Properties of Matter
Q.1 An iron rod of length 1m and cross-sectional area 0.1 cm2 with Young’s modules 1011N/m2 is to be pulled by applying force on its two ends so as to produce an elongation of 1mm. The force on each end is
(a) 1000N (b) 500N (c) 2000N (d) 100N
Q.2 Four wires of the same material are stretched by the same load. The dimensions are given below. Which of them will elongate the most?
(a) length 100cm, diameter 1mm (b) length 200cm, diameter 2mm
(c) length 300cm, diameter 3mm (d) length 400cm, diameter 0.5mm
Q.3 A wire can be broken by applying a load of 10kg wt. The force required to break the wire of the same material but the twice the diameter and of the same length is
(a) 5kg wt. (b) 10kg wt. (c) 20kg wt. (d) 40kg wt.
Q.4 A cable capable of supporting a load W is cut to half of its original length. The maximum load it can support now is
(a) W/2 (b) W (c) 2W (d) 4W
Q.5 A spring of force constant k is cut into two equal pieces. The force constant of each piece is
(a) k/2 (b) k (c) 2k (d) 4k
Q.6 If a gas is heated at constant pressure; its isothermal compressibility
(a) remains constant (b) increase linearly with temperature
(c) decrease linearly with temperature (d) increase inversely with temperature
Q.7 Two rods of different material having coefficients of liner expansion a1, a2 and Youngs modules Y1and Y2 respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of rods, if a1:a2=2:3, the thermal stresses developed in the two rods are equal provided Y1:Y2 is equal to
(a) 2:3 (b) 1:1 (c) 3:2 (d) 4:9
Q.8 A uniformly tapering vessel of height h whose lower and upper radii are r and R is completely filled with a liquid of density s. The force that acts on the base of the vessels due to the liquid is
(a) 1/3p (R2-r2) hsg (b) pr2 hsg
(c) pR2 hsg (d) p[r+R/2]2hsg
Q.9 An open vessel containing some liquid is given a constant acceleration a in the horizontal direction. The free surface of the liquid gets sloped with the horizontal at an angle q given by
(a) tan q =a/g (b) tan q =g/a (c) sin q =a/g (d) cos q =g/a
Q.10 A U-tube stands vertically such that its arm A is towards left and arm B is towards right and the distance AB is L. When it is at rest, a liquid stands at the same height is the two arms i.e., HA=HB. If the tube is given an acceleration a towards right, then
(a) HA=HB+ gL/a (b) HA =HB +aL/g
(c) HB=HA+ gL/a (d) HB =HA +aL/g
Q.11 When an air bubble rises from the bottom of a lake to the surface, its radius doubles. If the atmospheric pressure is equal to the column of water of height H. the depth of the lake is
(a) H (b) 2H (c) 7H (d) 8H
Q.12 A body is carrying a wood block weighing 0.1kg (density 500kg/m3) in his left-hand and a bucket partly filled with water and weighing 10kg in his right-hand. The boy drops the block in water of bucket so that the block starts floating. The load the boy is now carrying is
(a) 10kg (b) 9.9kg (c) 10.1kg (d) 10.2kg
Q.13 A body is partly floating in a liquid. The whole system falls freely under gravity. The up thrust on the body due to the liquid is
(a) zero
(b) equal to weight of liquid displaced
(c) equal to weight of the body in air
(d) equal to weight of the immersed portion of the body.
Q.14 A balloon filled with air is weighed so that it barely floats on water. When it is pushed down so that it gets submerged a short distance in water than the balloon will
(a) come up again to its former position
(b) remain in the position where it is left
(c) sink to the balloon
(d) emerge on the liquid
*Q.15 A fluid is flowing through a pipe. Its cross - sectional area decrease from A1 and A2.
(a) If the fluid is non-compressible, the velocity increase in the ratio of A1/ A2
(b) If the fluid is compressible, the velocity may remain constant provided its density varies as r1/r2 = A2/A1
(c) If the fluid is non-compressible, its pressure increase as it enters into narrower region
(d) If the fluid is viscous, then Bernoulli’s theorem is not applicable but equation of continuity still holds good
Q.16 Water is floating through a system of two tubes joined one after the other. The radius of first tubes is double that of the second tube, but the length of the two tubes are equal. Then if the pressure difference across the first tube is p1 and across the second tube is p2 then
(a) p2/p1=1 (b) p2/p1=2 (c) p2/p1=4 (d) p2/p1=16
Q.17 A small drop of water falls from rest through a great height h in air. The final velocity of drop is
(a) almost independent of h (b) proportional to Öh
(c) proportional to h (d) inversely proportional
Q.18 A compressible fluid flows steadily through a pipe of cross-sectional area A1 and out of a narrowed opening of area A2 = A1/5. If its density at a certain point P in the pipe is twice its density at the outlet Q and if its speed at P is 2m/s, the speed at the outlet Q is
(a) 2m/s (b) 5m/s (c) 10m/s (d) 20m/s
Q.19 A liquid can easily change its shape but a solid can not because
(a) the density of a liquid is smaller than that of a solid
(b) the forces between the molecules is stronger in sold than in liquids
(c) the atoms combine to form bigger molecules in a solid
(d) the average separation between the molecules is larger in solids.
Q.20 Consider the equations
P = Lim F/DS and P1 – P2 = rgz
In an elevator accelerating upward
(a) both the equations are valid (b) the first is valid but not the second
(c) the second is valid but not the first (d) both are invalid.
Q.21 Equal mass of three liquids are kept in three identical cylindrical vessels A, B and C. The densities are rA , rB, rc with rA < rB < rc. The force on the base will be
(a) maximum in vessel A (b) maximum in vessel B
(c) maximum in vessel C (d) equal in all the vessels.
Q.22 A beaker containing a liquid is kept inside a big closed jar. If the air inside the jar is continuously pumped out, the pressure in th4e liquid near the bottom of the liquid will
(a) increase (b) decrease
(c) remain constant (d) first decrease and then increase.
Q.23 The pressure in a liquid at two points in the same horizontal plane are equal. Consider an elevator accelerating upward and a car accelerating on a horizontal road. The above statements is correct in
(a) the car only (b) the elevator only (c) both of them (d) neither of them
Q.24 Suppose the pressure at the surface of mercury in a barometer due is P1 and the pressure at the surface of mercury in the cup is P2.
(a) P1 = 0, P2 = atmospheric pressure
(b) P1 = atmospheric pressure, P2 = 0
(c) P1 = P2 = atmospheric pressure
(d) P1 = P2 = 0
Q.25 A barometer kept in an elevator reads 76 cm when it is at rest. If the elevator goes up with increasing speed, the reading will be
(a) zero (b) 76 cm (c) < 76 cm (d) > 76 cm.
Q.26 A barometer kept in an elevator accelerating upward reads 76 cm. The air pressure in the elevator is
(a) 76 cm (b) < 76 cm (c) > 76 cm (d) zero.
Q.27 To construct a barometer, a tube of length 1 m is filled completely with mercury and is inverted in a mercury cup. The barometer reading on a particular day is 76 cm. Suppose a 1 m tube is filled with mercury up to 76 cm and then closed by a cork. It is inverted in a mercury column in the tube over the surface in the cup will be
(a) zero (b) 76 cm (c) >76 cm (d) < 76 cm.
Q.28 A 20 N metal block is suspended by a spring balance. A beaker containing some water is placed on a weighing machine which reads 40 N. The spring balance is now lowered so that the block gets immersed in the water. The spring balance now reads 16 N. The reading of the weighing machine will be
(a) 36 N (b) 60 N (c) 44 N (d) 56 N.
Q.29 A piece of wood is floating in water kept in a bottle. The bottle is connected to an air pump. Neglect the compressibility of water. When more air is pushed into the bottle from the pump, the piece of wood will float with
(a) larger part in the water (b) lesser part in the water
(c) same part in the water (d) it will sink.
Q.30 A metal cube is placed in an empty vessel. When water is filled in the vessel so that the cube is completely immersed in the water, the force on the bottom of the vessel in contact with the cube
(a) will increase (b) will decrease
(c) will remain the same (d) will become zero.
Q.31 A closed cubical box is completely filled with water and is accelerated horizontally towards right with an acceleration a. The resultant normal force by the water on the top of the box
(a) passes through the center of the top
(b) passes through a point to the right of the center
(c) passes through a point to the left of the center
(d) becomes zero.
Q.32 Consider the situation of the previous problem. Let the water push the left wall by a force F1 and the right wall by a force F2.
(a) F1 = F2
(b) F1 > F2
(c) F1 < F2
(d) The information is insufficient to know the relation between F1 and F2.
Q.33 Water enters through end A with a speed v1 and leaves through end B with a speed v2 of a cylindrical tube AB. The tube is always completely filled with water. In case I the tube is horizontal, in case II it is vertical with the end A upward and in case III it is vertical with the end B upward. We have v1 = v2 for
(a) case I (b) case II (c) case III (d) each case.
Q.34 Bernoulli’s theorem is based on conservation of
(a) momentum (b) mass
(c) energy (d) angular momentum.
Q.35 Water is flowing through a long horizontal tube. Let PA and PB be the pressures at two points A and B of the tube.
(a) PA must be equal to PB.
(b) PA must be greater than PB.
(c) PA must be smaller than PB.
(d) PA = PB only if the cross-sectional area at A and B are equal.
Q.36 Water and mercury are filled in two cylindrical vessels up to same height. Both vessels have a hole in the wall near the bottom. The velocity of water and mercury coming out of the holes are v1 and v2 respectively.
(a) v1 = v2 (b) v1 = 13.6 v2
(c) v1 = v2/13.6 (d) v1 = Ö13.6 v2.
Q.37 A larger cylindrical tank has a hole of area A its bottom. Water is poured in the tank by a tube of equal cross-sectional area A ejecting water at the speed v.
(a) The water level in the tank will keep on rising.
(b) No water can be stored in the tank.
(c) The water level will rise to height v2/2g and then stop.
(d) The water level will oscillate.
Q.38 A rope 1 cm in diameter breaks if the tension in it exceeds 500 N. The maximum tension that may be given to a similar rope of diameter 2 cm is
(a) 500 N (b) 250 N (c) 1000 N (d) 2000 N.
Q.39 The breaking stress of wire depends on
(a) material of the wire (b) length of the wire
(c) radius of the wire (d) shape of the cross-section.
Q.40 A wire can sustain the weight of 20 kg before braking . If the wire is cut into two equal parts, each part can sustain a weight
(a) 10 kg (b) 20 kg (c) 40 kg (d) 80 kg.
Q.41 Two wires A and B are made of same material. The wire A has a length l and diameter r while the wire B has a length 2l and diameter r/2. If the two wires are stretched by the same force, the elongation in A divided by the elongation in B is
(a) 1/8 (b) ¼ (c) 4 (d) 8.
Q.42 A wire elongates by 1.0 mm when a load W is hanged from it. If this wire goes over a pulley and two weights W each are hung at the two ends, the elongation of the wire will be
(a) 0.5 m (b) 1.0 mm (c) 2.0 mm (d) 4.0 mm.
Q.43 A heavy uniform rod is hanging vertically from a fixed support. It is stretched by its own weight. The diameter of the rod is
(a) smallest at the top and gradually increases down the rod
(b) largest at the top and gradually decreases down the rod
(c) uniform everywhere
(d) maximum in the middle.
Q.44 When a metal wire is stretched by a load, the fractional change in its volume DV/V is proportional to
(a) Dl/ l (b) (Dl/l)2 (c) ÖDl/l (d) none of these.
Q.45 The length of a metal wire is l1 when the tension in it is T1 and is l2 when the tension is T2. The natural length of the wire is
(a) l1 + l2 /2 (b) Öl1 l2
(c) l1T2 - l2T1/T2 – T1 (d) l1T2 + l2T1/T2 + T1.
Q.46 A heavy mass is attached to a thin wire and is whirled in a vertical circle. The wire is most likely to break
(a) when the mass is at the highest point
(b) when the mass is at the lowest point
(c) when the wire is horizontal
(d) at an angle of cos-1 (1/3) from the upward vertical.
Q.47 When a metal wire elongates by hanging a load on it, the gravitational potential energy is decreased.
(a) This energy completely appears as the increased kinetic energy of the block.
(b) This energy completely appears as the increased elastic potential energy of the wire.
(c) This energy completely appears as heat.
(d) None of these.
Q.48 By a surface of a liquid we mean
(a) geometrical plane like x = 0
(b) all molecules exposed to the atmosphere
(c) a layer of thickness of the order of 10-8 m
(d) a layer of thickness of the order of 10-4 m.
Q.49 An ice cube is suspended in vacuum in a gravity free hall. As the ice melts it
(a) will retain its cubical shape
(b) will change its shape to spherical
(c) will fall down on the floor of the hall
(d) will fly up.
Q.50 When water droplets merge to form a bigger drop
(a) energy is liberated (b) surface tension
(c) energy is neither liberated nor absorbed
(e) energy may either be liberated or absorbed depending on the nature of the liquid.
Q.51 The diameter ML-1T-2 can correspond to
(a) moment of force (b) surface tension
(c) modulus of elasticity (d) coefficient of viscosity.
Q.52 Air is pushed into a soap bubble of radius r to double its radius. If the surface tension of the soap solution is S, the work done in the process is
(a) 8pr2S (b) 12p r2S (c) 16 p r2S (d) 24 p r2S.
Q.53 If more air is pushed in a soap bubble, the pressure in it
(a) decreases (b) increases
(c) remains same (d) becomes zero.
Q.54 If two soap bubbles of different radii are connected by a tube,
(a) air flows from bigger bubble to the smaller bubble till the sizes become equal
(b) air flows from bigger bubble to the smaller bubble till the sizes are interchanged
(c) air flows from the smaller bubble to the bigger
(d) there is no flow of air.
Q.55 The excess pressure inside a soap bubble is twice the excess pressure inside a second soap bubble. The volume of the first bubble is n time the volume of the second where n is
(a) 4 (b) 2 (c) 1 (d) 0.125.
Q.56 Water rises in a vertical capillary tube upto a length of 10 cm. If the tube is inclined at 45°, the length of water risen in the tube will be
(a) 10 cm (b) 10Ö2 cm (c) 10/Ö2 cm (d) none of these.
Q.57 A 20 cm long capillary tube is dipped in water. The water rises up to 8 cm. If the entire arrangement is put in a freely falling elevator, the length of water column in the capillary tube will be
(a) 8 cm (b) 6 cm (c) 10 cm (d) 20 cm.
Q.58 viscosity is a property of
(a) liquids only (b) solids only
(c) solids and liquids only (d) liquids and gases only.
Q.59 The force of viscosity is
(a) electromagnetic (b) gravitational
(c) nuclear (d) weak.
Q.60 The viscous force acting between two layers of a liquid is given by F/A = - h dv/dz This F/A may be called
(a) pressure (b) longitudinal stress
(c) tangential stress (d) volume stress.
Q.61 A raindrop falls near the surface of the earth with almost uniform velocity because
(a) its weight is negligible
(b) the force of surface tension balances its weight
(c) the force of viscosity of air balances its weight
(d) the drops are charged and atmospheric electric field balances its weight.
Q.62 A piece of wood is taken deep inside a long column of water and released. It will move up
(a) with a constant upward acceleration
(b) with a decreasing upward acceleration
(c) with a deceleration
(d) with a uniform velocity
Q.63 A solid sphere falls with a terminal velocity of 20 m/s in air. If it is allowed to fall in vacuum,
(a) terminal velocity will be 20 m/s
(b) terminal velocity will be less than 20 m/s
(c) terminal velocity will be more than 20 m/s
(d) there will be no terminal velocity.
ANSWER SHEET
1.
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(a)
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2.
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(d)
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3.
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(d)
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4.
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(c)
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5.
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(c)
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6.
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(a)
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7.
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(c)
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8.
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(b)
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9.
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(a)
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10.
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(b)
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11.
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(c)
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12.
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(c)
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13.
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(a)
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14.
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(c)
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15.
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(a), (b), (d)
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16.
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(d)
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17.
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(a)
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18.
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(d)
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19.
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(b)
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20.
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(b)
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21.
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(d)
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22.
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(b)
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23.
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(b)
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24.
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(a)
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25.
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(c)
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26.
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(c)
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27.
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(d)
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28.
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(c)
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29.
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(c)
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30.
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(c)
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31.
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(d)
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32.
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(b)
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33.
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(d)
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34.
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(c)
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35.
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(d)
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36.
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(a)
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37.
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(c)
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38.
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(d)
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39.
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(a)
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40.
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(b)
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41.
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(a)
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42.
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(b)
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43.
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(a)
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44.
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(a)
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45.
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(c)
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46.
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(b)
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47.
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(d)
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48.
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(c)
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49.
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(b)
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50.
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(a)
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51.
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(c)
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52.
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(d)
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53.
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(a)
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54.
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(c)
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55.
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(d)
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56.
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(b)
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57.
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(d)
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58.
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(d)
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59.
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(a)
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60.
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(c)
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61.
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(c)
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62.
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(b)
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63.
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(d)
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