
Correct Answer
c.
20
d.
10
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Q9mcq
Four people P, Q, R, and S, of different ages, make the following observations. P โ I am younger than S. Q โ I am neither the youngest nor the oldest. R โ P is older than me. Based on these observations, the youngest person is ______.
a.
P
b.
Q
c.
R
Correct Answer
d.
S
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Q10mcq
Circles $C$ 1, $C$ 2, and $C$ 3, with centers $O$ 1, $O$ 2, and $O$ 3, and radii $r$ 1, $r$ 2, and $r$ 3, respectively, touch each other as shown in the following figure. Given $r$ 1 = 2 cm, $r$ 2 = 1 cm and the angle $โ O$ 1 $O$ 3 $O$ 2 is 90ยฐ, $r$ 3 = _____ cm.
a.
1 (-3 + $\sqrt{17}$) 2
Correct Answer
b.
1 (3 + $\sqrt{17}$) 2
c.
1 (-2 + $\sqrt{17}$) 2
d.
1 (-3 + $2\sqrt{17}$) 2
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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
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Let $C$ be the circle $(x$ - 1) 2 + $y$ 2 = 25 oriented counterclockwise. Then, the value of the line integral
2 $\oint [(x$ 5 - $3y)dx$ + $(-2x$ + $e y)dy$ ]
$C$ is
a.
$10ฯ$
b.
$15ฯ$
c.
$20ฯ$
d.
$25ฯ$
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Let $W(x)$ denote the Wronskian of two linearly independent solutions $y$ 1 $(x)$ and $y$ 2 $(x)$ of the differential equation
$(x$ - 1) + 2 + $xe x y$ = 0, $x$ > 1.
$d$ 2 $y dy$
2 $dx dx$ If $W(2)$ = 2, then the value of $W(5)$ is
a.
1 8
b.
1 5
c.
5
d.
8
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$Y$ = 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 $\pm1.$
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Let L be the lamina of the form $x$ 2 + $4y$ 2 $\le$ 64, 0 $\le y \le$ 4, with density $ฯ(x, y)$ = $|x|y.$ Then, the mass of L (in integer) is __________
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Let $X$ be a random variable having probability density function (pdf)
1
$e$
$e -x$, 0 < $x$ < 1,
$2(e$ - 1)
$f X (x)$ = 1
{ 0, elsewhere.
, 1 < $x$ < 2,
2 Then, the value of the expectation of $X, E[X]$ (rounded off up to two decimal places) is __________
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Match each entry of List-1 with a suitable entry in List-2 and choose the correct option.
List-1 List-2 P I The sum of the series โ $\infty n=1$ is equal to
3 1
2 $(n+2)(n+1)$
II 1 3 $x$ Q lim ($\int sin(t) dt)$ is equal to
the $a$ 0 + โ $\infty n=1 (a n$ cos $nx$ + $b n$ sin $nx)$ be R Let
III 1
2 2
series function Fourier expansion of the
2 0 $x x\to0$
1 1 $f(x)$ = sin $x$ - cos $x$ + 1 sin $2x$, $x$ โ [0, $2ฯ].$
Then, 2 2 โ $\infty (a$ + $b$) is equal to $n n=0 n$
2 2 $\sqrt{2}$
a.
P โถ I, Q โถ III, R โถ II
b.
P โถ III, Q โถ II, R โถ I
c.
P โถ III, Q โถ I, R โถ II
d.
P โถ II, Q โถ I, R โถ III
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0 1 $u u$ 0 ] [ 0 1 $u$ ] be the LU decomposition of the matrix -10 0 0 1
12 13
23 The initial value problem
$du$
= $u$ 2 + $t$ 2, $t \ge$ 0,
$dt$
with $u(0)$ = 1, is solved by using the explicit Euler method with step size โ = 0.2. Then, the value of $u(0.4)$ (rounded off upto two decimal places) is __________
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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
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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 $\ge$ 10 4 ?
a.
Body P
b.
Body Q
c.
Body R
d.
Body S
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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 $ฮด.$ Which one of the following assumptions is correct for deriving the Prandtl boundary layer equations?
a.
$ฮด\approxL$
b.
$ฮด>L$
c.
$ฮดโซL$
d.
$ฮดโชL$
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Three different siphons steadily discharge water at velocities V I, V II, and V III, 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.
$V$ I > $V$ III > $V$ II
b.
$V$ I > $V$ II > $V$ III
c.
$V$ I = $V$ II = $V$ III
d.
$V$ II > $V$ III > $V$ I
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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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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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A piezometer and a Pitot tube are tapped into a horizontal water pipe, as shown in the figure, where โ 1 = 4 cm, โ 2 = 6 cm and โ 3 = 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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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 2โ, as shown in the figure. The fully-developed velocity profile of the flow is
$dp$
โ 2
$y$ 2
-
-)
$dx$
$2ฮผ$
โ 2
where $ฮผ$ is the dynamic viscosity. The values of $y,$ for which the local flow velocity is equal to the average flow velocity, are
a.
b.
c.
d.
$\pm$ โ $\sqrt{3}$
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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 $(ฯ T$ - $ฯ B$) 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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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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A two-dimensional source flow (with stream function, $ฯ$ 1 = $m$ tan -1) is placed
$x$ at the origin in a uniform flow (with stream function, $ฯ$ 2 = $Uy).$ 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.
$u=U+ mx$
2 $x$
$mx$
b.
$u=$
c.
$u=U+$
2
d.
$u= mx$; $v=U- my$
$x$ 2 $+y$ 2 $x$ 2 $+y$ 2
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Consider a steady, laminar, and incompressible flow over a flat plate, as shown in the figure. With freestream velocity $U \infty$ and kinematic viscosity $ฮฝ$ 1, the boundary layer thickness at a distance $x$ 1 from the leading edge is $ฮด$ 1. If the kinematic viscosity of the fluid is increased by a factor of four $(ฮฝ$ 2 = $4ฮฝ$ 1), the boundary layer thickness $(ฮด$ 2) at $x$ 1 with same $U \infty$ will be equal to
U y
$$ (x)
x
a.
$ฮด$ 1 2
b.
$ฮด$ 1
c.
$2ฮด$ 1
d.
$4ฮด$ 1
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A vertical jet of diameter $d$ 1 strikes a horizontal plate with a velocity U, as shown in the figure. The plate has a hole of diameter $d$ 2 (< $d$ 1) 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 $d$ 2 decreases keeping other parameters unchanged.
c.
F increases as $U$ increases keeping other parameters unchanged.
d.
F remains constant as $d$ 1 increases keeping other parameters unchanged.
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The velocity of a fluid particle in a flow is given as: โ = $(a$ - $x)iฬ$ + $(b$ + $y)jฬ$ + $(c$ + $z)kฬ V$ where a, b, c are constants, and $iฬ$, $jฬ$, $kฬ$ 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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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 cm 2. A metallic block of 13 kg is placed on the piston. The atmospheric pressure $(p a$) is 1 bar. Assume acceleration due to gravity as 10 m.s -2. The pressure inside the cylinder, $p i$ (in bar) is __________. (rounded off to three decimal places)
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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)
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A rectangular block (density = 600 kg.m -3) with base area of 0.06 m 2 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, โ (in m) of the block in the water is _________. (rounded off to two decimal places)
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For a steady, laminar, and incompressible flow over a flat plate, the local skin friction coefficient is given as $C f$ =, where $Re x$ is the local Reynolds number.
0.664
$\sqrt{Re} x$ The density and kinematic viscosity of the fluid are 1.2 kg.m -3 and $1.5\times10$ -5 m 2.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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The axial velocity profile of a laminar, incompressible, and fully-developed flow in a circular pipe of radius $R$ is given as $v z$ = $(r$ 2 - $R$ 2), where ยต, p, z, and $r$
1 $dp$
$4ฮผ dz$ are dynamic viscosity, pressure, axial coordinate, and radial coordinate, respectively. If the magnitude of shear stress at the pipe wall is given as $|ฯ$ | = $w$
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$R dp$ $K dz$ , then the value of $K$ is __________. (answer in integer) 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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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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The interplanar spacing of (โ $k l)$ planes is 4.5 nm in a given crystal. For the (3โ $3k 3l)$ planes, the interplanar spacing, in nm, is _________ (rounded off to one decimal place).
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The equilibrium vacancy concentration in aluminum at 900 K is 1.1 $\times$ 10 $-$ 4. The enthalpy of formation of vacancies, in kJ.mol $-$ 1, is _________ (rounded off to one decimal place). Given: Universal gas constant = 8.314 J.K $-$ 1.mol $-$ 1
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Three phases, ฮฑ, ฮฒ and L are shown in the binary phase diagram below. Identify the correct G โ X (Gibbs free energy vs Composition) plot corresponding to temperature T 0.
a.
b.
c.
d.
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$a$ In a cubic crystal, the Burgers vector for a mixed dislocation line is [110]. The 2 dislocation line lies along the [011] direction. The slip plane of the dislocation is
a.
(11ฬ 1)
b.
(111)
c.
(01ฬ 1)
d.
(11ฬ 0)
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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.
b.
c.
d.
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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 Youngโs modulus 3 Differential scanning calorimetry S Heat of fusion 4 Acoustic measurement
a.
b.
c.
d.
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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.
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Fe has a density of 7.87 g.cm $-$ 3, atomic mass of 55.84 g.mol $-$ 1 and net magnetic moment per atom of 2.22 Bohr magnetons (ยต B). The saturation magnetization of Fe, in A.m $-$ 1, is _________ $\times10$ 5 (rounded off to one decimal place). Given: ยต B = $9.27\times10 -$ 24 A.m 2, Avogadro number = $6.023\times10$ 23 mol $-$ 1
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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 $(ฯ)$ vs. true strain $(ฮต)$ relationship follows the equation: $ฯ$ = $Kฮต 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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A 1 cm 3 Si cube is doped with As with a concentration of 1 atom per 10 9 Si atoms. The resistance of the doped Si cube, in Ohms, is _________ (rounded off to one decimal place). Given: Atomic concentration of Si = $5\times10$ 22 cm $-$ 3 Intrinsic concentration of electrons in Si = $1\times10$ 10 cm $-$ 3 Electron mobility in Si = 1350 cm 2.V $-$ 1.s $-$ 1 Hole mobility in Si = 450 cm 2.V $-$ 1.s $-$ 1 Electronic charge = $1.6\times10 -$ 19 C
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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 diskโs relative density, in %, is _________ (rounded off to one decimal place).
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The standard electrode potential of Cu 2+ | Cu is +0.34 V and Zn 2+ | Zn is -0.76 V. For the Zn | Zn 2+ || Cu 2+ | Cu cell, the EMF, in Volts, is _________ (rounded off to two decimal places).
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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 $\sqrt{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.
30ยฐ
b.
45ยฐ
c.
60ยฐ
d.
75ยฐ
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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. N 1, N 2, and N 3 in the options are reaction forces and F f is the frictional force.
a.
b.
c.
d.
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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.
b.
c.
d.
$3k$ $โ$ $m$
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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/s 2. 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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A cart of weight $(W)$ 5 kN, stands on an inclined smooth surface at an angle $(ฮธ)$ of 45ยฐ 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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A 2D state of stress at a point in a body is given by $ฯ xx$ = -40 MPa, $ฯ yy$ = 100 MPa and $ฯ xy$ = 50 MPa. The radius of the Mohrโs circle for the given state of stress is ______MPa (rounded off to two decimal places).
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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 (โ) is 0.01 m, which one of the following is the corresponding angle $(ฮธ)$ in radians?
a.
$ฯ$ 3
b.
$ฯ$ 4
c.
$ฯ$ 5
d.
$ฯ$ 6
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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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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 $F$ rect and $F$ sq, respectively. Then
a.
$p$ $q$
b.
$q$ $p$
c.
$r$ $q$
d.
$r$ 2 $pq$
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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 (Youngโs modulus = 210 GPa) and another is made of aluminum (Youngโs 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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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.
b.
c.
d.
$2k$ $โ$ $3m$
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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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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.
$ฯ$ At the instant when the angle $ฮธ$ = rad and the velocity of point Q in the positive
3 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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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 30ยฐ 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/s 2. 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
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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 m 2. The absolute value of the maximum shear stress on the cross-section at x = 0.75 m is ______ N/m 2 (in integer).
Figure is not to scale
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A thin walled cylindrical container of diameter 2 m and wall thickness of 2.5 cm is made of steel whose Youngโs 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).
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A solid axial bar made of steel with Youngโs modulus, 200 GPa and Poissonโs 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 $______\times$ 10 -4 (rounded off to two decimal places).
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EFGH (solid lines) is the initial configuration and EโฒFโฒGโฒHโฒ (dashed lines) is the deformed configuration of an object as shown in the figure. Eโฒ coincides with E and Fโฒ coincides with F. The average normal strain along the line segment OP is ______ (rounded off to three decimal places).
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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:
$M$ 2 $l U$ =
48 $EI$ The section modulus of the beam is $EI$ = 25 $\times$ 10 5 Nm 2. 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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Consider any substance whose mass specific heat capacity at constant pressure and mass specific heat capacity at constant volume are c and c, respectively. If the
P V gas constant is R, which ONE of the following relations is CORRECT for the substance at all conditions?
a.
c c P V
b.
c c R P V
c.
c c P V
d.
c c P V
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Consider a mixture of ideal gases, nitrogen (N 2) and carbon-dioxide (CO 2), at 25 โ and 101 kPa. The molar mass of N 2 is 28 kg/kmol and molar mass of CO 2 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% N 2 and 37.5% CO 2 by mass
b.
62.5% N 2 and 37.5% CO 2 by volume
c.
37.5% N 2 and 62.5% CO 2 by mass
d.
37.5% N 2 and 62.5% CO 2 by volume
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In a mixing chamber hot water enters at a temperature of 80 โ with a flowrate of 0.5 kg/s. From another entry, cold water enters the chamber at 20 โ. The desired temperature after mixing at the exit of the chamber is 40 โ. 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
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A mixture of carbon-dioxide (CO 2), nitrogen (N 2) and oxygen (O 2) are introduced in a rigid and impermeable tank containing only liquid water (H 2 O). 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
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A stream of moist air at 101 kPa and 25 โ 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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A house looses heat at a rate of 150 MJ per hour. The temperature outside the house is $-$ 3 โ. The minimum power (in kW) required to maintain the temperature inside the house at 25 โ using a heat pump is ________________ (rounded off to two decimal places).
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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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Consider a real gas, which obeys the following equation-of-state:
RT
C
$=$
$+$ C
$-$ 2
P
1
Pv
where v is the mass specific volume, P is the pressure, T is the temperature and R is the gas constant. C and C are constants. If s is the mass specific entropy,
1 2
$ $ s $$ the quantity $ $ for the gas is given by $$
$$ v $$
T
a.
v
b.
Pv 2
c.
v $-$ C 1
d.
1 2 Tv
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M kg of a liquid at a temperature T is mixed with M kg of the same liquid at
1 another temperature T in an isolated tank at constant pressure. The mass specific
2 heat capacity at constant pressure of the liquid is c, which is a constant. The total
P entropy change in the process is
a.
b.
c.
d.
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A fluid undergoes a process where its pressure (P), temperature (T) and volume (V) changes from (P, T, V) to (P, T, V). During the process, volume
1 1 1 2 2 2 expansivity ($$) and isothermal compressibility ($$) remains constant. Given that
T $ =$ V 2 1 V 1 V $ $ and $ = - $, the ratio $ $ is
$ $
T V $ $ T $$ V $ $ P $ $ V $$
P T 1
a.
b.
c.
d.
(T $-$ T) $-$ (P $-$ P) 2 1 T 2 1
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Consider an ideal Rankine cycle with fixed conditions at the turbine inlet. If the condenser pressure is lowered, which of the following statements is/are CORRECT?
a.
Pump work input remains the same.
b.
Moisture content at turbine exit decreases.
c.
Heat rejected in the condenser decreases.
d.
Turbine work output increases.
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An adiabatic rigid and impermeable tank of volume 10 m 3 contains air at 800 kPa and 70 โ. The air is allowed to leave the tank until the pressure is one-fourth of its original value. During the process, the air in the tank is maintained at 70 โ using an electrical heater. Assume that the air behaves as an ideal gas having gas constant and ratio of specific heat capacities as 287 J/kg-K and 1.4, respectively. The total electrical energy (in MJ) supplied by the heater is _____________ (rounded off to two decimal places).
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Two kg of a gas is compressed in a process. Pressure (P) and mass specific volume (v) of the gas during the process follows: Pv 1.2 $=$ constant. The temperature of the gas before and after compression is 300 K and 600 K, respectively. Assume that the gas behaves as an ideal gas with gas constant and ratio of specific heat capacities equal to 287 J/kg-K and 1.4, respectively. The heat rejected (in kJ) during the process is ________________(rounded off to two decimal places).
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Consider a single component fluid at saturation conditions having the following properties. Latent heat of vaporization, h $=$ 39.6 $$ 10 3 kJ/kmol
fg Compressibility factor for the vapor phase, z $=$ g $=$ sat g $=$ 0.95
g v R T
v P v
ideal u P is the saturation pressure sat T is the temperature v is the molar specific volume of the vapor phase g Assume that v $=$ v, where v is the difference in the molar specific volume of
fg g fg the vapor and the liquid phases Universal gas constant, R $=$ 8.314 kJ/kmol-K
u Using the Clapeyron equation, the quantity $-$ (in K) is ________ $()$
d ln P
d 1 T
saturation (rounded off to two decimal places).
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$ $ h $ $ h $$ It is given that: $ =$ c and $ =$ (v $- $ Tv). Here h is the mass specific $ $ p $$ P $ $ T $$
T P
1 $ $ v $ =$ enthalpy, v is the mass specific volume, $ $ is the volume expansivity, $$
v $$ T $$
P and c is the mass specific heat capacity at constant pressure. T and P represent p the temperature and the pressure, respectively. The inversion temperature is the
$ $ T $$ temperature at which the Joule-Thomson coefficient, $ = $, goes to zero. $$
JT $$ P $$
h Consider a fluid with properties: v $=$ 1.03 m 3 /kg, c $=$ 1 kJ/kg-K, and
P $ =$ 4.39 $$ 10 $-$ 3 1/K; The inversion temperature (in K) for the fluid is ________ (rounded off to two decimal places).
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A stream of moist air enters an adiabatic saturator at 45 โ and 101 kPa and leaves as a saturated mixture at 30 โ. Make-up water to the saturator is supplied at 30 โ. 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 โ: 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 โ: 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
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A rigid spherical solid ball at 1000 โ is cooled slowly to 200 โ in a surrounding air at 25 โ. The density, specific heat capacity, and diameter of the ball are 8000 kg/m 3, 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).
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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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A mixture of helium (He) and nitrogen (N 2) expands in a turbine from 800 kPa to 100 kPa. The mixture composition is 40% He and 60% N 2 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 N 2 behaves as ideal gases. Specific heat capacities are constant. Use the following data: Ratio of specific heat capacities for He and N 2 are 1.67 and 1.4, respectively. Specific heat capacities at constant pressure for He and N 2 are 5.19 kJ/kg-K and 1.04 kJ/kg-K, respectively.
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A rigid and impermeable tank has only moist air with a specific humidity of 0.025 kg water-vapor /kg dry-air at 30 โ and 101 kPa. The air is heated to 90 โ. 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 โ is 4.25 kPa and at 90 โ is 70.18 kPa.
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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.
Stress
P
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 โ Matrix; Q โ Glass fibre; R โ Composite
b.
P โ Glass fibre; Q โ Composite; R โ Matrix
c.
P โ Glass fibre; Q โ Matrix; R โ Composite
d.
P โ Composite; Q โ Glass fibre; R โ Matrix
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For a polydisperse polymer, the viscosity-average molecular weight (Mฬ v) becomes equal to the weight-average molecular weight (Mฬ w), when the MarkโHouwink constant a is ___________________.
a.
0.1
b.
0.5
c.
0.7
d.
1.0
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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.
PโIII; QโII; RโI; SโIV
b.
PโIV; QโIII; RโII; SโI
c.
PโII; QโI; RโIII; SโIV
d.
PโIII; QโI; RโII; SโIV
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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 $\times$ 10 โ12 F/m. The permittivity of the polymer is _____________ $\times$ 10 โ12 F/m (rounded off to two decimal places).
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Select the correct option to match the Polymer to its most suitable Monomer(s) from the table given below:
Polymer Monomer(s) P Poly(p-phenylene I CH 3
sulfide)
Cl C Cl + HO C
O
Q
Poly(ether
II
S
R
Poly(ether
III
O
ketone)
C
S
Polycarbonate
IV
S O PโII; QโIV; RโIII; SโI
b.
PโII; QโIV; RโI; SโIII
c.
PโIV; QโIII; RโII; SโI
d.
PโIV; QโI; RโIII; SโII
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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.
PโIV; QโIII; RโII; SโI
b.
PโIII; QโIV; RโII; SโI
c.
PโI; QโIII; RโII; SโIV
d.
PโIII; QโIV; RโI; SโII
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The variation of steady shear viscosity ($ฮท$) of a polymer melt with shear rate ($ฮณฬ$) is shown in the figure, where $ฮณฬ s$ 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 ($ฯ$) with shear rate for the same polymer melt?
a.
P
b.
Q
c.
R
d.
S
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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.
PโIV; QโIII; RโI; SโII
b.
PโIII; QโIV; RโI; SโII
c.
PโIV; QโIII; RโII; SโI
d.
PโIII; QโIV; RโII; SโI
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A certain amount of plasticizer with a glass transition temperature (T g) of โ50 ยฐC was added to a polymer to reduce its T g from 70 ยฐC to 30 ยฐC. Using the Fox equation, the weight fraction of the plasticizer used is ________________ (rounded off to two decimal places).
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A rectangular plastic specimen with a cross-sectional area of 240 mm 2 is subjected to tension with a force of 15000 N resulting in elastic deformation. If the Youngโs modulus of the specimen is 34.55 MPa, the value of strain is ________________ (rounded off to two decimal places).
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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 (Mฬ w) of the synthesized polyester is ________________ g/mol (rounded off to the nearest integer).
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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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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 8ยฐ. 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 ________________ cm 3 /min (rounded off to the nearest integer).
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Match the bacteria in Column I with their respective characteristic features in Column II.
Column I (P) E. coli (Q) B. subtilis (R) S. aureus (S) L. monocytogenes
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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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/m 3. The Reynolds number for this flow is _______ (Round off to nearest integer)
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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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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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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)
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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/m 2. (Round off to two decimal places)
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A tubular centrifuge separates 5 micron particles of density 1500 kg/m 3 from a slurry. The slurry is fed at a volumetric flow rate of 0.5 m 3 /s. The equivalent clarification area of the centrifuge is _______m 2. (Answer in integer) Assume g = 10 m/s 2 and for water, density = 1000 kg/m 3, coefficient of viscosity (ยต) = 10 -3 Pa-s
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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 ]
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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)
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The required magnitude of heat transfer to reduce the temperature of 10 kg of dry air by 5 โ is ____________ kilo Joules. (rounded off to one decimal place) [Specific heat capacity of dry air is 1004 $J kg$ -1 $K$ -1 ]
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The mass (in kg) of dry air in a room, measuring 10 m $\times$ 7 m $\times$ 3 m, is ______. (rounded off to two decimal places) [Density of dry air is $1.029\times$ 10 -3 $g cm$ -3 ]
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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 โsalt fingeringโ is likely to occur?
a.
Only P
b.
Only Q
c.
Q and R
d.
P and R
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A body radiates heat at a rate of 5 $cal m$ -2 $s$ -1, when its temperature is 227 โ. 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 โ?
a.
25
b.
80
c.
150
d.
625
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The given figure illustrates a subtropical gyre in the Southern Indian Ocean. Identify the currents in the correct sequence of P, Q, R and S, respectively from the following options.
a.
Indian Ocean Current
b.
Indian Ocean Current
c.
West Australian Current
d.
West Australian Current
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The temperature of a dry air parcel is 20 โ 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 โ) 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.]
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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)
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A steady westerly wind is blowing over the ocean surface at a latitude of 30ยฐN and exerting a wind stress of 0.8 $N m$ -2. The magnitude of net volume transport (in $m$ 2 $s$ -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 $\times$ 10 -5 $s$ -1.]
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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 $kg m$ -3 and the Coriolis parameter is 10 -4 $s$ -1.]
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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 ]
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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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Which one of the following biomass treatment processes occurs in an oxygen limited condition approximately between 450 โ and 600 โ, and produces biochar and bio-oil as primary products?
a.
Gasification
b.
Pyrolysis
c.
Anaerobic Digestion
d.
Steam Reforming
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An energy conservation project requires an initial investment of โน 50,000 with an expected annual operation and maintenance cost of โน 5,000. This project is expected to reduce the monthly energy cost by โน 1,250. The simple payback period (in years) is_________________. (Answer in integer)
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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)
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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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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
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A hydro turbine works under a head of 20 m and has a maximum volume flow rate of 4 m 3 s โ1 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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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
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A radioactive isotope sample has a decay constant $ฮป$ = 2.31 $\times$ 10 -4 year โ1. Initially the sample contains 8000 $\times$ 10 15 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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A fuel with composition by mass is given as 78 % carbon (C), 16 % hydrogen (H 2), 3.2 % sulphur (S), 1.6 % oxygen (O 2), 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 (SO 2) 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 โ1) of C, H 2, S, and O 2 are 12, 2, 32, and 32, respectively, and the volumetric ratio of nitrogen (N 2) and oxygen (O 2) in the air as 3.76:1.
a.
14.8
b.
7.4
c.
22.2
d.
3.1
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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__________________________.
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A nonlinear load connected to a sinusoidal voltage source (of peak value $V m$ and 50 Hz frequency) draws a quasi-square wave shaped current (of maximum value $I m$) as shown in the figure below. The power factor of the nonlinear load (rounded off to two decimal places) is__________________________________.
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A resident has โน 50,000 to purchase a 5-star rated air conditioner with a life of 10 years. The annual energy cost savings (in โน) needed to recover this investment in 6 years assuming a discount rate of 10 % per annum is_____________________. (Answer in integer)
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A countryโs 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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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 m 2 Absorbed solar flux by the absorber plate = 600 Wm โ2 Overall loss coefficient = 4 Wm โ2 K โ1 Water inlet temperature = 60 โ Ambient temperature = 25 โ
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