SURFACE TENSON
1. A bubble of 8 mm diameter is formed in the air. The surface tension of soap solution is 30 dyne/cm. The excess pressure inside the bubble is
(a) 150 dyne/cm2 (b) 300 dyne/cm2
(c) 3 ´ 10-3 dyne/cm2 (d) 12 dyne/cm2
2. The surface tension of a liquid is 5 Nm-1. If a thin film is formed on a loop of area 0.02 m2, then its surface energy will be
(a) 5 ´ 10-2 J (b) 2.5 ´ 10-2 J (c) 2 ´ 10-2 J (d) 3 ´ 10-1 J
3. The excess pressure inside an air bubble of radius r, which is inside a liquid of surface tension s is
(a) 2s/r (b) s/r (c) 4s/r (d) zero.
4. A capillary tube made of glass is dipped into mercury.
(a) mercury rise in the capillary tube
(b) mercury rises and flows out of the capillary tube
(c) mercury descends in the capillary tube
(d) mercury neither rises nor descends in the capillary tube.
5. Two tubes of same material but of different radii are dipped in a liquid. The height to which a liquid rises in one tube is 2.2 cm and in the other is 6.6 cm. The ratio of their radii is
(a) 9 : 1 (b) 1 : 9 (c) 3 : 1 (d) 1 : 3
6. Two soap bubbles, each with a radius r, coalesce in vacuum under isothermal conditions to form a bigger bubble of radius R. Then R is equal to
(a) 2-1/2r (b) 21/3r (c) 21/2r (d) 2r.
7. A liquid tens to assume a spherical shape because of
(a) the surface tension force (b) the viscous force
(c) the gravity effect (d) the elastic force.
8. The meniscus of mercury in the glass capillary tube is
(a) convex (b) concave (c) plane (d) uncertain.
9. It is difficult to write legibly with a fountain pen on a newspaper because of
(a) inertia (b) capillary action (c) elasticity(d) surface tension.
10. The potential energy of a molecule on the surface of a liquid compared to one inside the liquid is
(a) zero (b) smaller (c) the same (d) greater.
11. The angle of contact between a solid and a liquid is a characteristic property of
(a) solid only (b) liquid only (c) both the solid and liquid
(d) shape of the solid.
12. The area enclosed by a thread of a given perimeter is maximum when its shape is a
(a) Square (b) Rectangle (c) Circle (d) Ellipse.
13. Two water drops, each of radius r coalesce to from a bigger drop of radius R. Then R is equal to
(a) 2-1/2r (b) 21/3r (c) 21/3r (d) 2r.
14. If FC and FA denote cohesive and adhesive force on a liquid molecule near the surface of a solid, then the surface of liquid is convex if
(a) FA > FC/Ö2 (b) FA = FC/Ö2 (c) FA < FC/Ö2 (d) FA < FC.
15. A liquid will rise in a capillary tube if the angle of contact is
(a) < 90° (b) > 90° (c) - 90° (d) 90°.
16. The surface area of a body of given volume is least when its shape is
(a) cubic (b) ellipsoidal (c) paraboloidal (d) spherical.
17. Water rises to a height of 10 cm in a glass capillary tube. If the area of cross-section of the tube is reduced to one fourth of the former value, the water will rise to
(a) 20 cm (b) 5 cm (c) 2.5 cm (d) 40 cm
18. A liquid is contained in a vessel. The liquid-solid adhesive force is very weak as compared to the cohesive force in the liquid. The shape of the liquid surface will be
(a) horizontal (b) vertical (c) concave (d) convex
19. Two liquids drops coalesce to form a large drop. Now,
(a) energy is liberated (b) energy is neither liberated nor absorbed
(c) some mass gets converted into energy (d) energy is absorbed.
20. The lower end of a capillary tube is at a depth of 12 cm and the water rises 3cm in it. The mouth pressure required to blow an air bubble at the lower end will be x cm of water column, where x is
(a) 12 (b) 15 (c) 3 (d) 9
21. The addition of soap changes the surface tension of water to
(a) s1 > s2 (b) s1 < s2 (c) s1 = s2
(d) it is not possible to predict the above.
22. The term ‘surface of a liquid’ means
(a) a layer of thickness of the order of 10-8 m (b) a geometrically plane surface of the liquid
(b) an assembly of molecules exposed to air (d) a group of molecules on the surfaces of a liquid.
23. Water rises in a vertical glass capillary tube up to a length of 8 cm. If the tube is inclined at 45°, the length of water column in the tube will be
(a) 4 cm (b) 3 dm (c) 8Ö2 cm (d) 8/Ö2 cm
24. Water rises in a capillary tube up to a height h. Water wets the tube completely. The tube is gradually depressed into the water. The height at which the surface becomes flat is
(a) h/2 (b) 3h/4 (c) h/4 (d) zero.
25. A number of droplets, each of radius r, combine to form a drop of radius R. If T is the surface tension, then the rise in temperature will be
(a) 2T/r (b) 3T/R (c) 2T [1/r – 1/R] (d) 3T [1/r – 1/R].
26. The amount of work done in increasing size of soap film 6 cm ´ 4 cm to 12 cm ´ 8 cm is (surface tension 30 dyne /cm)
(a) 2160 erg (b) 4320 erg (c) 720 erg (d) 1440 erg
27. The amount of work done in forming a soap film of size tube 10 cm ´ 10 cm is
(a) 6 ´ 10-4 J (b) 3 ´ 10-4 J (c) 2 ´ 10-3 J (d) 3 ´ 10-2 J
28. When two soap bubbles of radii r1 and r2 (r2 > r1) coalesce, the radius of curvature of common surface is
(a) r2 – r1 (b) r2 – r1/ r1r2 (c) r1 r2/ r2 – r1 (d) r2 + r1
29. If work W is done in blowing a bubble of radius R from a soap solution, then the work done in blowing a bubble of radius 2R from the same solution is
(a) W/2 (b) 2 W (c) 4W (d) 21/3 W.
30. The surface tension of a soap solution is 2 ´ 10-2 Nm-1. To blow a bubble of radius 1 cm, the work required to be done is
(a) 4p ´ 10-6 J (b) 8p ´ 10-6 J (c) 12p ´ 10-6 J (d) 16p ´ 10-6 J
ANSWER SHEET
1.
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(b)
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2.
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(c)
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3.
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(a)
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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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(c)
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7.
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(a)
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8.
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(a)
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9.
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(b)
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10.
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(d)
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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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(b)
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14.
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(c)
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15.
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(a)
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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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(a)
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20.
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(b)
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21.
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(b)
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22.
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(a)
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23.
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(c)
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24.
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(d)
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25.
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(d)
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26.
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(b)
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27.
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(a)
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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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(d)
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SHM
Q.1 The maximum speed of a particle of mass 0.2kg executing SHM is 1.57m/s and maximum acceleration is 2.465m/s2. Then
(a) Its angular frequency is 1/1.57 rad/s (b) Its time period is 4s
(c) Its amplitude is 0.1m (d) Its total energy is 0.25J
Q.2 The displacement of a particle of mass 0.1 kg executing SHM is given by y =5sin 200t where distance are in cm and time in s.
(a) Maximum velocity is 10m/s.
(b) Acceleration at y = 2.5cm is –103m/s2
(c) Restoring force when at one extremity is 100N
(d) Time period of oscillatic is p/100s.
Q.3 The displacement of a particle from its mean position is given by the equation
Y=0.4(cos2pt/2-sin2pt/2)
(a) The motion of particle is not SHM
(b) The motion is SHM with a period of 2s
(c) The amplitude of SHM is 0.4m
(d) The maximum velocity is 0.4pm/s.
Q.4 The total energy of a simple pendulum executing SHM with amplitude A is E. When its displacement is half the amplitude, then
(a) its KE is ½ E (b) its PE is ½ E
(c) its PE is ¼ E and KE is ¾ E (d) its restoring force is E/A.
Q.5 For a particle executing SHM, the kinetic energy varies as K = K0 cos2 wt
(a) The maximum kinetic energy is K0
(b) he maximum potential energy is K0
(c) The total mechanical energy is 2K0
(d) The frequency with which KE varies is 2w.
Q.6 Which of the following does represent SHM ?
(a) sin wt + sin 2wt (b) tan wt
(c) sin wt + cos wt (d) none of the above
Q.7 A particle moving with SHM passes through points A and B with the same velocity. It takes 2s in going from A to B and after another 2s, it again returns to B. The period in seconds of motion is
(a) 2 (b) 4 (c) 6 (d) 8
Q.8 A linear harmonic oscillator of force constant 2 ´ 106 N/m and amplitude 0.01m has a total mechanical energy of 160J. Its
(a) maximum potential energy is 100J
(b) maximum kinetic energy is 100J
(c) maximum potential energy is160J
(d) maximum potential energy is zero
Q.9 Two particle are oscillating along the same line with the same frequency and same amplitude. They meet each other at points mid-way between the mean position and extreme position while going in opposite directions. The phase difference between their motions is
(a) p/3 (b) p/2 (c) 2p/3 (d) 5p/4
Q.10 Two pendulums have the time periods T and 5T/4. They start SHM at the same time from the mean position. After hoe many oscillations of the smaller pendulum they will be again in the same phase
(a) 5 (b) 4 (c) 11 (d) 9
Q.11 Two pendulum of period T and 4T are given small displacements in the same direction at the same instant. They will be out of phase after the shorter pendulum has completed n oscillations where n is
(a) 2/3 (b) 4/3 (c) 3 (d) 5
Q.12 The length of a simple pendulum is infinite. Its time period T in terms of radius R of the earth is
(a) 2pÖR/g (b) 2pÖR/2g (c) 2pÖ2R/g (d) infinite
Q.13 A simple pendulum of length l has been set up inside a railway wagon sliding down a frictionless inclined plane having an angle of inclination q with the horizontal. What will be its period of oscillation as recorded by an observer inside the wagon?
(a) 2pÖ l/g cos q (b) 2pÖ l/g sin q
(c) 2pÖ l/g (d) 2pÖl cosq/g
Q.14 A simple pendulum has time period given by T = 2pÖl/g. If it is falling down with its support with acceleration a, its new time period T’ is
(a) T’ = 2pÖl/g (b) T’ = 2pÖl / (g-a)
(c) T’ = 2pÖl / (g+a) (d) It will not oscillate at all.
Q.15 A simple pendulum with metal bob has a period T. The metal bob is non-immersed in a liquid having density 1/10 that of the metal of the bob. The liquid is non-viscous. Now the period of the same pendulum with its bob remaining all the time in the liquid will be
(a) 9/10T (b) TÖ10/9 (c) T (d) TÖ9/10
Q.16 A heavy brass-sphere is hung from a spiral spring and it executes vertical vibrations with period T. The ball is now immersed in non-viscous liquid with a density 1/10 that of brass. When set into vertical vibrations with the sphere remaining inside the liquid all the time, the period will be
(a) 9/10T (b) TÖ10/9 (c) T (d) TÖ9/10
Q.17 Two spring of the same material but of length L and 2L are suspended with masses. M and 2M attached at their lower ends. Their times periods when they are allowed to oscillate will be in the ratio
(a) 1:2 (b) 2:1 (c) 1:4 (d) 4:1
Q.18 Masses M and 4M are suspended from two identical springs of the same spring constant k. They start oscillating in the same phase and they are again in the same phase after every 4 seconds. If M = 1kg, the value of k is N/m is
(a) p (b) p2 (c) 2p (d) 4p
Q.19 A simple spring has length l and force constant k. It is cut into parts of lengths l1 and l2 such that l1= nl2 (n= an integer). The force constant of spring of length l1 is
(a) k(1+n) (b) k/n (1+n) (c) k (d) k/n
Q.20 A block of mass m is attached to two springs as shown in Fig. 12-28, with spring constant k and 2k. The mass oscillates with an amplitude A.
(a) The angular frequency of oscillation is Ö2k/3m
(b) The maximum energy of oscillation is 3/2 kA2
(c) The maximum restoring force is 3k A/m.
(d) The maximum velocity of oscillation is AÖk/m
Q.21 A body of mass m is suspended from a spring of force constant k. The maximum distance upto which the body can be pulled down for the oscillation to remain harmonic is
(a) 2mg/k (b) mg/k (c) 2k/mg (d) k/mg
Q.22 One end of a long metallic wire of length L is tied to the ceiling. The other end is tied to massless spring of spring constant k. A mass m hangs freely from the free end of the spring. The area of cross-section and Young’s modules of the wire are A and Y respectively. If the mass is slightly pulled down and released, it will oscillate with a time period T equal to
(a) 2pÖm/k (b) 2pÖm(YA+kL)/YAk
(c) 2pÖmYA/kL (d) 2pÖmL/YA
Q.23 A frictionless piston of mass M is just fit in the vertical cylindrical neck of a large container of volume V. The container is filled with a gas and there is a vacuum above the piston. Assuming Boyle’s law, the time period T of oscillation will be
(a) TµM1/2 (b) TµM-1/2 (c) TµM0 (d) TµM
Q.24 A uniform cylinder of length L and mass M having cross sectional area A is suspended with its length vertical from fixed point by a massless spring such that it is half submerged in a liquid of density r at equilibrium position. When the cylinder is given a small downwards push and released it starts oscillating vertically with small amplitude. If the force constant of the spring is k, the frequency of oscillation of the cylinder is
(a) 1/2p[k-Arg/M]1/2 (b) 1/2p[k+Arg/M]1/2
(c) 1/2p[k-rgL2/M]1/2 (d) 1/2p[k-Arg/Arg ]1/2
Q.25 Consider three u-tubes containing the same liquid. The radii and length of the horizontal tube are related as follows:
r1 = r, r2 = 2r r3 = r
l1 = l, l2 = l l3 = 3l
and they are filled up to the same height h. When the liquid is disturbed, it oscillates in simple harmonic motion with periods T1, T2 and T3, then
(a) T1< T2< T3
(b) T1= T2> T3
(c) T1= T2< T3
(d) T2< T1< T3
Q.26 A bottom loaded stick performs SHM in a liquid of density r1with time period T1 and in a liquid of density r2 with time period T2. If the lengths insides the two liquids are l1 and l2 respectively, then
(a) l1r1/l2r2 (b) l2r1/l1r2
(c) T1Ör1 = T2Ör2
(d) T2Ör2 = T1Ör1
ANSWER SHEET
1.
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(b), (d)
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2.
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(a),(b), (c)
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3.
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(b), (c), (d)
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4.
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(c), (d)
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5.
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(a), (b), (d)
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6.
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(c)
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7.
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(d)
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8.
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(b), (c)
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9.
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(c)
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10.
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(a)
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11.
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(a)
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12.
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(a)
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13.
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(a)
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14.
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(b)
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15.
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(b)
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16.
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(c)
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17.
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(a)
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18.
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(b)
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19.
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(b)
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20.
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(b), (c)
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21.
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(b)
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22.
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(b)
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23.
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(c)
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24.
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(b)
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25.
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(c)
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26.
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(a), (d)
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