Directions:
Q. No. 1  5 Carry One Mark Each
Q.
If you choose plan P, you will have to _______ plan Q, as these two are mutually _________.
P looks at Q while Q looks at R. P is married, R is not. The number of people in which a married person is looking at an unmarried person is
If a and b are integers and a – b is even, which of the following must always be even?
According to the given relation of a–b = even, there is a possibility of oddodd (or) eveneven is equal to even. From the options, Option (D) is correct. Since, odd x odd–odd (or) even x even–even → is always even number.
Alternate Method: Let a – b =2K ⇒ a = b + 2K
abb = (b + 2K) bb = b^{2} + 2Kb b = b^{2} b + 2Kb = b b 1)+ 2Kb
Even; since 2Kb always even & b (b1) also even, if with b is odd or even.
The property of a material which enables it to resist fracture due to high impact loads is known as
The ways in which this game can be played __________ potentially infinite.
Directions:
Q. No. 6 10 Carry Two Marks Each
Q.
“If you are looking for a history of India, or for an account of the rise and fall of the British Raj, or for the reason of the cleaving of the subcontinent into two mutually antagonistic parts and the effects this mutilation will have in the respective sections, and ultimately on Asia, you will not find it in these pages; for though I have spent a lifetime in the country, I lived too near the seat of events, and was too intimately associated with the actors, to get the perspective needed for the impartial recording of these matters.”
Which of the following closest in meaning to „cleaving‟?
There are 4 women P, Q, R, S, and 5 men V, W, X, Y, Z in a group. We are required to form pairs each consisting of one woman and one man. P is not to be paired with Z, and Y must necessarily be paired with someone. In how many ways can 4 such pairs be formed?
In the graph below, the concentration of a particular pollutant in a lake is plotted over (alternate) days of a month in winter (average temperature 10°C) and a month in summer (average temperature 30°C).
Consider the following statements based on the data shown above:
(i) Over the given months, the difference between the maximum and the minimum pollutant concentrations is the same in both winter and summer.
(ii) There are at last four days in the summer month such that the pollutant concentrations on those days are within 1 ppm of the pollutant concentrations on the corresponding days in the winter month.Which one of the following options is correct?
The difference between the maximum and the minimum pollutant concentrations
(i) in winter = 80=8 ppm,
(ii) in summer = 10.51.5=9 ppm
∴ (i) is false & (ii) is correct from the graph.
All people in a certain island are either 'Knights' or 'Knaves' and each person knows every other person‟s identity. Knights NEVER lie, and knaves ALWAYS lie.P says “Both of us are knights”. Q says “None of us are knaves”.Which one of the following can be logically inferred from the above?
X bullocks and Y tractors take 8 days to plough a field. If we halve the number of bullocks and double the number of tractors, it takes 5days to plough the same field. How many days will it take X bullocks alone to plough the field?
Given Number of days required that X bullocks and Y tractors to plough a field = 8 days → (1) ( i.e, X + Y → 8D ⇒8X + 8Y → 1day )
Number of days required that X/2 bullocks and 2 y tractors to plough field = 5→(2)
Directions:
Q. No. 11 to 35 Carry One Mark Each
Q.
A mass m of a perfect gas at pressure p_{1} and volume V_{1} undergoes an isothermal process. The final pressure is p_{2} and volume is V_{2}. The work done on the system is considered positive. If R is the gas constant and T is the temperature, then the work done in the process is
Which one of the following statements is TRUE for the ultrasonic machining (USM) process?
The standard deviation of linear dimensions P and Q are 3 mm and 4 mm, respectively. When assembled, the standard deviation (in mm ) of the resulting linear dimension (P+Q) is ________
Given that Standard deviate of P is 3 μm ⇒ Variance of P is 9 μm
Standard deviation of Q is 4 μm ⇒ Variance of Q is 16 μm
Variance of P + Q = Var (P+Q) = Variance P + Variance Q
= 9 + 16= 25
∴standard deviation of P + Q =
The emissive power of a blackbody is P. If its absolute temperature is doubled, the emissive power becomes.
Emissive power of black body (E_{b}) =σT^{4}
Given (E_{b})_{1}=P =σT^{4}
now T → 2T
(E_{b})_{2} =(σ2T)^{4} = 16σT^{4} ⇒ (E_{b})_{2} =16P
The state of stress at a point is σ_{x}=σ_{y} =σ_{z} = τ_{xz} = τ_{zx}=τ_{zy} = τ_{yz} and τ_{xy }= τ_{yx} =50MPa.
The maximum normal stress (in MPa) at that point is _________
It is a pure torsion case in 2D
so maximum Normal stress σ_{1} = 50MPa
The determinant of a 2×2 matrix is 50. If one eigenvalue of the matrix is 10, the other eigenvalue is ___________
Given that det of 2×2 Matrix is 50 and are Eigen Value is 10.
⇒ Other Eigen value is 5 (∴ det= product of eigenvalues )
Which one of the following statement is TRUE?
Two coins are tossed simultaneously. The probability (upto two decimal points accuracy) of getting at least one head is ____________
Total No of outcomes when two coins are tossed is 4 and sample space
S = { HH, HT, TH, TT }
Favorable out comes for existence of at least one head are HH, HT, TH.
Required probability = 3/4 = 0.75
A cantilever beam of length L and flexural modulus EI is subjected to a point load P at the free end. The elastic strain energy stored in the beam due to bending (neglecting transverse shear)
It is desired to make a product having Tshaped crosssection from a rectangular aluminium block. Which one of the following processes is expected to provide the highest strength of the product?
The heat loss from a fin is 6W. The effectiveness and efficiency of the fin are 3 and 0.75, respectively. The heat loss (in W) from the fin, keeping the entire fin surface at base temperature, is __________.
Given Q_{loss} = 6W
ε = 3, η = 0.75
For a single server with Poisson arrival and exponential service time, the arrival rate is 12 per hour. Which one of the following service rates will provide a steady state finite queue length?
λ = 12/ hour
For steady state finite queue length
μ > λ
So, μ = 24/hour
For the stability of a floating body the
Stability of floating body is measure with the help of Meta center.
Floating body to be stable, Meta center must be above C.G
For stability MG > 0
The divergence of the vector yi+ xj __________
For a loaded cantilever beam of uniform crosssection, the bending moment (in N.mm) along the length is M(x) = 5x^{2}+10x, where x is the distance (in mm) measured from the free end of the beam. The magnitude of shear force (in N) in the crosssection at x =10 mm is ________.
A sample of 15 data is a follows: 17, 18, 17, 17, 13, 18, 5, 5, 6, 7, 8, 9, 20, 17, 3. The mode of the data is
We know that mode is the value of the data which occurred most of
∴ 17 is mode
If a mass of moist air contained in a closed metallic vessel is heated, then its
Given that mass of moist air contained in a closed metallic vessel is heated, means its specific humidity (ω) is constant.
So, from the psychometric chart
We can say that at constant specific humidity, as temperature increases relative humidity decreases i.e.,
Ø_{2} < Ø_{1} So, Answer is (A)
In a slidercrank mechanism, the lengths of the crank and the connecting rod are 100mm and 160mm, respectively. The crank is rotating with an angular velocity of 10 radian/s counterclockwise. The magnitude of linear velocity (in m/s) of the piston at the instant corresponding to the configuration shown in the figure is ___________
A machine component made of a ductile material is subjected to a variable loading with
σ_{min} = 50 MPa and σ_{max} = 50 MPa. If the corrected endurance limit and the yield strength for the material are σ_{e}= 100 MPa and σy = 300MPa, the factor of safety is __________
σ_{max} = 50MPa
σ_{min }= 50MPa
σ_{y } = 300MPa
σ_{e} = 100MPa
The crystal structure of aluminium is
Uniformly distributed load of 5 kN acts on a simply supported beam of length 10 m. What are the reactions at end points of the beam?
The Laplace transform of te^{t} is
Consider a laminar flow at zero incidence over a flat plate. The shear stress at the wall is denoted by τ_{w} . The axial positions x_{1} and x_{2} on the plate are measured from the leading edge in the direction of flow. If x_{2} > x_{1}, then
A mass m is attached to two identical springs having spring constant k as shown in the figure. The natural frequency w of this single degree of freedom system is
Equivalent stiffness k_{eq }= k+k = 2k
Natural frequency =
Given the atomic weight of Fe is 56 and that of C is 12, the weight percentage of carbon in cementite (Fe_{3}C) is _________.
Percentage of carbon by weight in cementite =
Directions:
Q. No. 36 to 65 Carry Two Marks Each
Q.
In an orthogonal machining with a tool of 9° orthogonal rake angle, the uncut chip thickness is 0.2mm. The chip thickness fluctuates between 0.25 mm and 0.4 mm. The ratio of the maximum shear angle to the minimum shear angle during machining is ___________
α = 9^{o}
t_{1} = 0.2mm
t_{c} = 0.25mm to 0.4mm
if t_{c} = 0.25mm, r = 0.8 and Ø = 42.08^{o}
if t_{c} = 0.4mm, r = 0.5 and Ø = 28.18^{o}
A cylindrical pin of diameter is electroplated. Plating thickness is 2.0^{+}^{0.005} mm. Neglecting the gauge tolerance, the diameter (in mm, up to 3 decimal points accuracy) of the GO ring gauge to inspect the plated pin is _________.
Diameter of GO end of ring gauge = 25.02 + 2(2.005) = 29.030mm
A helical compression spring made of wire of circular crosssection is subjected to a compressive load. The maximum shear stress induced in the crosssection of the wire is 24 MPa. For the same compressive load, if both the wire diameter and the mean coil diameter are doubled, the maximum shear stress (in MPa) induced in the crosssection of the wire is _____.
P_{1}=P_{2} , d_{2} = 2d_{1} , D_{2} =2D_{1}
In a counterflow heat exchanger, water is heated at the rate of 1.5kg/s from 40°C to 80°C by an oil entering at 120°C and leaving at 60°C. The specific heats of water and oil are 4.2kJ/kg.K and 2kJ/kg.K respectively. The overall heat transfer coefficient is 400 W/m2.K. The required heat transfer surface area (in m^{2}) is
Given counter flow Heat Exchanger
The rod PQ of length L = √2 m, and uniformly distributed mass of M = 10 kg, is released from rest at the position shown in the figure. The ends slide along the frictionless faces OP and OQ. Assume acceleration due to gravity, g = 10 m/s^{2}. The mass moment of inertia of the rod about its centre of mass and an axis perpendicular to the plane of the figure is (ML^{2}/12). At this instant, the magnitude of angular acceleration (in radian/s^{2}) of the rod is ____________
M = 10kg, g=10m/sec^{2 }
A steel plate, connected to a fixed channel using three identical bolts A, B and C, carries a load of 6kN as shown in the figure. Considering the effect of direct load and moment, the magnitude of resultant shear force (in kN) on bolt C is.
Resultant shear at ' C ' =2+15=17 kN.
Resultant shear=15+2=17 kN.
The volume and temperature of air (assumed to be an ideal gas) in a closed vessel is 2.87 m^{3} and 300K, respectively. The gauge pressure indicated by a manometer fitted to the wall of the vessel is 0.5bar. If the gas constant of air is R = 287 J/kg. K and the atmospheric pressure is 1 bar, the mass of air (in kg) in the vessel is
V = 2.87m^{3} , T = 300K
P_{gauge} = 0.5bar
R = 287 J/kg.K
P_{atm} = 1 bar
P_{abs} = P_{g} + P_{atm} = 1.5 bar
PV = mRT
For the laminar flow of water over a sphere, the drag coefficient C_{F} is defined as
C_{F} = F /(ρU^{2} D^{2}) , where F is the drag force, r is the fluid density, U is the fluid velocity and D is the diameter of the sphere. The density of water is 1000 kg/m^{3}. When the diameter of the sphere is 100mm and the fluid velocity is 2m/s, the drag coefficient is 0.5. If water now flows over another sphere of diameter 200mm under dynamically similar conditions, the drag force (in N) on this sphere is _____________
Given that the condition is dynamic similarity, and in the given condition, Inertia and viscous force plays major role, hence Reynold‟s number should be same for both model and prototype.
(Re)_{1} = (Re)_{2}
In the first case:
U_{1} = 2m/sec, D_{1} = 100 mm, ρ = 1000 kg/m^{3}
In the second case: U_{2} = 2m/s , D_{2}= 200mm, ρ = 1000kg/m^{3}
Since same water is flowing over both sphere
μ_{1} = μ_{2} , ρ_{1} = ρ_{2}
U_{1}D_{1} = U_{2}D_{2}
A rod of length 20mm is stretched to make a rod of length 40 mm. Subsequently, it is compressed to make a rod of final length 10mm. Consider the longitudinal tensile strain as positive and compressive strain as negative. The total true longitudinal strain in the rod is
ℓ_{1} = 20mm ℓ_{f} =10mm
∴ true strain,
A gear train shown in the figure consists of gears P, Q, R and S. Gear Q and gear R are mounted on the same shaft. All the gears are mounted on parallel shafts and the number of teeth of P, Q, R and S are 24, 45, 30 and 80, respectively. Gear P is rotating at 400 rpm. The speed (in rpm) of the gear S is _________.
T_{p} = 24 , T_{Q} = 45 , T_{R} = 30, T_{S}= 80
N_{p }= 400rpm
N_{p}.T_{p} = N_{Q}.T_{Q}
In the Rankine cycle for a steam power plant the turbine entry and exit enthalpies are 2803 kJ/kg and 1800 kJ/kg, respectively. The enthalpies of water at pump entry and exit are 121 kJ/kg and 124 kJ/kg, respectively. The specific steam consumption (in kg/k W.h) of the cycle is ______
Given that
h_{1} = 2803kJ/kg , h_{2} = 1800kJ/kg
h_{3} = 121kJ/kg , h_{4} = 124kJ/kg
W_{T} = h_{1 } h_{2}
= 2803  1800 = 1003kJ / kg
W_{p} = h_{4}  h_{3}
= 124 121 = 3kJ/kg
W_{net} = W_{T}  W_{p }= 1000Kj/kg
Specific Steam consumption =
A calorically perfect gas (specific heat at constant pressure 1000 J/kg.K) enters and leaves a gas turbine with the same velocity. The temperatures of the gas at turbine entry and exit are 1100 K and 400 K. respectively. The power produced is 4.6 MW and heat escapes at the rate of 300 kJ/s through the turbine casing. The mass flow rate of the gas (in kg/s) through the turbine is.
Given that
C_{p} = 1000J/kgK
T_{1} = 1100K P=4.6MW
T_{2} = 400K Q_{L} = 300kJ/s
Three masses are connected to a rotating shaft supported on bearings A and B as shown in the figure. The system is in a space where the gravitational effect is absent. Neglect the mass of shaft and rods connecting the masses. For m_{1} = 10kg, m_{2} = 5kg and m_{3} = 2.5 kg and for a shaft angular speed of 1000 radian/s, the magnitude of the bearing reaction (in N) at location B is _________.
m_{1} = 10kg r_{1} = 0.1m
m_{2} = 5kg, r_{2} = 0.2m
m_{3} = 2.5, r_{3} = 0.4m
A strip of 120 mm width and 8mm thickness is rolled between two 300 mmdiameter rolls to get a strip of 120 mm width and 7.2 mm thickness. The speed of the strip at the exit is 30 m/min. There is no front or back tension. Assuming uniform roll pressure of 200 MPa in the roll bite and 100% mechanical efficiency, the minimum total power (in kW) required to drive the two rolls is _________.
Width = 120mm
Initial thickness to = 8mm
Diameter of Roller = 300mm
Radius of Roller = 150mm
Final thickness = 7.2mm
Δh = t_{i}  t_{f} = 8  7.2= 0.8
Power require to drive one roller
So, power require to drive 2 roller = 2P = 2 x 4.8 kW = 9.6 kW
A product made in two factories p and Q, is transported to two destinations, R and S. The per unit costs of transportation (in Rupees) from factories to destinations are as per the following matrix:
Factory P produces 7 units and factory Q produces 9 units of the product. Each destination requires 8 units. If the northwest corner method provides the total transportation cost as X (in Rupees) and the optimized (the minimum) total transportation cost Y (in Rupees), then (XY), in Rupees, is
Total minimum Cost,
y = 3×8+4×1+7×7=Rs.77
So, x–y = Rs.28
One kg of an ideal gas (gas constant R = 287 J/kg.K) undergoes an irreversible process from state1 (1 bar, 300 K) to state 2 (2 bar, 300 K). The change in specific entropy (s_{2} – s_{1}) of the gas (in J/kg. K) in the process is ___________
Given
m =1kg, R = 287J/kg.K
P_{1}=1bar, P_{2}= 2bar
T_{1}= 300K, T_{2}= 300K
∴Same Temperature
A 60 mmdiameter water jet strikes a plate containing a hole of 40mm diameter as shown in the figure. Part of the jet passes through the hole horizontally, and the remaining is deflected vertically. The density of water is 1000 kg/m^{3}. If velocities are as indicated in the figure, the magnitude of horizontal force (in N) required to hold the plate is _________
Force in X–direction = Rate of change of momentum =
(P_{i}  P_{f} )_{xdirection}
= (m_{1}V_{1}  m_{2}V_{2})_{xdirection}
= V(ρA_{1}V_{1}  ρA_{2}V_{2}) (∵ V_{1} = V_{2} )
The arrangement shown in the figure measures the velocity V of a gas of density 1 kg/m^{3 } flowing through a pipe. The acceleration due to gravity is 9.81 m/s2. If the manometric fluid is water (density 1000 kg/m^{3}) and the velocity V is 20 m/s, the differential head h (in mm) between the two arms of the manometer is ____________
Given
ρ_{g} = 1kg/m^{3} , g = 9.81m/s^{2}
ρ_{m} = 1000kg/m^{3 }, V=20m/s
h= 0.0204m = 2.04cm ∴h = 20.4mm
A metal ball of diameter 60mm is initially at 220 °C. The ball is suddenly cooled by an air jet of 20°C. The heat transfer coefficient is 200 W/m^{2}.K and 9000kg/m^{3}, respectively. The ball temperature (in °C) after 90 seconds will be approximately.
D = 60mm = 0.06m
T_{i} = 220^{o }C, h = 200W/m^{2}K
ρ = 9000Kg/m^{3}
T_{∝} = 20^{o}C , C_{p} = 400J/Kgk
K= 400W/mK , t = 90sec
T= ?
A single – plate clutch has a friction disc with inner and outer radii of 20mm and 40 mm, respectively. The friction lining in the disc is made in such a way that the coefficient of friction m varies radially as μ = 0.01r, where r is in mm. The clutch needs to transmit a friction torque of 18.85kN.mm. As per uniform pressure theory, the pressure (in MPa) on the disc is 
r_{i} = 20mm , r_{o} = 40mm , μ = 0.01r
T = 18.85kNmm
p = ?
The surface integral over the surface S of the sphere x^{2} + y^{2} + z^{2} = 9, where F=(x+y) i+ (x+z) j+(y+z) k and n is the unit outward surface normal, yields ______.
Block 2 slides outward on link 1 at a uniform velocity of 6 m/s as shown in the figure. Link 1 is rotating at a constant angular velocity of 20 radian/s counterclockwise. The magnitude of the total acceleration (in m/s^{2}) of point P of the block with respect to fixed point O is 
Acceleration of the block,
v = 6m / sec, ω = 20rad / sec
r = OP,
a_{cr} = 2vω = 2 x 6 x 20 = 240m/s^{2}
a_{r} = ω^{2}r = (20)^{2} x 0.1 = 40
During the turning of a 20mmdiameter steel bar at a spindle speed of 400 rpm, a tool life of 20 minute is obtained. When the same bar is turned at 200 rpm, the tool life becomes 60 minute. Assume that Taylor‟s tool life equation is valid. When the bar is turned at 300 rpm, the tool life (in minute) is approximately.
Taylors Tool life equation,
VT^{n} = C
∴ V_{1}T_{1} = V_{2}T_{2}^{n}
T_{3} =31.57 minutes
T_{3} =32 minutes
Consider the matrix A = whose eigenvectors corresponding to eigenvalues λ_{1 }and λ_{2} are x_{1} = and x_{2} = respectively. The value of x_{1}^{T}x_{2 } is 
The radius of gyration of a compound pendulum about the point of suspension is 100mm. The distance between the point of suspension and the centre of mass is 250mm. Considering the acceleration due to gravity as 9.81 m/s^{2}, the natural frequency (in radian/s) of the compound pendulum is _________.
k = 100mm = 0.1m
L = 250mm = 0.250m
g = 9.81m/sec
I= mK^{2} = m(0.1)^{2}
Consider the differential equation 3y"( x ) + 27 y ( x )= 0 with initial conditions y(0) = 0 and y '(0) = 2000. The value of y at x = 1 is ________.
3y"(x)+27y(x) = 0 , y(0) = 0 , y'(0) = 2000
Auxillary equation, 3m^{2} + 27 = 0
⇒m^{2}+ 9 = 0 ⇒m = 0 +3i
If f(z) = (x^{2}+ay^{2}) + ibxy is a complex analytic function of z = x + iy, where , then
Given f ( z ) = ( x^{2} + ay^{2} ) + i bxy is analytic
value u= x^{2 }+ ay , v = bxy
Clearly for b = 2 and a= –1 above CauchyRiemann equations holds
A project starts with activity A and ends with activity F. The precedence relation and durations of the activities are as per the following table:
The minimum project completion time (in days) is ______
∴ Minimum project completion Time = Length of longest path = 4+3+14+9=30 Days.
Maximize Z = 5x_{1}+3x_{2 }
Subject to
x_{1} + 2x_{2} ≤ 10,
x_{1}  x_{2 }≤ 8,
x_{1} , x_{2} ≥ 0.
In the starting Simplex tableau, x_{1} and x_{2} are nonbasic variables and the value of Z is zero. The value of Z in the next Simplex tableau is _________.
1^{st} Table at (0,0) → Z = 0
2^{nd }Table at (8,0)→ Z = 40
The principal stresses at a point in a critical section of a machine component are σ_{1}= 60MPa, σ_{2}= 5MPa and σ_{3} = 40 MPa. For the material of the component, the tensile yield strength is σ_{y} = 200 MPa. According to the maximum shear stress theory, the factor of safety is
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