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GATE ME 2020 Set 2

All 65 solved GATE ME 2020 Set 2 questions in exam order. Open a question, commit to an answer, and learn from the step-by-step solution. One question at a time.

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Difficulty mixEasy 22Medium 38Hard 5

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65 of 65 questions

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Mechanical Engineering

11
Q11MCQ1 markMedium
The sum of two normally distributed random variables $X$ and $Y$ is
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Question
$X$
A. $always normally distributed$
B. $X$
C. $X$
D. $X$
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$X$
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12
Q12MCQ1 markEasy
A matrix $P$ is decomposed into its symmetric part $S$ and skew symmetric part $V$ . If…
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Question
$P$
Your answer
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A. $\begin{pmatrix} -4 & 6 & -1 \\ 2 & 3 & 0 \\ 5 & 7 & 2 \end{pmatrix}$ B. $\begin{pmatrix} -4 & 2 & 5 \\ 6 & 3 & 7 \\ -1 & 0 & 2 \end{pmatrix}$ C. $\begin{pmatrix} 4 & -6 & 1 \\ -2 & -3 & 0 \\ -5 & -7 & -2 \end{pmatrix}$ D. $\begin{pmatrix} -2 & 9/2 & -1 \\ -1 & 81/4 & 11 \\ -2 & 45/2 & 73/4 \end{pmatrix}$
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$P$
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13
Q13MCQ1 markMedium
Let $I = \int_{x=0}^{1} \int_{y=0}^{x^2} xy^2 \, dy \, dx$ . Then, $I$ may also be expressed as
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Question
$I = \int_{x=0}^{1} \int_{y=0}^{x^2} xy^2 \, dy \, dx$
Your answer
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A. $\int_{y=0}^{1} \int_{x=0}^{\sqrt{y}} xy^2 \, dx \, dy$ B. $\int_{y=0}^{1} \int_{x=\sqrt{y}}^{1} yx^2 \, dx \, dy$ C. $\int_{y=0}^{1} \int_{x=\sqrt{y}}^{1} xy^2 \, dx \, dy$ D. $\int_{y=0}^{1} \int_{x=0}^{\sqrt{y}} yx^2 \, dx \, dy$
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$I = \int_{x=0}^{1} \int_{y=0}^{x^2} xy^2 \, dy \, dx$
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14
Q14MCQ1 markEasy
The solution of $\frac{d^2y}{dt^2} - y = 1,$ which additionally satisfies $y|_{t=0} = \frac{dy}{dt}|_{t=0} = 0$ in the Laplace $s$ -domain is
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Question
$\frac{d^2y}{dt^2} - y = 1,$
Your answer
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A. $\frac{1}{s(s+1)(s-1)}$ B. $\frac{1}{s(s+1)}$ C. $\frac{1}{s(s-1)}$ D. $\frac{1}{s-1}$
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$s$
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15
Q15MCQ1 markMedium
An attempt is made to pull a roller of weight $W$ over a curb (step) by applying a horizontal force $F$ as shown in the figure. [figure] The coefficient of static friction between…
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Question
$W$
Your answer
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A.B.C.D.
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$N_1 = 0$
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16
Q16MCQ1 markMedium
A circular disk of radius $r$ is confined to roll without slipping at P and Q as shown in the figure. [figure] If the plates have velocities as shown, the magnitude of the angular…
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Question
$r$
Your answer
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A. $\frac{v}{r}$ B. $\frac{v}{2r}$ C. $\frac{2v}{r}$ D. $\frac{3v}{2r}$
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$\omega$
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17
Q17MCQ1 markEasy
The equation of motion of a spring-mass-damper system is given by $\frac{d^2x}{dt^2} + 3 \frac{dx}{dt} + 9x = 10 \sin(5t)$ The damping factor for the system is
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Question
$\frac{d^2x}{dt^2} + 3 \frac{dx}{dt} + 9x = 10 \sin(5t)$
Your answer
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A. $0.25$ B. $0.5$ C. $2$ D. $3$
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$\frac{d^2x}{dt^2} + 2\zeta\omega_n \frac{dx}{dt} + \omega_n^2x = f(t)$
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18
Q18MCQ1 markMedium
The number of qualitatively distinct kinematic inversions possible for a Grashof chain with four revolute pairs is
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Question
$The number of qualitatively distinct kinematic inversions possible for a Grashof chain with four revolute pairs is$
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A. $1$ B. $2$ C. $3$ D. $4$
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$s + l \le p + q$
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19
Q19MCQ1 markEasy
The process, that uses a tapered horn to amplify and focus the mechanical energy for machining of glass, is
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Question
$The process, that uses a tapered horn to amplify and focus the mechanical energy for machining of glass, is$
Your answer
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A. $electrochemical machining$ B. $electrical discharge machining$ C. $ultrasonic machining$ D. $abrasive jet machining$
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$Correct answer (C) ultrasonic machining Step-by-step solution In Ultrasonic Machining (USM), a transducer converts electrical energy into high-frequency mechanical vibrations. These vibrations are transmitted to the tool through a tapered horn (also known as a concentrator or velocity transformer), which amplifies the vibration amplitude. This mechanical energy, combined with an abrasive slurry, is used to machine hard and brittle materials like glass. Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.$
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20
Q20MCQ1 markMedium
Two plates, each of 6 mm thickness, are to be butt-welded. Consider the following processes and select the correct sequence in increasing order of size of the heat affected zone.…
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Question
$Two plates, each of 6 mm thickness, are to be butt-welded. Consider the following processes and select the correct sequence in increasing order of size of the heat affected zone. 1. Arc welding 2. MIG welding 3. Laser beam welding 4. Submerged arc welding$
Your answer
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A. $1-4-2-3$ B. $3-4-2-1$ C. $4-3-2-1$ D. $3-2-4-1$
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$Correct answer (D) 3-2-4-1 Step-by-step solution The size of the Heat Affected Zone (HAZ) is primarily determined by the heat input density of the welding process. Processes with higher power density concentrate heat more effectively, resulting in a smaller HAZ. 1. Laser beam welding (3) has the highest power density and thus the smallest HAZ. 2. MIG welding (2) has a higher power density than submerged arc welding. 3. Submerged arc welding (4) typically has a larger heat input than MIG but is more concentrated than manual arc welding. 4. Manual Arc welding (1) generally has the lowest power density and highest relative heat input per unit length, leading to the largest HAZ. Therefore, the increasing order of HAZ size is 3-2-4-1. Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.$
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21
Q21MCQ1 markEasy
Which one of the following statements about a phase diagram is INCORRECT?
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Question
$Which one of the following statements about a phase diagram is INCORRECT ?$
Your answer
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A. $It indicates the temperature at which different phases start to melt$ B. $Relative amount of different phases can be found under given equilibrium conditions$ C. $It gives information on transformation rates$ D. $Solid solubility limits are depicted by it$
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$Correct answer (C) It gives information on transformation rates Step-by-step solution Phase diagrams are equilibrium diagrams that represent the stable phases of a material system at various temperatures, pressures, and compositions. (A) Correct: Solidus and liquidus lines indicate melting/solidification temperatures. (B) Correct: The lever rule is used to find the relative amounts of phases in equilibrium. (D) Correct: Solvus lines indicate the limits of solid solubility. (C) Incorrect: Phase diagrams do not provide kinetic information such as transformation rates. Transformation rates are found in TTT (Time-Temperature-Transformation) or CCT (Continuous Cooling Transformation) diagrams. Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.$
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22
Q22MCQ1 markMedium
The figure below shows a symbolic representation of the surface texture in a perpendicular lay orientation with indicative values (I through VI) marking the various specifications…
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Question
$The figure below shows a symbolic representation of the surface texture in a perpendicular lay orientation with indicative values (I through VI) marking the various specifications whose definitions are listed below. P: Maximum Waviness Height (mm); Q: Maximum Roughness Height (mm); R: Minimum Roughness Height (mm); S: Maximum Waviness Width (mm); T: Maximum Roughness Width (mm); U: Roughness Width Cutoff (mm).$
Your answer
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A. $I-R, II-Q, III-P, IV-S, V-U, VI-T$ B. $I-R, II-P, III-U, IV-S, V-T, VI-Q$ C. $I-U, II-S, III-Q, IV-T, V-R, VI-P$ D. $I-Q, II-U, III-R, IV-T, V-S, VI-P$
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$Correct answer (A) I-R, II-Q, III-P, IV-S, V-U, VI-T Step-by-step solution According to the standard for surface texture symbols (ISO 1302), the positions around the check-mark symbol correspond to specific parameters: Position I (top left): Roughness value (R in this context). Position II (inside the check): Production method or additional roughness height (Q). Position III (above horizontal line, left): Sampling length or waviness height (P). Position IV (above horizontal line, right): Lay direction or waviness width (S). Position V (right of the symbol): Machining allowance or roughness width cutoff (U). Position VI (below horizontal line): Other roughness values or roughness width (T). Matching these with the provided list leads to the sequence: I-R, II-Q, III-P, IV-S, V-U, VI-T. Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.$
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23
Q23MCQ1 markEasy
In Materials Requirement Planning, if the inventory holding cost is very high and the setup cost is zero, which one of the following lot sizing approaches should be used?
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Question
$In Materials Requirement Planning, if the inventory holding cost is very high and the setup cost is zero, which one of the following lot sizing approaches should be used?$
Your answer
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A. $Economic Order Quantity$ B. $Lot-for-Lot$ C. $Base Stock Level$ D. $Fixed Period Quantity, for 2 periods$
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$Correct answer (B) Lot-for-Lot Step-by-step solution In Materials Requirement Planning (MRP), the Lot-for-Lot (L4L) technique is a lot-sizing approach where the order quantity is set exactly equal to the net requirements for each period. 1. If the setup cost is zero, there is no penalty for placing frequent orders. 2. If the inventory holding cost is very high, the primary goal is to minimize the stock held at any time. Since L4L results in zero ending inventory for every period (as we only order what is immediately needed), it minimizes holding costs to zero. Therefore, it is the ideal approach under these conditions. Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.$
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24
Q24MCQ1 markEasy
Which of the following conditions is used to determine the stable equilibrium of all partially submerged floating bodies?
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Question
$Which of the following conditions is used to determine the stable equilibrium of all partially submerged floating bodies?$
Your answer
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A. $Centre of buoyancy must be above the centre of gravity$ B. $Centre of buoyancy must be below the centre of gravity$ C. $Metacentre must be at a higher level than the centre of gravity$ D. $Metacentre must be at a lower level than the centre of gravity$
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$M$
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25
Q25MCQ1 markEasy
In the space above the mercury column in a barometer tube, the gauge pressure of the vapour is
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Question
$In the space above the mercury column in a barometer tube, the gauge pressure of the vapour is$
Your answer
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A. $positive, but more than one atmosphere$ B. $negative$ C. $zero$ D. $positive, but less than one atmosphere$
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$P_{gauge} = P_{absolute} - P_{atmospheric}$
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26
Q26MCQ1 markMedium
A closed vessel contains pure water, in thermal equilibrium with its vapour at $25^\circ\text{C}$ (Stage #1), as shown. [figure] The vessel in this stage is then kept inside an…
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Question
$25^\circ\text{C}$
Your answer
Choose one option, then check your answer.
A. $Water vapor inside the vessel will come out of the Valve A$ B. $Hot air will go inside the vessel through Valve A$ C. $Nothing will happen - the vessel will continue to remain in equilibrium$ D. $All the vapor inside the vessel will immediately condense$
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$80^\circ\text{C}$
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27
Q27MCQ1 markEasy
For an air-standard Diesel cycle,
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Question
$For an air-standard Diesel cycle,$
Your answer
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A. $heat addition is at constant volume and heat rejection is at constant pressure$ B. $heat addition is at constant pressure and heat rejection is at constant pressure$ C. $heat addition is at constant pressure and heat rejection is at constant volume$ D. $heat addition is at constant volume and heat rejection is at constant volume$
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$Correct answer (C) heat addition is at constant pressure and heat rejection is at constant volume Step-by-step solution The air-standard Diesel cycle consists of four processes: 1. Isentropic compression 2. Constant pressure heat addition 3. Isentropic expansion 4. Constant volume heat rejection Therefore, heat addition is at constant pressure and heat rejection is at constant volume. Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.$
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28
Q28MCQ1 markMedium
The values of enthalpies at the stator inlet and rotor outlet of a hydraulic turbomachine stage are $h_1$ and $h_3$ respectively. The enthalpy at the stator outlet (or, rotor…
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Question
$h_1$
Your answer
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A. $zero$ B. $50%$ C. $75%$ D. $100%$
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$R$
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29
Q29NAT1 markEasy
Let $I$ be a 100 dimensional identity matrix and $E$ be the set of its distinct (no value appears more than once in $E$ ) real eigenvalues. The number of elements in $E$ is ______.
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Question
$I$
Your answer
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Numerical answer
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$I$
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30
Q30NAT1 markMedium
A beam of negligible mass is hinged at support P and has a roller support Q as shown in the figure. [figure] A point load of 1200 N is applied at point R. The magnitude of the…
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Question
$A beam of negligible mass is hinged at support P and has a roller support Q as shown in the figure. A point load of 1200 N is applied at point R. The magnitude of the reaction force at support Q is__________N.$
Your answer
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Numerical answer
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$P_x$
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31
Q31NAT1 markMedium
A machine member is subjected to fluctuating stress $\sigma = \sigma_{o} \cos(8\pi t)$ . The endurance limit of the material is 350 MPa. If the factor of safety used in the design…
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Question
$\sigma = \sigma_{o} \cos(8\pi t)$
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$\sigma(t) = \sigma_o \cos(8\pi t)$
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32
Q32NAT1 markMedium
A bolt head has to be made at the end of a rod of diameter $d = 12$ mm by localized forging (upsetting) operation. The length of the unsupported portion of the rod is $40$ mm. To…
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Question
$d = 12$
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Numerical answer
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$L \leq 3d$
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33
Q33NAT1 markMedium
Consider the following network of activities, with each activity named A-L, illustrated in the nodes of the network. [figure] The number of hours required for each activity is…
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Question
$Consider the following network of activities, with each activity named A-L, illustrated in the nodes of the network. The number of hours required for each activity is shown alongside the nodes. The slack on the activity L, is______hours.$
Your answer
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Numerical answer
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$2+4+10+7+8+5+6 = 42$
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34
Q34NAT1 markMedium
In a furnace, the inner and outer sides of the brick wall ( $k_1 = 2.5$ W/m.K) are maintained at $1100^\circ$ C and $700^\circ$ C, respectively as shown in figure. [figure] The brick…
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Question
$k_1 = 2.5$
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Numerical answer
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$q = \frac{k_1(T_{inner} - T_{interface})}{L_1}$
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35
Q35NAT1 markEasy
If a reversed Carnot cycle operates between the temperature limits of $27^\circ\text{C}$ and $-3^\circ\text{C}$ , then the ratio of the COP of a refrigerator to that of a heat pump…
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Question
$27^\circ\text{C}$
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Numerical answer
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$T_H = 27^\circ\text{C} = 27 + 273 = 300\text{ K}$
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36
Q36MCQ2 marksEasy
The directional derivative of $f(x, y, z) = xyz$ at point $(-1, 1, 3)$ in the direction of vector $\hat{i} - 2\hat{j} + 2\hat{k}$ is
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Question
$f(x, y, z) = xyz$
Your answer
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A. $3\hat{i} - 3\hat{j} - \hat{k}$ B. $-\frac{7}{3}$ C. $\frac{7}{3}$ D. $7$
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$f$
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37
Q37MCQ2 marksEasy
The function $f(z)$ of complex variable $z = x + iy$ , where $i = \sqrt{-1}$ , is given as $f(z) = (x^3 - 3xy^2) + i v(x, y)$ . For this function to be analytic, $v(x, y)$ should be
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Question
$f(z)$
Your answer
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A. $(3xy^2 - y^3) + \text{constant}$ B. $(3x^2y^2 - y^3) + \text{constant}$ C. $(x^3 - 3x^2y) + \text{constant}$ D. $(3x^2y - y^3) + \text{constant}$
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$f(z) = u + iv$
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38
Q38MCQ2 marksMedium
A cantilever of length $l$ , and flexural rigidity $EI$ , stiffened by a spring of stiffness $k$ , is loaded by a transverse force $P$ , as shown. [figure]
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Question
$l$
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A. $\frac{Pl^3}{3EI} \left[ \frac{3EI}{3EI + 2kl^3} \right]$ B. $\frac{Pl^3}{3EI} \left[ \frac{6EI - kl^3}{6EI} \right]$ C. $\frac{Pl^3}{3EI} \left[ \frac{3EI - kl^3}{3EI} \right]$ D. $\frac{Pl^3}{3EI} \left[ \frac{3EI}{3EI + kl^3} \right]$
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$P$
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39
Q39MCQ2 marksMedium
The sun (S) and the planet (P) of an epicyclic gear train shown in the figure have identical number of teeth. If the sun (S) and the outer ring (R) gears are rotated in the same…
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Question
$\omega_S$
Your answer
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A. $\frac{3}{4} \omega_R + \frac{1}{4} \omega_S$ B. $\frac{1}{4} \omega_R + \frac{3}{4} \omega_S$ C. $\frac{1}{2} \omega_R - \frac{1}{2} \omega_S$ D. $\frac{3}{4} \omega_R - \frac{1}{4} \omega_S$
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$T_S$
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40
Q40MCQ2 marksHard
A thin-walled cylinder of radius $r$ and thickness $t$ is open at both ends, and fits snugly between two rigid walls under ambient conditions, as shown in the figure. The material…
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Question
$r$
Your answer
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A. $\Delta T = \frac{3\nu pr}{2\alpha t E}$ B. $\Delta T = \left( \nu - \frac{1}{4} \right) \frac{pr}{\alpha t E}$ C. $\Delta T = \frac{\nu pr}{\alpha t E}$ D. $\Delta T = \left( \nu + \frac{1}{2} \right) \frac{pr}{\alpha t E}$
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$\epsilon_a$
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41
Q41MCQ2 marksEasy
A helical spring has spring constant $k$ . If the wire diameter, spring diameter and the number of coils are all doubled then the spring constant of the new spring becomes
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$k$
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A. $k/2$ B. $k$ C. $8k$ D. $16k$
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$k = \frac{G d^4}{8 D^3 n}$
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42
Q42MCQ2 marksMedium
Two rollers of diameters $D_1$ (in mm) and $D_2$ (in mm) are used to measure the internal taper angle in the V-groove of a machined component. The heights $H_1$ (in mm) and $H_2$ …
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Question
$D_1$
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A. $\sin \alpha = \frac{(D_1 - D_2)}{2(H_1 - H_2) - (D_1 - D_2)}$ B. $\cos \alpha = \frac{(D_1 - D_2)}{2(H_1 - H_2) - 2(D_1 - D_2)}$ C. $\text{cosec } \alpha = \frac{(H_1 - H_2) - (D_1 - D_2)}{2(D_1 - D_2)}$ D. $\sin \alpha = \frac{(H_1 - H_2)}{(D_1 - D_2)}$
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$D$
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43
Q43MCQ2 marksMedium
The forecast for the monthly demand of a product is given in the table below. | Month | Forecast | Actual Sales | | :---: | :---: | :---: | | 1 | 32.00 | 30.00 | | 2 | 31.80 |…
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Question
$The forecast for the monthly demand of a product is given in the table below. Month Forecast Actual Sales 1 32.00 30.00 2 31.80 32.00 3 31.82 30.00 The forecast is made by using the exponential smoothing method. The exponential smoothing coefficient used in forecasting the demand is$
Your answer
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A. $0.10$ B. $0.40$ C. $0.50$ D. $1.00$
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$F_t = F_{t-1} + \alpha(A_{t-1} - F_{t-1})$
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44
Q44MCQ2 marksMedium
One kg of air in a closed system undergoes an irreversible process from an initial state of $p_1 = 1$ bar (absolute) and $T_1 = 27^\circ\text{C}$ , to a final state of $p_2 = 3$ …
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Question
$p_1 = 1$
Your answer
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A. $-26.3$ B. $28.4$ C. $172.0$ D. $indeterminate, as the process is irreversible$
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$\Delta s = C_p \ln\left(\frac{T_2}{T_1}\right) - R \ln\left(\frac{p_2}{p_1}\right)$
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45
Q45NAT2 marksMedium
For the integral $\int_0^{\pi/2} (8 + 4 \cos x) dx$ , the absolute percentage error in numerical evaluation with the Trapezoidal rule, using only the end points, is ________…
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Question
$\int_0^{\pi/2} (8 + 4 \cos x) dx$
Your answer
Enter a number. Decimals, negative values and scientific notation are accepted.
Numerical answer
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$I = \int_0^{\pi/2} (8 + 4 \cos x) dx = [8x + 4 \sin x]_0^{\pi/2}$
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46
Q46NAT2 marksMedium
A fair coin is tossed 20 times. The probability that 'head' will appear exactly 4 times in the first ten tosses, and 'tail' will appear exactly 4 times in the next ten tosses is…
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Question
$A fair coin is tossed 20 times. The probability that 'head' will appear exactly 4 times in the first ten tosses, and 'tail' will appear exactly 4 times in the next ten tosses is________(round off to 3 decimal places).$
Your answer
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Numerical answer
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$n = 10, k = 4, p = 0.5, q = 0.5$
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47
Q47NAT2 marksHard
A hollow spherical ball of radius $20\text{ cm}$ floats in still water, with half of its volume submerged. Taking the density of water as $1000\text{ kg/m}^3$ , and the…
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Question
$20\text{ cm}$
Your answer
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$W = F_B = \rho_w g V_{sub} = \rho_w g \left(\frac{1}{2} V_{total}\right) = \rho_w g \left(\frac{1}{2} \cdot \frac{4}{3} \pi R^3\right) = \frac{2}{3} \rho_w g \pi R^3$
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48
Q48NAT2 marksMedium
Uniaxial compression test data for a solid metal bar of length $1\text{ m}$ is shown in the figure. [figure] The bar material has a linear elastic response from O to P followed by…
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$1\text{ m}$
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$\sigma_y = 100\text{ MPa}$
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49
Q49NAT2 marksMedium
The turning moment diagram of a flywheel fitted to a fictitious engine is shown in the figure. [figure] The mean turning moment is $2000\text{ Nm}$ . The average engine speed is…
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$2000\text{ Nm}$
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$T_{mean} = 2000\text{ Nm}$
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50
Q50NAT2 marksMedium
A rigid block of mass $m_1 = 10\text{ kg}$ having velocity $v_0 = 2\text{ m/s}$ strikes a stationary block of mass $m_2 = 30\text{ kg}$ after traveling $1\text{ m}$ along a…
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$m_1 = 10\text{ kg}$
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$m_1$
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51
Q51NAT2 marksMedium
A steel spur pinion has a module ( $m$ ) of $1.25\text{ mm}$ , $20$ teeth and $20^\circ$ pressure angle. The pinion rotates at $1200\text{ rpm}$ and transmits power to a $60$ teeth…
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$m$
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$W^t$
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52
Q52NAT2 marksMedium
A mould cavity of $1200\text{ cm}^3$ volume has to be filled through a sprue of $10\text{ cm}$ length feeding a horizontal runner. Cross-sectional area at the base of the sprue is…
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$1200\text{ cm}^3$
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$v$
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53
Q53NAT2 marksHard
A cylindrical bar with $200$ mm diameter is being turned with a tool having geometry $0^\circ - 9^\circ - 7^\circ - 8^\circ - 15^\circ - 30^\circ - 0.05$ inch (Coordinate system,…
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$200$
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$\psi_s$
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54
Q54NAT2 marksMedium
There are two identical shaping machines $S_1$ and $S_2$ . In machine $S_2$ , the width of the workpiece is increased by $10\%$ and the feed is decreased by $10\%$ , with respect to…
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$S_1$
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$T = \frac{B(1+m)}{f \cdot N}$
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55
Q55NAT2 marksHard
Bars of $250$ mm length and $25$ mm diameter are to be turned on a lathe with a feed of $0.2$ mm/rev. Each regrinding of the tool costs Rs. 20. The time required for each tool…
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$250$
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$T_{opt}$
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56
Q56NAT2 marksMedium
A point 'P' on a CNC controlled XY- stage is moved to another point 'Q' using the coordinate system shown in the figure below and rapid positioning command (G00). [figure] A pair…
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$A point 'P' on a CNC controlled XY- stage is moved to another point 'Q' using the coordinate system shown in the figure below and rapid positioning command (G00). A pair of stepping motors with maximum speed of 800 rpm, controlling both the X and Y motion of the stage, are directly coupled to a pair of lead screws, each with a uniform pitch of 0.5 mm. The time needed to position the point 'P' to the point 'Q' is________minutes (round off to 2 decimal places).$
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$V_{max} = \text{pitch} \times \text{RPM} = 0.5 \text{ mm} \times 800 \text{ rpm} = 400 \text{ mm/min}$
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57
Q57NAT2 marksMedium
For a single item inventory system, the demand is continuous, which is 10000 per year. The replenishment is instantaneous and backorders ( $S$ units) per cycle are allowed as shown…
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$S$
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$D$
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58
Q58NAT2 marksMedium
Consider a flow through a nozzle, as shown in the figure below. [figure] The air flow is steady, incompressible and inviscid. The density of air is $1.23 \text{ kg/m}^3$ . The…
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$1.23 \text{ kg/m}^3$
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$\rho = 1.23 \text{ kg/m}^3$
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59
Q59NAT2 marksMedium
Water (density $1000\text{ kg/m}^3$ ) flows through an inclined pipe of uniform diameter. The velocity, pressure and elevation at section A are $V_A = 3.2\text{ m/s}$ ,…
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$1000\text{ kg/m}^3$
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$h_L$
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60
Q60NAT2 marksEasy
The spectral distribution of radiation from a black body at $T_1 = 3000\text{ K}$ has a maximum at wavelength $\lambda_{\text{max}}$ . The body cools down to a temperature $T_2$ .…
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$T_1 = 3000\text{ K}$
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$\lambda_{\text{max}} T = \text{constant}$
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61
Q61NAT2 marksMedium
Water flows through a tube of $3\text{ cm}$ internal diameter and length $20\text{ m}$ . The outside surface of the tube is heated electrically so that it is subjected to uniform…
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$3\text{ cm}$
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$Q$
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62
Q62NAT2 marksMedium
Air is contained in a frictionless piston-cylinder arrangement as shown in the figure. [figure] The atmospheric pressure is $100\text{ kPa}$ and the initial pressure of air in the…
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$100\text{ kPa}$
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$P_1 = 105\text{ kPa}$
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63
Q63NAT2 marksHard
Moist air at $105\text{ kPa}$ , $30^\circ\text{C}$ and $80\%$ relative humidity flows over a cooling coil in an insulated air-conditioning duct. Saturated air exits the duct at…
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$105\text{ kPa}$
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$P_1 = 105\text{ kPa}$
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Month	Forecast	Actual Sales
1	32.00	30.00
2	31.80	32.00
3	31.82	30.00

Q64NAT2 marksMedium

In a steam power plant, superheated steam at

10\text{ MPa}

and

500^\circ\text{C}

, is expanded isentropically in a turbine until it becomes a saturated vapour. It is then…

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Question

10\text{ MPa}

Pressure, $p$ (MPa)	Temperature, $T$ ( $^\circ$ C)	Enthalpy, $h$ (kJ/kg)	Entropy, $s$ (kJ/kg.K)
10	500	3373.6	6.5965
1	500	3478.4	7.7621

Pressure, $p$	Sat. Temp. $T_{sat}$ ( $^\circ$ C)	$h_f$ (kJ/kg)	$h_g$ (kJ/kg)	$s_f$ (kJ/kg.K)	$s_g$ (kJ/kg.K)
1 MPa	179.91	762.9	2778.1	2.1386	6.5965
20 kPa	60.06	251.38	2609.7	0.8319	7.9085

P_1 = 10\text{ MPa}, T_1 = 500^\circ\text{C} \Rightarrow h_1 = 3373.6, s_1 = 6.5965

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P_1 = 10\text{ MPa}, T_1 = 500^\circ\text{C} \Rightarrow h_1 = 3373.6, s_1 = 6.5965

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65
Q65NAT2 marksMedium
Keeping all other parameters identical, the Compression Ratio (CR) of an air standard diesel cycle is increased from 15 to 21. Take ratio of specific heats = 1.3 and cut-off ratio…
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$r_c = 2$
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$\eta = 1 - \frac{1}{CR^{\gamma-1}} \left[ \frac{r_c^{\gamma} - 1}{\gamma(r_c - 1)} \right]$
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