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Quiz 8
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Q.1
Four rods of same material are taken. the length l and radius of cross-section r are given below. In which rod the heat flow will be maximum when temperature difference across the end rods is same under steady state? [ MPPMT 1987]
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a)l=50 cm, r=0.5 cm
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b) l=100 cm, r=1.0 cm
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c)l=75 cm, r=1.5 cm
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d)l=100 cm, r=2.0 cm
Explanation
Formula for heat conducted by rod is Here K=coefficient of thermal conductivity,A=Area normal to the heat flowθ1 - θ2=Temperature differencet=timed=length of the rodThus if A/d is maximum Q is max or r2 /d is maximum Q is maximumFor option 'd'; r2 /d is maximumAnswer: (d)
Q.2
Solar radiation emitted by sun resembles that emitted by a black body at a temperature of 6000K. Maximum intensity is emitted at wave length of about 4800 Å. if the sun were to cool down from 6000K to 3000K, then the peak intensity would occur at a wave length [ MPPMT 1991]
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a) 4800
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b) 9600
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c)2400
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d)19200
Explanation
According to Wien's displacement law λmax T=constant Thus λ1T1=λ2T2 4800×6000=λ2×3000λ2=9600 Answer:(b)
Q.3
Equal temperature difference exists between the ends of two metallic rods 1 and 2 of equal length. their thermal conductivity is K1 and K2 and cross-sectional areas are respectively A1 and AThe condition for equal rate of heat transfer will be [ MPPMT 1991]
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a) K1 / A1=K2/A2
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b) K1 A22=K2 A12
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c) K1 A1=K2 A2
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d) K1 A12=K2 A22
Explanation
Rate of heat conducted by rod is given by given same length same temperature difference thus Rate of heat transfer ∝ KA Answer: (c)
Q.4
The speediest mode of heat transfer is [ MPPMT 1994]
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a)conduction
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b) convection
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c)radiation
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d)combustion
Explanation
Answer: (c)
Q.5
The coefficient of thermal conductivity of copper, mercury and glass are respectively Kc., Km and Kg such that Kc>Km>Kg. If the same quantity of heat is to flow per sec unit area of each and corresponding temperature gradients are Xc,Xm and Xg[ MPPMT 1990]
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c)Xc < Xm < Xg
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a) Xc=Xm=Xg
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b) Xc > Xm > Xg
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d)Xm < Xc < Xb
Explanation
From the formula for the rate of conduction of heat Here Q/At is the rate of flow of heat per second per unit time given that it is same for all materials and X is temperature gradient Thus X∝ (1/K) So option (c) is correctAnswer: (c)
Q.6
Ice starts forming in a lake with water at 0°C, when the atmospheric temperature is -10°C. If the time taken for 1cm of ice to be formed in 7 hrs, the time taken for the thickness of ice to change from 1cm to 2 cm is [ MPPT 1988]
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a) 7 hours
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b) Less than 7 hours
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c)more than 7 hours but less than 14 hours
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d)more than 14 hours
Explanation
coefficient of thermal conductivity of ice is very small therefore heat from water will not transfer to atmosphere through ice form in the lake Answer:(d)
Q.7
A wall has two layers A and B each made of different material. Both the layers have the same thickness. The thermal conductivity of the material of A is twice that of B. Under thermal equilibrium, the temperature difference across the wall is 36°C. The temperature difference across the layer A is [ IIT 1980]
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a) 6°C
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b) 12°C
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c) 18°C
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d) 24°C
Explanation
At equilibrium rate of flow of heat through both the layers is same given that K1=2K2Thus 2(θ1-θ)=θ - θ2 --eq(1) Given that θ1 - θ2=36 θ2 = θ1 + 36 Substituting value of θ2 in equation (1) we get 2θ1 -2θ = θ - θ1 + 36 3(θ1-θ) =36 θ1 - θ=12Answer: (b)
Q.8
A piece of blue glass heated to high temperature and piece of red glass at room temperature are taken inside a dim-light room then
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a)the blue piece will look blue and the red piece will look red as usual
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b) the red piece will look brighter red and the blue piece will look ordinary blue
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c)the blue piece will look brighter as compared to the red piece
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d)both the pieces will look equally red
Explanation
blue colour is good absorber and radiator of heat compared to redAnswer: (c)
Q.9
A cylinder of radius R made of a material of thermal conductivity K1 is surrounded by a cylindrical shell of inner radius R and outer radius 2R made of material of thermal conductivity KThe two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in steady state. the effective thermal conductivity of the system is [ IIT 1988]
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a) K1 + K2
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b) K1 K2 / ( K1 + K2)
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c)(K1 + 3K2 ) /4
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d)(3K1 + K2) / 4
Explanation
Rate of heat flow is given by If K is equivalent conductivity then Comparing above equations we get Answer: (c)
Q.10
For a perfectly black body, its absorptive power is [ MPPMT 1989]
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a) 1
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b) 0.5
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c)0.8
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d)2.0
Explanation
Answer:(a)
Q.11
Two idential rods of copper and iron are coated with wax uniformly. When one end of each is kept at temperature of boiling water the length upto which wax melts are 8.4 cm and 4.2cm, respectively. If thermal condutiuvity of copper is 0.92, then thermal concutivity of iron rod is [ MPPMT 1995]
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a) 0.23
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b) 0.46
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c) 0.115
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d) .69
Explanation
from Ingen Hausz Experiment for similar rod Answer: (a)
Q.12
Which of the following combinations of properties would be most desirable for cooking pot [ MPPMT 1995]
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a)high specific heat and low conductivity
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b) low specific heat and high conductivity
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c)high specific heat and high conductivity
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d)low specific heat and low conductivity
Explanation
Answer: (b)
Q.13
At a certain temperature for given wave length, the ratio of emmissive power of a body to emissive power of black body in same circumstances is known as [ Raj. PMT 1997]
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a) Relative emissivity
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b) Emissivity
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c)Absorption coefficient
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d)Coefficient of reflection
Explanation
Answer: (c)
Q.14
A object is at temperature of 400°C. At what temperature would it radiate energy twice as fast? The temperature of the surroundings may be assumed to be negligible [ MPPT 1990]
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a) 200 °C
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b) 200K
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c)800°C
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d)800 K
Explanation
From Stefan's law radiation emitted per-second per unit area E∝T4 400°C = 400+273 = 673K Let 2E ∝ (x)4 taking ratio of E∝ T4 and 2E ∝ X4 2T4 = X4 ∴ x = 21/4 T x = 1.189 × 683K x = 800.197K Answer:(d)
Q.15
A piece of glass is heated to high temperature and then allowed to cool. If it cracks, a probable reason for this is the following property of glass [ CPMT 1985]
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a) low thermal conductivity
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b) high thermal conductivity
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c) high specific heat
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d) high melting point
Explanation
Answer: (a)
Q.16
Certain substance emits only the wave lengths λ1, λ2, λ3 and λ4 when it is at high temperature. When this substance is at a colder temperature it will absorb only the following wave lengths [ PET 1990]
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a)λ1
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b) λ1 and λ2
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c)λ2
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d)λ1, λ2, λ3 and λ4
Explanation
Answer: (d)
Q.17
Two stars A and B radiate maximum energy at 3600Å and 4800Å respectively. Then the ratio of absolute temperature of A and B is [ MPPMT 1991]
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a) 4 : 3
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b) 3 : 4
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c)256 : 81
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d)81 : 256
Explanation
According to Wien's dispacement law λmaxT=constant λ2 /λ1=T1 / T2 T1 / T2=4800/3600=4/3Answer: (a)
Q.18
Two walls of thickness d1 and d2 and thermal condutivities k1 and k2 are in contact. in the steady state, if the temperatures at the outer surface are T1 and TThe temperature at the common wall is [ CPMT 1998]
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a)
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b)
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c)
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d)
Explanation
Let the interface temperature be T, then Answer:(a)
Q.19
The ends of two rods of different materials with their thermal conductivities, radii of cross-sections and lengths all are in ratio 1 : 2 are maintained at the same temperature difference. If the rate of flow of heat in the larger rod is 4 cal/sec, then in the shorter rod in cal/sec will be [ EAMCET 1986]
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a) 1
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b) 2
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c) 8
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d) 16
Explanation
Given d1=2d2radii r1=2r2 ∴ A1=4A2k1=2k2 formula for rate of flow of heat Answer: (a)
Q.20
A cylindrical rod with one in a steam chamber and the other end in ice results in melting of 0.1gm of ice per second. If the rod is replaced by another with half the length and double the radius of the first and if the thermal conductivity of material of second rod is (1/4) that of first, the rate at which ice melts in gm/sec will be [ EAMCET 1987]
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a)3.2
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b) 1.6
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c)0.2
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d)0.1
Explanation
Rate at which heat flows in rod=rate at which ice receives heat Here L is latent heat offusion for ice L=80For longer rod For shorter rod By taking ratio of above equation we get 0.1/m=1/2 m=0.2 gm Answer: (c)
Q.21
Two spheres of different materials, one with double the radius and one-fourth wall thickness of the other, are filled with ice. If the time taken for complete melting of ice in the larger radius one is 25 minutes and that for smaller one in 16 minutes, the ratio of thermal conductivities of the materials of larger sphere to the smaller sphere is [ EAMCET 1991]
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a) 4 : 5
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b) 5 : 4
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c)25 : 8
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d)8 : 25
Explanation
Amount of heat conducted through sphere=amount of heat absorbed by ice for melting . If L is the latent heat of melting, ρ is density of ice, V is volume of sphere Smaller sphere:Large sphere :r2=2 r1d2=¼ d1Taking the ratio of above equationsk2 / k1=8 : 25Answer: (d)
Q.22
One end of a copper rod of length 1.0m and area of cross-section 10-3 m2 is immersed in boiling water and the other end in ice. If the coefficient of thermal conductivity of copper is 92 cal/m/s/°C and the latent heat of ice is 8×104 cal/kg, then the amount of ice which will melt in one minute is [ MNR 1994]
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a) 9.2 × 10-3 kg
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b) 8 × 10-3 kg
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c) 6.9 × 10-3 kg
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d) 5.4 × 10-3 kg
Explanation
Amount of heat conducted by rod = amount of heat absorbed by ice to melt L is the latent heat of fusion, m be the mass of ice melt then Answer:(c)
Q.23
Which of the following statement is wrong [ MPPMT 1993]
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a) Stefan's constant is the same for all black bodies
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b) Thermal radiations travel with the speed of 3×108 m/s
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c) Thermal radiations exhibits diffraction
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d) Stefan's law is applicable for all heated bodies
Explanation
Answer: (d)
Q.24
A sphere, a cube and a thin circular plate all made of the same material and having the same mass are heated to the same temperature of 200°C when these are left in room [ MPPMT 1993]
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a) the sphere reaches room temperature last
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b) the cube reaches room temperature last
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c) the circular plate reaches room temperature last
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d) all will reach the room temperature simultaneously
Explanation
Rate of cooling depends on surface area, sphere have smallest area for given voume Answer: (a)
Q.25
A piece of metal and a piece of wood are kept in a room at room temperature which is 45°C. On touching the two with hand [ MPPET 1993]
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a) the two will appear equally hot
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b) the piece of wood will appear hotter than the piece of metal
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c) the piece of metal will appear hotter than the piece of wood
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d) the distinction in the hotness will not be possible
Explanation
Answer: (c)
Q.26
An electric heater, kept in vacuum is heated continuously by passing electric current. Its temperature will [ MPPMT 1993]
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a) go on rising with time
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b) stop rising after some time as it will lose heat to the surrounding by conduction
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c) will rise for some time and thereafter will start falling
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d) will become constant after some time due to loss of heat by radiation
Explanation
Answer:(d)
Q.27
At specific temperature, the energy densities for black body for three different wavelengths are 10,19 and 7 units. For these wavelengths if the absorption coefficient of a body is respectively 0.8, 0.3 and 0.9, then the emissive power of this body for these wave-lengths are in the ratio
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a) 10 : 19 : 7
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b) 8 : 3 : 9
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c) 8 : 5.7 : 6.3
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d) 8 : 95 : 4.3
Explanation
According to Kirchoff's "law at any temperature and for particular wave length the ratio of the emissive power to the absorptive power of all substance is same and equal to the emissive power of perfectly black body" Thus Answer: (b)
Q.28
On investigation of light from three different stars A, B, and C it was found that in the spectrum of A, the intensity of red colour is maximum, in B, the intensity of blue colour is maximum. and in C the intensity of yellow colour is maximum. From these observations it can be concluded that [ CPMT 1989]
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a) the temperature of A is maximum, B is minimum and C is intermediate
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b) the temperature of A is maximum, C is minimum and B is intermediate
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c) the temperature of B is maximum, A is minimum and C is intermediate
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d) the temperature of C is maximum, B is minimum and A is intermediate
Explanation
Answer: (c)
Q.29
A blackened metal foil is warmed by radiation from a point source whose temperature is T and distance from the foil is d. It is found that the power received from the foil is P. If both the temperature and distance are doubled, the power received by the foil will be [ MPPMT 1997]
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a) P
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b) 2P
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c) 4P
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d) 16P
Explanation
Power P ∝T4 / d2 P' ∝ (2T)4 / (2d)2 By taking ratio of P' and P P' = 4P Answer: (c)
Q.30
Three rods of identical area of cross-section and made from the same metal, from the sides of an isosceles triangle ABC, right-angled at B. The points A and B are maintained at temperature T and (√2) T, respectively. in the steady state, the temperature of the part C is Tc. Assuming that only heat conduction takes place Tc / T is [ IIT 1995]
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a)
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b)
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c)
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d)
Explanation
For steady state HBA = HAC Answer:(a)
0 h : 0 m : 1 s
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