9_NAT_SOL

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Solutions for Class : 9

Mathematics

1. (D) Probability of getting 1 or 6 in a single toss

2=

6

Probability not getting 1= =2

6

4

6

2. (D)

AB

CD

E40

o

60o

80o

In BCD, BDC = 180o 40o 60o 80o

DEC = AEB = 80o

In DEC, ECD = 180o 80o 80o = 20o

AC bisects BCD.3. (C) AF, ED and BC are parallel lines and AB, AM

are transversals. As AE = EB, by Equal InterceptsTheorem, AN = NM. So, AM = 2NM.

A

B M C

ND

F

E

Now, ar( ABC) = 1

2 base altitude

= 1

2 BC AM ..... (i)

ar(parallelogram BCDE)

= base altitude = BC NM ... (ii)

From (i) and (ii), ar(parallelogramBCDE)

ar(ABC)

=

BC NM

1BC AM

2

2ar(parallelogramBCDE) NM

=120 cm

2NM2

= 1

ar(parallelogram BCDE) = 20 cm2

4. (D) For x = 0 and =1

3x (verify by substitution)

5. (A) The diagonals of a rectangle are equal in lengthand the rectangle being a parallelogram, itsdiagonals bisect each other.

AC = BD

1

2AC =

1

2 BD

OC = OD

In ODC, ODC = OCD = xo

But ODC = OBA = 30o

(Since AB PDC).

xo = 30o

Now, yo = AOB = COD (oppositeangles)

= 180o xo xo (sum of threeangles of ODC is 180o)

= 180o 30o 30o = 120o

6. (D) NML = 180o 125o = 55o

Since, =LN LM

LNM = NML = 55o

UNIFIED COUNCILUNIFIED COUNCILA n I S O 9 0 0 1: 2008 C e r t i f i e d O r g a n i s a t i o n

NATIONAL LEVEL SCIENCE TALENT SEARCH EXAMINATION - 2015 (UPDATED)

Paper Code: UN412


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NLM = 180o 55o 55o = 70o

KLN = 180o 90o 70o = 20o

In KLN, xo = 180o 20o 90o = 70o

7. (D)120

x of the planned distance.

8. (C) Area = ( )( )( ) s s a s b s c = A

where a + b + c

s =2

and a, b, c are sides of

the triangle.

When the sides are increased by 200%, thesides become 3a, 3b and 3c.

=1

3a + 3b + 3cs

2 =

( )=

a + b + c3 = 3s

2

( )( )( )1 1 1 1 1A = s s - 3a s - 3b s - 3c ( ) ( ) ( ) = 3s.3 s a .3 s b .3 s c ( )( )( ) = 9 s s a s b s c = 9A Increase in area = 9A A = 8A or 800%

9. (C) Edge of the cube = = 2 2

a 4 23 3

= 8

3cm

Diagonal of the cube = 3 (edge)

= 8

3 3

= 8 cm

10. (D) (5, 6), (6, 5) i.e.,

The probability 2

= =36

1

18

11. (C) pq = 36, since p and q are positive integers,hence 36 can be factorised as (36 1) and(18 2), (12 3), (9 4), and (6 6). Hencep q can be 6 6 = 0, 3 12 = 9, (9 4) = 5, 36 1 = 35, but it can NOT be 8.

12. (A) Since, AB = BC wo = zo

BD bisects AC AD = DC xo = yo

wo = xo is not possible.

13. (C) ( ) ( ) 2 22 0 + 1 0 = 5 (2, 1) is the nearest point.

14. (A) Since, in the list 5 appears 4 times and 6appears 3 times.

So, the value of n can be any value otherthan 6 as mode of the given list is 5.

15. (D)1

2

a

a=

3 1=

12 4

1

2

b

b

=

4 1=

16 4

1

2

c 5

c 2=

1=

0 4

Since, 1 1 1

2 2 2

a b c

a b c= = ,

The given equations are coincident lines.

There are more than two solutions.

16. (C) AB PCDPEF

ar. AGB = 1

2Pgm AEFB

GE F

A B

D C

(Since AGB and Pgm AEFB are on thesame base and between the same PlinesAB and EF).

area AGB = 1

4Pgm ABCD =

S

4

17. (A) Area of rectangle = xy =

x h

y y

x

Area of parallelogram = y h =

Since, h < x y h < x y

< 18. (C) AP + PB = AB

A P B


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19. (B)

h

d

h

d

Hence, the dimensions of rectangular boxis d d h.

Volume of rectangular box = d2h

20. (Del)

21. (C) Since, x + y + z = 0

x2 + y2 + z2 + 2(xy + yz + zx) = 0

x2 + y2 + z2 = 2 (xy + yz + zx)

= 2[x(y + z) + yz]

= 2(x x + yz)

(Since, x + y + z = 0)= 2(x2 yz)

2 2 2

2

+ +=

2x y z

x yz

22. (D) Of the given statements only (ii) and (iii)are true.

23. (C) A : Getting prime number

A = (2, 3, 5, 7, 11, 13, 17, 19, 23)

n(A) = 9, n(S) = 25

Required probability

= n (A )

P(A ) = =n (S)

9

25

24. (C) FDG = KCD (corresponding angles) = ECA (vertically opp. angles)

ECA = 55o

EAC = 40o (given)

E = 180o (55o + 40o) = 85o

xo = 85o (corresponding angles)

25. (D) B = C

AB = AC

CAD = 30o

CAD > CDA

CD > AC

(In a triangle, greater angle has longer sideopposite to it)

BAC = 180o 110o = 70o > ABC BC > AB and BC > AC

BC > CA and CA < CD

Physics

26. (C) Initial kinetic energy = 21

mv2

= ( )( )1 22 3 = 9 J2

Final kinetic energy =21 mv

2

= ( )( )21 2 7 = 49 J2

Increase in kinetic energy = 49 J 9 J

= 40 J

27. (A) A cat that has become wet shakes its bodyfrom head to tail to shed the water from itscoat by moving its head and tail on rightand left sides respectively to make thewater droplets to fall down. It is based onthe concept of inertia of motion.

28. (B) Statements (A), (C) and (D) are not true ofmass. Mass of an object is always constantwhether it is on the earth, the moon or evenin outer space.

29. (C) The momentum of a body is the product ofits mass and velocity ( P = m v ). Themomentum of four objects P,Q,R and S arecalculated below.

Object P = Mass velocity =

0.3 kg 5 m s1 = 1.5 kg m s1

Object Q = Mass velocity =

0.6 kg 2 m s1 = 1.2 kg m s1

Object R = Mass velocity =

1.2 kg 0.3 m s1 = 0.36 kg m s1

Object S = Mass velocity =

1.5 kg 1.8 m s1 = 2.7 kg m s1

So, object R has the lowest momentum.

30. (D) Car I is not moving, so it has no kineticenergy. Bus I has a bigger mass than car II,so bus I has more kinetic energy eventhough they are moving at the same speed.Bus II has the same mass as bus I, but it ismoving at the fastest speed, so it has the


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most kinetic energy. Bus I and car II aremoving at the same speed, but car II hasless kinetic energy because it has a smallermass.

31. (Del)

32. (B) Time taken for sound to travel from thelightning to the observer = 2.5 s

Speed of sound in air is approximately330 m/s.

Therefore, distance travelled by the sound= speed time

= 330 2.5 = 825 m

33. (B) Pressure = Force / Area, the smaller thearea, the greater the pressure.

34. (D) Statement (i), (ii) and (iii) are the safetymeasures, few are inbuilt in the vehiclesand some are to be followed by passengersmoving in various vehicles to reduce thenegative effects of inertia.

The speed and weight limits for heavyvehicles are strictly enforced. For examplebuses, lorries etc., are allowed to travel ata maximum speed of 90 kmh1. This isbecause the above vehicles have greatermass and if they travel at high speeds, itwill difficulat for them to stop the vehicle.

35. (C) Potential energy is stored in the bow. Torelease an arrow from the bow, there is achange in the shape of stretched string ofthe bow. Hence, potential energy of thebow is converted to kinetic energy tostretch the string and release an arrow fromit.

36. (A) Mass is a measure of the inertia of a body.Mass = Density volume.

Density in g cm3

Copper 8.9 Aluminium 2.7

Glass 2.4 to 2.8 Wood 0.48

The heaviest material copper has thegreatest inertia.

37. (D) Power = work done time = force distance time. When the applied forceon the weight is higher, the power used todo the work will increase.

Force = mass acceleration. When a higherforce is applied, the weight will move at ahigher acceleration. In other words, theobject will move faster and thus the workcan be completed in a shorter time.

The energy used to lift the weight comesfrom the boy. From the conservation of

energy point of view, the faster the energyhas gone to work, the faster will the energyof the boy be used up.

38. (D) The correct order of density of threesubstances P, Q, R from least to most denseis Q, P and R.

Density of a substance =

Massof substance

Volume of substance

Density of substance P = 65

15 = 4.33 ...... (2)

Density of substance Q = 80

20 = 4 ...... (1)

Density of substance R = 60

12 = 5 ...... (3)

39. (B) Point Q has the deepest water becauseultrasound took the longest time to returnback to the receiver on the ship.

40. (B) Work done is the product of the appliedforce and the distance moved by the objectin the direction of the force. When thespaceship is cruising in space, althoughthere is distance travelled but there is noforce acting on it. As a result, no work isdone.

41. (A) If an object moves with a constant speedalong a circular path, then its velocity willnot be constant because velocity changesin a specified direction. So, the objectmoving in a circular path has a variablevelocity.

42. (C) The frequency will not change as the sourceis not being disturbed. Sound travels fasterin water than in air as vibrations travelfaster when the particles are closertogether. According to the relationship v =

f , when the frequency is constant, thespeed increases and the wavelength willalso increase.

43. (B) The smallest base area = 6 8 = 48 cm2

Pressure = Force / Area

= 24 / 48 = 0.5 N cm2

44. (D) Net force = Mass acceleration

45. (A) Work is force times displacement. Since, thegirl does not displace at all from her initialpoint, the work done remains at zero.


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Common mistake occurs when we thinkthat the work done by the girl depends onthe distance travelled by her as she jumps.

Displacement is a different term withdistance, and they are often usedambiguously. In this case, the initial andfinal position of the girl remains unchanged,which means she does not displace at all,i.e, her displacement iz zero.

46. (D) Based on the fact that iron must have a higherdensity than feathers and the formula ofdensity = mass volume and weight =mass gravitational acceleration, a table ofthe situation is given below.

tMaterial Density Mass Volume Weigh

Sack X iron high 2 kg low 20 N

Sack Y feathers low 2kg high 20 N

47. (B) Applied force opposing force

= Resultant force = ma

90 60 = 15a ; a = 2 m s2

48. (D) When the speed of a truck changes in anirregular manner, then the velocity-timegraph is a curved line.

49. (A) Distance is the total length travelled by theman whereas displacement is the position ofthe man as compared to his original position.

Final position

6 m to the south

(3 s)

8 m to the east

(2 s)

Ini al

posi on

Total Distance = 8 m + 6 m = 14 m

Total time = 2 s + 3 s = 5 s

Average speed = total distance total time

= 14 m 5 s = 2.8 m s1

Displacement = 2 28 + 6 = 10 m

Velocity = displacement time

= 10 m 5 s

= 2.0 m s1

50. (C) As radius is maximum at the equator, thevalue of g will be minimum at the equator.

Due to flattening of the earth at the poles,radius is minimum and g is maximum atthe poles. An object when weighed at thenorth pole will be the heaviest.

Chemistry

51. (C) Uranium-235 isotope is used as a fuel in thereactors of nuclear power plants forgenerating electricity.

52. (C) Mercury-ethanol is an immiscible liquidmixture. Hence, it can be separated by aseparating funnel.

(i) Distillation is the process of heating aliquid to form vapour, and then coolingthe vapour to get back the liquid e.g.,salt water. Both salt and water can berecovered by this process.

(ii) Fractional distillation is the process ofseparating two or more miscible liquidsbased on the difference in their boilingpoints. Mercury-ethanol is animmiscible liquid mixture which cannotbe separated either by distillation orfractional distillation.

53. (C) Among the three states of matter, the rateof diffusion is very fast in gases. Theparticles in gases move very quickly in alldirections. The rate of diffusion of a gasdepends on its density. Lighter gases diffusefaster than heavier gases.

Nitrogen and carbon monoxide are a pairof gases which diffuse into the vacuum atthe same speed due to their equalmolecular weights.

Nitrogen (N2) = 2 14 = 28

Carbon monoxide (CO) = Carbon 12,Oxygen 16 = 28

54. (C) Relative atomic mass of neon =

20 90 + 21 1 + 22 9

90 + 1 + 9 = 20.19

55. (C) The perfume molecules travel only shortdistances in straight lines before theycollide with another molecule, changedirection to collide again and so on. Infactat room temperature and atmosphericpressure, a perfume (gas) molecule in theair experiences several billion collisionsper second. As the room is very large, slowdiffusion occurs and perfume moleculestravel in haphazard paths. So, it takes


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several minutes before its smell can bedetected at the other end.

56. (B) Number of glucose molecules =

(no. of moles) (6.0 1023)

= 0.8 6.0 1023

= 4.8 1023

One glucose molecule contains 12 H atoms.

Hence, total number of H atoms

= 4.8 1023 12 = 57.6 1023 atoms

= 5.76 1024 atoms

57. (C) Soap solution is a colloid.

Brass is a solution of zinc in copper, a solidin a solid metallic alloy.

Milk of magnesia is a sol, i.e., a collidalsuspension of magnesium hydroxide inwater.

Copper sulphate dissolves in water, it is atrue solution.

58. (A) The atomic number of the element = 7, whichis nitrogen, N. The number of electrons inthe particle = 10. Hence, the atom has gained3 e to form a nitride ion = N3 .

59. (B) 60 g of KNO3 dissolves in 100 g of water at

40 oC

............. ? g of KNO3 dissolves in 25 g of

water at 40 oC

= 60 25

= 15 g100

So, 15 g of KNO3 dissolves in 25 g of water to

produce a saturated solution at 40 oC.

60. (C) Chlorine atom has 7 electrons in itsoutermost shell. It needs 1 more electron toachieve the 8-electron configuration oroctet. So, the chlorine atom gains (accepts)1 electron to form a chloride ion, Cl

having an inert gas electronic configurationof 2, 8, 8.

Cl

Chlorine atom

Protons = 17 (+charge)

Electrons = 17 (charge)

Cl

Chloride ion

Protons = 17 (+charge)

Electrons = 18 (charge)

Overall charge = 0 Overall charge = 1

+ 1 electron

61. (D) An atom gains or loses electrons when itbecomes an ion. The number of protonsbefore the gain/lose of electrons in an atomis same. Its atomic number or protannumber remains the same as shown below.

O

Oxygen atom

Protons = 8

Electrons = 8

O2

Oxide ion

Protons = 8

Electrons = 10

Overall charge = 0 2

+ 2 electrons

Oxygen atomOxide / oxygen ion

E.C. 2, 6

E.C. [2, 8]2

2

An atom gains or loses the right number ofelectron to produce an ion with a completeouter shell of electron or a stable octet.

62. (D) Condensation and freezing both involve theloss of heat energy by particles of asubstance. However, the change of statefrom a gas to a liquid/solid involves thelarger change in volume as particles ingaseous state are far apart, and when theycondense, they come very close togetherto form a liquid/solid.

63. (B) Element T has 12 protons. It is magnesium,a metal

(i) Magnesium reacts with oxygen to forman oxide MgO not MgO

2.

2 Mg + O2 2MgO

(ii) Magnesium reacts with chlorine toform Magnesium chloride (Mg Cl

2)

(iii) Magnesium forms a dipositive ion withcharge +2 (Mg+2) by losing 2 electrons.

(iv) Magnesium is a metal.

64. (D) It has the highest nucleon number, indicatingthe largest number of neutrons, since theisotopes share the same number of protons.

Carbon 12 Carbon 13 Carbon 14

Protons 6 6 6

Neutrons 6 7 8

Carbon 14 has 8 neutrons, highest but notthe least among the three isotopes ofcarbon.

65. (B) The melting point of pure substance X is1535 oC. It belongs to iron.

Melting point of ice is 0 oC


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Melting point of copper is 1083 oC

Melting point of wax is 63 oC

66. (A) Ethanol is a compound made up of carbon,hydrogen and oxygen elements chemicallybonded together - C

2H

5OH . Petrol is a

mixture of C5 C

10 hydrocarbons (alkanes).

Steel is an alloy made up of iron and 12%of carbon. Tap water has dissolved minerals,chloride and fluoride ions.

67. (D) Isotopes are the atoms of the sameelement having the same atomic numberbut different mass numbers. The numberof protons and electrons are equal in anatom but the number of protons andneutrons inside the nucleus differ due toincrease in the number of neutrons. Thestability of an isotopic nucleus depends onits neutron-to-proton ratio.

68. (C) In the purification of water, some alum isadded to the sedimentation tank. Theheavy particles of dissolved alum depositon the suspended clay particles in water.The suspended clay particles in water getclumped with alum particles, become heavyand settle down at the bottom of thesedimentation tank.

69. (C) (i) The electron structure of atom X ismagnesium. Its atomic number is 12 andmass number is 24.

(ii) The electron structure of atom Y isfluorine. Its atomic number is 9 andmass number is 19

(iii) Valency of magnesium is +2 andfluorine is 1

(iv) Atoms X and Y combine to form onemolecule of compound calledMagnesium fluoride (MgF

2).

Mg

2

F

1

(v) Atomic mass of magnesium = 24 g

Atomic mass of fluorine (2 19) = 38 g

= 62 g

The mass of one molecule of compoundMgF

2 is 62 g.

70. (B) Helium and nitrogen have differentmolecular masses. Helium (M

r=4) is much

lighter than nitrogen (Mr=28) and thus will

diffuse faster out of the balloon. Over thesame period of time, more of the lighter

helium will have escaped from the balloon,compared to the heavier nitrogen, thusleaving behind a higher proportion ofnitrogen. Helium diffuses faster as it has asmaller molar mass.

N2 = 2 14 = 28 g/mole

He = 1 4 = 4 g/mole

Rate = 2

28g / moleHe2.6

N 4g / mole= =

Biology

71. (B) In the given figure the part labelled as P is

the cytoplasm. Most of the cell processes

take place here.

72. (D) Euglena is a single called organism that has

both plant and animal characteristics.

73. (A) Monocotyledons are the flowering plants

that are reproduced through flowers.

74. (B) Marchantia is a bryophyte.

75. (B) Mitochondria produce energy by cellular

respiration. They are also called power

houses of the cell.

76. (D) All insects body is divided into three parts

head, thorax and abdomen. They have six

legs. Birds, fishes, amphibians and reptiles

reproduce by laying eggs. A pair of wings

are present in birds and mammal like bat.

77. (B) The increase in food grains production after

the introduction of improved varieties of

crop production is called green revolution.

78. (B) Frog is a cold blooded animal.

79. (A) Cell Tissue organ system organism.

Cell Muscles Heart System organism.

80. (B) Centipedes from latin prefix centi-

hundred and Pedere, foot are arthropods

with jointed legs.

81. (B) As per the given information, Cell P is a

plant cell and cell Q is an animal cell.

Respiration takes place in plant cell all the

time.

82. (A) The given figures P is a nerve cell, Q a RBC

and R is a sperm cell. Red blood cell does

not have a well defined nucleus.

83. (B) The science of classification is called

taxonomy.


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84. (D) In the given diagram 4 represents the host

3 pathogen and 1 vector.

85. (A) Bat and dolphin are mammals.

86. (C) Tapeworm is a parasite. The relationship

between the tape worm and the man is

called parasitism.

87. (B) The characteristic feature of

dicotyledonous plants is the reticulate type

of venation and tap root system. By

observing the leaves we can identify the

plant as dicotyledenous plant.

88. (B) Tendon is the inelastic band which connects

muscle and bone together and is able to

withstand tension. Tendon and muscle

works together to exert a pulling force.

89. (A) Organism W is most probably yeast because

yeast is a single called organism that does

not produce its own food.

90. (A) Energy leaving the decomposer is lost as

heat.

99. (Del) The chairman of ISRO was K. Radhakrishnan

at the time of questionpaper setting, but

he had retired on December 31st, 2014. So,

now the present chairman of ISRO is A.S.

Kiran Kumar.

Hence, the question is deleted.

9_NAT_SOL

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