Kvpy Sa Stream-paper-2008

 YEAR-2008  YEAR-20 08 (KVPY-STREA (KVPY-STREAM M-SA) PART-I (1 Mark) MATHEMATICS 1.

If a and b are any two real numbers with opposite signs, which of the f ollowing is the greatest ? (A) (a–b)2

2.

(B) (|a| – |b|) 2

 (C) |a2 – b2|

(D) a2 + b2

The sum of the infinite series : 1 2 3 n  2  3  ...  n  .... 10 10 10 10

(A)

3.

1 9

(C)

1 8

(D)

17 22

(B) 642

(C) 6464

(D) 160

The smallest value the expression x 2 + 6x+ 8 attains on the set { x  R | x2 – 2x – 8   0} is (A) 0

5.

10 81

The number (1024) 1024 is obtained by raising (16) 16  to the power n. What is the value of n ? (A) 64

4.

(B)

(B) –1

(C) 8

(D) 3

Let P1 be the set of all prime numbers, i.e., P1 = {2, 3, 5, 7,11, . . .}, Let Pn = {np | p   P1|}, i.e., the set of all prime m ultiples of n. Then which of the following sets is non em pty ? (A) P1  P23

6.

(C) P12  P20

(D) P20  P24

The number of integers a such that 1   a   100 and aa is a perfect square is : (A) 50

7.

(B) P7  P21

(B) 53

(C) 55

(D) 56

On a card, the following three statements are f ound : (1) On this card exactly one statement is false. (2) On this card exactly two statements arc false. (3) On this card exactly three statements are false. The number of false statements on the card is exactly (A) 0

8.

(B) 1

(C) 2

(D) 3

In triangle ABC, with  A = 90°, the bisectors of the angles angles B and C meet at P. The distance from P to the hypotenuse is 4 2 . The distance AP is : (A) 8

(B) 4

(C) 8 2

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(D) 4 2

Page # 11

9.

In a rhombus one of the diagonals is twice the other diagonal. Let A be the area of t he rhombus in square units. Then each side of the rhombus is : (A)  A

10.

(B)

1 2 A 2

(C)

1 5 A 2

(D)

1 4 A 4

In the following figure, AE = EB, BD = 2DC What is the ratio of the areas of PED and ABC ?

 A E P B

(A)

11.

1 4

(B)

1 6

C

D

(C)

1 9

(D)

1 12

Let P be a point in the interior of the rectangle ABCD Which of the following sets of numbers can form the areas of the four tr iangles PAB, PAB, PBC, PCD, PDA in same order ? (A) 10,9,12,5

12.

(B) 21,15,6,12

(C) 10,9,8,6

(D) 12,8,7,5

The sum of 7 consecutive positive positi ve integers is equal to the sum of the next five consecutive integers. W hat is the largest among the 12 numbers ? (A) 24

13.

(B) 23

(C) 22

(D 21

 A large tanker can be filled by two pipes A and B in 60 minutes and 40 minutes respectively. respectively. How many minutes will it take to fill the empty tanker if only B is used in the first- half of the time and A and B are both used in the second-half of the time ? (A) 15

14.

(B) 20

(C) 27.5

(D) 30

Let 0 < a < b < c be 3 distinct digits. The sum of all 3-digit num bers formed by using all the 3 digits once each is 1554. The value of c is : (A) 3

15.

(B) 4

(C) 5

(D) 6

Let a sequence have 200 zeroes to start with. In step 1, to every position in the sequence we add1. In step2, to every even position in the sequence we add1. In step 3, to every position which is a multiple of  3, we add 1. This is continued up to 200-t h step. After the 200-th step, what will be the value in the 128t 128th h position ? (A) 8

(B ) 16

(C) 128

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(D) 200

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PHYSICS 16.

 A ball is thrown vertically upwards with a certain initial velocity. Assume that there is no resistance due to air. Among the graphs below, below, the graph that is not an appropriate representation of the m otion of the ball is :

(i)

     y      g      r      e      n       E      c       i       t      e      n       i       K

(ii) )

     y      g      r      e      n       E       l      a       i       t      n      e       t      o       P

     y      g      r      e      n       E      c       i       t      e      n       i       K

(iii)

Time

(A) A 17.

Height of the ball

Time

(B) B

(C) C

Speed of the ball

(D) D

 An electron of mass me initially at rest takes time t1 to move a distance s in a uniform electric field in the same field environment, a proton of mass m p initially at rest takes time t 2 to move the same distance (in the opposite direction). lgnoring gravity, the ratio t 2/t1 is : 1/ 2

(A) 1

18.

(iv)

     y      g      r      e      n       E       l      a       i       t      n      e       t      o       P

 me    (B)   m p    

(C)

1/ 2

 mp    (D)  m e    

mp me

 A simple camera with with a converging lens of 60 60 mm focal length is focused on very far objects. To focus focus the camera on a nearby object 1.5 m away, away, the distance between the film and lens will have to be: (A) decreased by 2.5 mm (B) increased by 2.5 mm (C) kept fixed as before. but aperture increased by a factor of 2.5 (D) kept fixed as before, hut aperture decreased by a factor of 2.5

19.

 A molecule of gas in a container hits one wall (1) normally and rebounds rebounds back. It suffers no collision and hits the opposite wall (2) which is at an angle of 30º with wall 1. Wall 1

30º Wall 2

 Assuming the collisions to be elastic and the small collision time to be the same for both the walls, the magnitude of average force by wall 2. (F 2) provided to the molecule during collision satisfy : (A) F1 > F2

(B) F1 < F2

(C) F1 = F2, both non-zero

(D) F1 = F2 = 0

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20.

 A stone dropped from the window of a stationary train hits the ground and comes t o rest. An identical stone is dropped from the window when the same train is moving with speed v and it comes to rest on the ground. Assume that in each case, the entire energy lost in impact goes into heating the st one. Then (A) The first st one is is slightly more heated than the second. (B) The second stone is slightly more heated than the first. (C) Both the stones will be raised to the sam e slightly higher) temperature. (D) The second stone will be slightly more heated than the first only if its horizontal speed during fall is more than the f inal vertical speed.

21.

 A negatively charged particle initially at rest is placed in an electric electric field that varies from point to point. There are no other fields. Then : (A) the particle moves along the electric line of force passing through it. (B) the particle moves opposite to the electric line of for ce passing through it. (C) the direction of acceleration of t he particle is tangential to the electric line of force at every instant. (D) the direction of acceleration of the particle is normal to the electric line of f orce at every instant.

22.

There is a steady water flow in a horizontal tube in which one part has cross sectional area A 1 and the other part has cross sectional area A 2. Assume that water is incompressible. If A1/A2 = 16, the ratio of the speed u 1 in part 1 and the speed u 2 in part 2, i.e. u1/u2 is : (A)

23.

1 16

(B) 4

(C)

1 4

(D) 1

Positive point charges of magnitude are placed at all the twelve ‘hour positions of a clock of radius r. The clock is mounted on a wall in the normal way. The charge at the position ‘6 is removed. The resulting electric field at the centre of the clock is : (A) 0

(C)

24.

(B)

1

q

4o r 2

 ve  vertically upward.

(D)

1

q

in the horizontal direction. direction.

4o r 2 1

q

4o r 2

 vertically downward

The pair of quantities that do not have the same dimensions is : (A) Latent heat, specific heat (B) Gravitational force, Coulomb force (C) Kinetic energy pf a f reely falling body, body, potential energy of a com pressed spring (D) Coefficient of f riction, number of molecules in a container.

25.

 A block of wood is floating on oil with half of its volume submerged. If the density of oil 840 kg m –3, the relative density of wood (relative to water) is : (A) 0.84

26.

(B) 0.42

(C) 0.21

(D) 1.00

We are given n resistors, each of resistance R. The ratio of the maximum to minimum resistance that can be obtained by combining them is : (A) nn

(B) n

(C) n2

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(D) logn

Page # 14

27.

 A light string goes over a frictionless polley. polley. At its one end hangs a mass of 2 kg and at the other end hangs a mass of 6 kg. Both the masses are supported by hands to keep them at rest. When the masses are released, they being to move and the string gets taut. (Take (Take g = 10 ms –2) The tension in the string during the motion of the masses is : (A) 60 N

28.

(B) 30 N

(C) 20 N

(D) 40 N

The escape escape speed of a body from the earth regarded regarded as a uniform (non-rotating) (non-rotating) sphere sphere depends depends on : (A) the m ass of the body. body. (B) the direction of projection. (C) the location of the projection on the earth’s surface. (D) the height of location from the earths surface fr om where the body is launched.

29 .

On a day day during during the the Monso Monsoon on seaso season, n, the the relativ relative e humidi humidity ty at at a place place is 90% 90% and the tempe temperatu rature re is 15°(C) The saturation vapour pressure of water at this temperature is 0.0169 × 10 5 Pa. The partial pressure of water vapour in the air on that day is (A) 0.9 × 105 Pa  Pa

30.

(B) 0.0169 × 105 Pa  Pa

(C) 0.0152 x 105 Pa  Pa

(D) 1.0 x 105 Pa

It is now known that a proton and a neutron consist of three elementary units called ’quarks’. Two Two types of quarks are involved: the the ’up’ quark quark (u) of charge +

2 1 e and the ‘down quark (d) of charge – e, where 3 3

e is the magnitude of election’s charge. u  and d  are their antiparticles. An antiparticle has the same magnitude of charge as the particle but of opposite sign. The possible compositions of a proton and a neutron are : (A) p : uud

;

n:

udd

(B) p : uuu

;

n:

ddd

(C) p : uu d

;

n:

ud d

(D) p : uu u

;

n:

ud d

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CHEMISTRY 31.

The volume of 0.5 M aqueous NaOH solution required to neutralize 10 ml of 2 M aqueous HCl solution is: (A) 20ml

32.

33.

34.

(C) 80ml

(D) 120ml

The compound that can be pur ified by sublimation is : (A) Ammonium Sulphate

(B) Calcium Carbonate

(C) Calcium Oxide

(D) Aluminium Chloride

 Penicillin was discovered by : (A) Alexander G. Fleming

(B) Emil Fisher  

(C) Robert B. W oodward

(D) vant Hoff  

 Among butane,1-butene,1-butanol butane,1-butene,1-butanol and butanal, the compound which is most polar is (A) butane

35.

(B) 40ml

(B) 1-butene

(C) 1-butanol

(D) butanal

 Among ethanol, dimethyl ether, ether, methanol, and propanal, propanal, the isomers are : (A) ethanol, dimethyl ether, methanol and pr opanal (B) ethanol and methanol (C) ethanol, dimethyl ether, and methanol (D) ethanol and dimethyl ether 

36.

 Among Li, Be, N and F, the element having the largest atomic radius, is : (A) Li

37.

38.

40.

(A) O2

(B) H2O

(C) both H2O and O 2

(D) both H3O+ and O2

42.

(D) F

 A gel toothpaste is a mixture of a : (B) solid in a gas

(C) liquid in a liquid

(D) gas in a solid

3.01×1023 molecules of elemental Sulphur will react with 0.5 mole of oxygen gas completely to produce (A) 6.02 × 1023 molecules of SO 3

(B) 6.02 × 1023 molecules of SO 2

(C) 3.01 × 1023 molecules of SO 3

(D) 3.01 x 1023 molecules of SO 2

The pair of metals which will produce hydrogen gas in reaction with acid is : (A) Mg, Cu

41.

(C) N

The proof of oxidizing action of hydrogen peroxide in acid solution is in the formation of :

(A) liquid in a solid 39.

(B) Be

(B) Mg, Ag

(C) Zn, Pb

(D) Cu, Zn

The correct order of pH is : (A) (A) Lemon Lemon juice juice < wat water er < Milk Milk of of Mag Magne nesi sia a

(B) (B) Lemo Lemon n juic juice e > wate waterr > Milk Milk of of Magn Magnes esia ia

(C) Water Water > lemon lemon juice juice > milk milk of of Magn Magnes esia ia

(D) Milk Milk of of Magn Magnes esia ia > lemo lemon n jui juice ce > wat water  er 

The solubility of a gas in a solution is measured in thr ee cases as shown in the figure given below where w is the weight of a solid slab placed on the top of the cylinder lid. The solubility will follow the order :

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Page # 16

w

w

solution

43.

44.

w

(C) a = b = c

(D) a >b < c

 A Daniel cell converts : (A) (A) elec electr tric ical al energ nergy y to to che chemi mica call en energ ergy

(B) (B) chem chemic ical al ene energy rgy to to ele elect ctri rica call ene energ rgy y

(C) mecha mechani nica call energ energy y to chemi chemica call ene energy rgy

(D) pote potent ntia iall ene energy rgy to elec electri trica call ene energy rgy

One of the major components in com pressed natural gas (CNG) is : (A) carbon dioxide

45.

w

solution

solution

(B) a < b < c

w

gas

gas

gas

(A) a > b > c

w

(B) acetylene

(C) methane

(D) water gas

Dehydration of 2-pentanol gives : (A) pentane

(B) Only 1-pentene

(C) Only 2-pentene

(D) A mixture of 1-pentene and 2-pentene

BIOLOGY 46.

 A cancer which is not a tumor is : (A) Lymphoma

47.

(C) Prostate cancer

(D) Oral cancer  

The phase of the cell cycle in which DNA synthesis takes place is : (A) G1 phase

48.

(B) Leukemia

(B) S phase

(C) G2 phase

(D) G0 phase

You have a tube containing 10 2 bacteria. You have taken out 10 2 bacteria. How many bacteria are left in the tube ? (A) approximately 10 7

49.

(C) approximately 105

(D) approximately 109

 Association in which both the organisms get benefited benefited is : (A) Commensalism

50.

(B) approximately 10 6

(B) Mutualism

(C) Ammensalism

(D) Parasitism

You are part of a scientific expedition that has ventured deep into the Amazon rain forest. You You spot a tree with branches spread over a large area. What can you conclude about the root structure of the tree? (A) It is dicotyledonous (B) It is monocotyledonous m onocotyledonous (C) It may m ay be either monocotyledonous or dicotyledonous (D) There is no correlation between foliage and root structure

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Page # 17

51.

52.

53.

 Alleles are : (A) Different form s of the same protein

(B) Two different genes

(C) Different forms of the same gene

(D) Two different proteins

Diet rich in carotenoids is beneficial because : (A) (A) Th They act as as fre free ra radical cal sc scavengers

(B) (B) Th They absorb harmfu rmfull UV ra rays

(C) They help in curing cancer

(D) They are rich source of iron

The amount of CO 2 plant is greater at night than during the day because : (A) The rate of respiration is higher at night. (B) More CO2 is produced because it is colder during the night. (C) Photosynthesis during the day uses up some of the CO 2 produced by respiration. (D) More glucose is available for respiration during the night

54.

Osmosis takes place between two solutions separated by a semipermeable m embrane because. (A) Water molecules move from the m ore dilute solution to the less dilute solution (B) Solute molecules move from the less dilute solution to the more dilute solution (C) Water W ater molecules move from the less dilute solution to the more dilute solution (D) Solute molecules move from the m ore dilute solution to the less dilute solution

55.

 Arteries do not have have valves valves but veins do, because because : (A) Arteries have a narrower lumen than veins (B) Arteries have thicker walls than veins (C) Arteries carry oxygenated blood whereas veins carry deoxygenated blood (D) Valves prevent backflow of blood in veins

56.

If a person’s spinal cord is injured which of the following functions might be aff ected ? (A) Talking

57.

(B) Seeing

(C) Sneezing

(D) Hearing

Use of an insecticide in an island made a certain insect species extinct. A few years years later a tree species was also found to be extinct. This may be because :

58.

(A) (A) Th The tr tree is is po pollinated by by the in insect

(B) (B) Th The in insect used to live on on the tre tree

(C) The insect insect used to eat the leaves leaves of the tree

(D) The The tree tree is insectivo insectivorous rous

Why is it advisable to take antibiotics if someone is suffering from gastric ulcers ? (A) Antibiotics reduce gastric acid secretion (B) antibiotics prevent ulcers from being infected (C) Antibiotics reduce gastric enzyme secretion (D) Gastric ulcers are caused by bacteria

59.

You are synthesizing a 5 amino acid containing peptide from the pool of 20 standard amino acids by choosing amino acids r andomly. andomly. What W hat is the probability of selecting Gly–Gly–Gly-Gly Gly–Gly–Gly-Gly (A) 0

60.

(B) 1/205

(C) 1/20

(D) 1/(20 × 5)

The appropriate description of animal hormones is, (A) Have size smaller than 5 kDa

(B) Comprise of proteins only

(C) Comprise of lipid molecule only

(D) Are pour directly into the blood

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PART-II (2 Mark) MATHEMATICS 61.

Five real numbers x 1, x2, x3, x4, x5 are such that : x1  1  2 x 2  4  3 x 3  9  4 x 4  16  + 5 x 5   25 =

The value of 

62.

x1  x 2  x 3  x 4  x 5 2

x1  x 2  x 3  x 4  x 5 is 2

(A) not uniquely determined

(B) 55

(C) 110

(D) 210

The coefficient of x 30 in the expansion of : (1 + 2x + 3x 2 + .... 21x20)2 is : (A) 2706

63.

(B) 2450

(C) 1481

(D) 256

 A billiards table of grid size 8 × 10 has four holes holes in the A, B, C, D. A ball starting from the point P on the side AD, as in the figure, strik es against CD at an angle 45°, gets reflected and moves on striking against the other sides. Which hole will the ball fall into ?

D

C

 A

B

P

(A) B 64.

(B) C

(C) D

(D) no hole

In triangle ABC, the coordinates of A and B are respectively (2,3) and (8,10). It is known that C also has integer coordinates. The minimum possible area of ABC is : (A) 0

65.

(B)

1 2

(C) 1

(D)

3 2

 A shop-keeper increases the price of a commodity by x%. some time later, he reduces the new price by y% and notices that the pric e is now the sam e as it was originally. originally. The value of 

(A) 

1 100

(B) 0

(C)

1 100

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1 1  is : y x

(D) not uniquely determinable determinable

Page # 19

PHYSICS

66.

 An Insulated vessel vessel contains 0.4 kg of warer at 0ºC. A piece of 0.1 kg ice at –15°C is put into it and steam at 100ºC is bubbled into it until all ice is melted and finally the contents are liquid water at 40ºC.  Assume that the vessel does not give or take any heat and there is no loss of matter and heat to the surroundings. surroundin gs. Specific heat of ice is 2.2 × 10 3 J kg-1K-1, heat of fusion of water is 333 × 103 J kg –1 and heat of vaporization of water is 2260 × 10 3  J kg –1. The amount of steam that was bubbled into the water is about : (A) 34.7 gram

67.

(B) 236.0 gram

(C) 0.023 gram

(D) 48.0 gram

 A light source is placed 100 cm away from a screen. A converging lens placed at a certain position between the source and the screen focuses the image of the source on the screen. The lens is moved a distance of 40 cm and it is found that it again focuses the image of the source on the screen. The focal length of the lens is : (A) 21 cm

68.

(B) 30 cm

(C) 40 cm

(D) 67 cm

 A rubber pipe with a diameter diameter of 10 cm is connected connected to a nozzle 2 cm in diameter. Water flowing through the. pipe at a speed of 0.6 ms –1, comes out like a jet through the nozzle. nozzle. The backward force of the nozzle is about : (A) 7.7 N

69.

(B) 67.9 N

(C) zero

(D) 2.8 N

 A power supply of fixed emf E is connected to a variable resistor (resistance = R) and an am meter of  resistance R A. The internal resistance of the supply is r. The potential difference bctween the terminals of  the power supply in closed circuit is denoted by V and the current in the circuit is denoted by I. A graph is obtained between V and I by drawing varying amount of current from the supply. supply. The correct V-I graph for the given situation is : V

V E

E

E/r 

I

I

(I)

(II)

V

V I I

E/r 

(III) (A) Graph 1

(B) Graph II

(IV) (C) Graph III

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(D) Graph IV

Page # 20

70.

 A thermometer uses ‘density ‘density of water as thermometric property. property. The actual reading reading in the thermometer  is ‘height of water(h) which is inversely proportional to density of water water (d). In a certain temperature range, density of water varies with temperature as shown. The graph is symmetric about the maximum    r d    e    t    a    w     f    o    y    t     i    s    n    e     D

T2

T1

Tempeature

Two identical bodies (of same mass and specific heat) at differen t temperatures temperatur es T1 and T 2 show the same reading of height h 1 = h2 in the thermom eter. The bodies are brought into contact and allowed to reach thermal equilibrium. The thermom eter reading ‘height of water for final equilibrium state h 1 satisfies. (A) hf  =

h1  h2  = h1  h2 2

(B) hf  > h1 = h2 (C) hf  < h1 = h2 (D) hf  may be greater or less than h1 = h2 , depending on the specific heat of the bodies.

CHEMISTRY

71.

The density of a salt solution is1.13 g cm –3 and it contains 18% of NaCI by weight. The volume of the solution containing 36.0 g of the salt will be : (A) 200 cm3

72.

(B) 217 cm 3

(C) 177 cm 3

(D) 157cm3

 Esterification of a compound ‘X with molecular formula C 3H6O2 with an alcohol ‘Y produces a compound with molecular formula C 5H10O2. X and Y, Y, respectively, res pectively, are :

73.

(A) propanoic acid and methanol

(B) propanoic acid and ethanol

(C) acetic acid and ethanol

(D) butyric acid and methanol

 10 g of a crystalline crystalline metal sulphate salt when heated generates approximately 6.4 g of an anhydrous anhydrous salt of the same metal. The molecular weight of the anhydrous salt is 160 g. The number of water molecules present in the crystal is : (A) 1

74.

(B) 2

(C) 3

(D) 5

In the reaction of FeSO 4 with K2Cr 2O7 in the presence of an acid, the changes in the formal oxidation numbers of Cr and Fe, respectively, respectively, are : (A) 1 and 5

75.

(B) 3 and 1

(C) 5 and 1

(D) 1 and 3

 An aqueous aqueous solution solution of a metal salt (X) reacts with carbon dioxide to give a water soluble compound (Y) which on heating gives the starting metal salt back. Y when present in water does not produce lather with soap. The com pounds X and Y, Y, respectively are (A) CaCO3 and Ca(HCO 3)2

(B) Mg (HCO3)2 and MgCO3

(C) Ca(HCO3)2 and CaCO3

(D) MgCO3 and Mg (HCO3)2

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Page # 21

BIOLOGY

76.

Plasmolysis is not observed in boiled plant tissue because : (A) The cell wall becomes impermeable to water  (B) The cell m embrane disintegrates (C) The cell wall disintegrates (D) The cell mem brane becomes impermeable to water 

77.

If the analogy of a city is applied to a eukaryotic cell then which of the following statements is correct ? (A) Nucleus as a library librar y and ribosome as a slaughter house (B) Nucleus as a police station and mitochondria as powerhouse (C) Mitochondria as powerhouse and Golgi as a cargo sorting facility (D) Mitochondria as powerhouse and nucleus as slaughter house

78.

The placenta tissue in mammals originates from : (A) The mother only (B) The foetus only (C) Both the mother and the foetus (D) Originates from the mother but taken over by the foetus

79.

Both bacteria and amoeba are unicellular organisms or ganisms which may live in aqueous environment. Bacteria do not burst by taking up water fr om the surrounding because they have cell walls. Amoeba do not have cell walls but yet do not burst because : (A) Amoeba eliminates excess water by the help of contract ile vacuoles. (B) The cytoplasm of am oeba is isotonic to surrounding water. (C) The cytoplasm of amoeba is hypotonic to surrounding water. (D) Amoeba does not take up water from the surroundings.

80.

In the lunch, you ate boiled green vegetables , a piece of cooked meat, me at, one boiled egg and a sugar candy. Which one of these foods may have been digested first ? (A) Boiled green vegetables

(B) The piece of cooked meat

(C) Boiled egg

(D) Sugar candy

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