CHEMISTRY · The equivalent conductivity of a monobasic acid at infinite dilution is 348ohm cm eq 1...

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CHEMISTRY 1. The correct order of coagulation power of different ions is

1) 23Al Ba Na 2) 24

434 6Cl SO PO Fe CN

3) 24

4 36 4Fe CN PO SO Cl 4) 3 2Al Ba Na

2. 25ml of 2 2H O on treatment with excess of acidified KI solution liberates iodine.

Liberated iodine requires 40ml of 0.4N 2 2 3Na S O solution. The volume strength of

2 2H O solution is

1) 1.344 2) 3.584 3) 0.64 4) 1.584

3. The equivalent conductivity of a monobasic acid at infinite dilution is

1 2 1348ohm cm eq . If the resistivity of the solution containing 15g acid (M.Wt-49) in 1

lit is 18.5 ohm cm, what is the degree of dissociation of acid ?

1) 50.7% 2) 60.4% 3) 25.35% 4) 40%


4. For the reaction, 4 32CH g Cl g CH Cl g HCl g ; 25 .H k cal . Bond energy

of C H is 120 .K Cal mole greater than the bond energy of C Cl bond. Bond energy

of H H and H Cl are same in magnitude. Then H value for the reaction is

2 21 12 2

H g Cl g HCl g is

1) 120.5 .K Cal mole 2) 122.5 .K Cal mole

3) 145 .K Cal mole 4) 190 .K Cal mole

5. An impure sample of NaCl weighing 2 grams was dissolved in water and excess of

3AgNO solution was added. The weight of precipitate formed was 0.287g. The

percentage purity of the sample is

1) 11.7% 2) 5.85% 3) 25% 4) 2.85%

6. The density of an ionic crystal is 32.75g cm and edge length of unit cell is 660 pm.

The formula weight of ionic compound is 119. The number of unit cells present in

23.8 g of the ionic compound is

1) 231.2046 10 2) 223.011 10 3) 226.023 10 4) 221.2046 10


7. An organic compound has 14% of nitrogen. It is subjected to kjeldahl’s method and

the ammonia evolved is absorbed in 100ml of 1 normal sulphuric acid. About 400ml

of water was added. And 20 ml of this new solution now required 16ml 5N NaOH for

complete neutralization. Calculate the original weight of the organic compound taken.

1) 2 gm 2) 1.4 gm 3) 4 gm 4) 20 gm

8.

1) 3CH CHO 2) Racemic (2R, 3R) and (2S, 3S) – 2, 3 butanediol

3) cis 2,3 epoxylbutane 4) meso 2,3 butanediol

9. The velocity of electron is 6 12.2 10 secm . If the uncertainty in its velocity is 0.1% the

uncertainty in its position is

1) 102.63 10 m 2) 26.3A 3) 26.3 nm 4) 2.63nm


10. For the decomposition of 5PCl g in a closed vessel, the degree of dissociation is ‘x’

at a total pressure ‘P’. 5 3 2 ;PCl g PCl g Cl g Kp

Which among the following relations is correct?

1) p

p

Kx

K P

2) p

p

K Px

K

3) px K P 4) 1

px

K P

11. Observe the following statements

a) The almost identical radii of Zr and Hf is consequence of Lanthanide contraction

b) 2Eu act as a strong reducing agent

c) An alloy of lanthanoid metal called mischmetal is used in making bullets

d) Actinoid contraction is greater from element to element than lanthanide contraction.

The correct statements are

1) a, b, c 2) a, b, c, d 3) b, c, d 4) a, c, d

12. 22O ZnOre CN H O X Y metal . X and Y in this reaction is

1) 2

2 4;X Ag CN Y Zn CN

2) 2

4 42

;X Ag CN Y Zn CN

3) 2

2 4;X Au CN Y Zn CN

4) 1 and 3


13. Which of the following is correct

1) 3 24Co NH Cl

does not exhibit geometrical isomerism.

2) 3 2 25Co NH NO Cl

does not exhibit linkage isomerism.

3) 23

2cis CrCl ox

is optically active

4) 3 45Co NH SO Br

and 3 45Co NH Br SO

are coordination isomers.

14. The equilibrium constant for the following reaction at 400K is

22 2NOCl g NO g Cl g . Given 0 177.2H KJ mole ; 0 1 1122S JK mole

log1.95 0.292

1) 41.995 10cK 2) 35.105 10cK 3) 42.5 10cK 4) 41.95 10

15. Which of the following is a wrong statement.

1) Buna-N, Buna-S are elastomers

2) Urea – HCHO resin is thermosetting polymer.

3) Neoprene is a condensation polymer

4) Polystyrene is used in making television cabinets.


16. Which among the following are correct statements

a) Order of O O bond length is 2 2 26O AsF O KO

b) Though Ethylalcohol and Dimethyl ether have same molecular weights, Dimethyl

ether is more volatile than Ethylalcohol.

c) The order of bond order is 2 2 22N N N

d) Ice has more density than water

1) a, b, d 2) a, b, c 3) a, c, d 4) a, b, c, d

17. The osmotic pressure of 0.1M solution of 2MgCl at 300K is 4.92 atm. The percentage

ionization of the salt is

1) 20% 2) 39% 3) 49% 4) 69%

18. A salt ‘X’ on heating liberate one coloured gas and another coloureless gas. Both the

gases are paramagnetic. The salt ‘X’may be

1) 3NaNO 2) 3KNO 3) 2 3Na CO 4) 3LiNO

19. Compressibility factor for 2H behaving as real gas is

1) 1 2) 1 aRTV

3) 1 Pb

RT

4) 1RTV

a


20. In which of the following arrangements the order is not correct according to the

property indicated against it ?

1) 2 2 3O F Na Mg Al (ionic radii)

2) F Cl Br I (Electron gain enthalpy)

3) B C O N (First ionization enthalpy)

4) 5 72 2 3 2SiO P O SO Cl O (acidic nature)

21. Which of the following causes depletion of ozone layer.

1) CFC 2) NO 3) 2Cl 4) All the above

22. 93.75% of a 1st order reaction is completed in 120 minutes. If initial concentration of

the reactant is 2 mole/lit, the rate of reaction at the end of 120 min is

1) 2 14.62 10 minM 2) 3 12.31 10 minM 3) 3 12.88 10 minM 4) 4 16.93 10 minM

23. Which of the following is wrong statement. 1) 2 5I O is a very good oxidizing agent and is used in the estimation of carbon

monoxide. 2) 2ClO is used as bleaching agent for paper pulp and textiles.

3) When HCl reacts with finely powdered iron, it forms ferrous chloride and not ferric chloride. 4) The inter halogen compound 1XX hydrolysis as follows.

1 12XX H O HX HOX [when X = larger halogen]


24. Which of the following is wrong

1) Alkyl chloride when passed over silicon at 0300 C in the presence of Cu catalyst

organosilanes are formed.

2) Chloro silanes on hydrolysis followed by polymerization give silicones.

3) Buckminister fullerene contains twenty, 6- membered rings and twelve 5-

membered rings.

4) All the tetrahalides of IV A group elements readily undergo hydrolysis

25. A carbonyl compound ‘X’ with molecular formula 105C H O gives negative tollens and

iodoform tests and is reduced to n – pentane by Zn Hg & HCl . The compound ‘X’ is

1) 1 pentanol 2) pentanal 3) 2-pentanone 4) 3-pentanone

26. Three organic compounds A, B & C liberates 2H gas when react with Na metal.

Compounds ‘A’ and ‘B’ reacts with Tollens reagent but not ‘C’ . A decolourises

bromine water. But not ‘B’. Then ‘A’ is

1) H3C C CH3

O

2) HCOOH

3) CH CH 4) 3 3CH C C CH


27. Which of the following sequence of reagent is the good means to furnish the

conversion

2 2 2R CH OH R CH NH

(a) 4 2 3; ; , ;KMnO SOCl NH NaOBr (b) 2 2; ; /SOCl NaCN H Ni

(c) 3CrO in dilute acetone; 3 2; /NH H Ni (d) 03 4/ 300 ; ;Cu C NH LiAlH

1) a, b, c, d 2) a, b, c 3) b, c, d 4) c, d

28. Incorrect pair

1) Biuret test – Protein 2) Molish test – Carbohydrates

3) Neutral 3FeCl test – Phenols 4) Xanthanate test – Carboxylic acids

29. The number of chiral centres present in gluco pyranose and fructo furanose are

1) 4 and 5 2) 5 and 4 3) 4 in each 4) 5 in each

30.

2 43. .Conc HNO Conc H SO

6 6C H 060 C2 ,Br Fe

P

Q

X Major

Y Major

2 ,Br Fe

2 43. .Conc HNO Conc H SO

Then, the products X and Y are

1) Same compounds 2) Functional isomers

3) Chain isomers 4) Positional isomers


PHYSICS

31. The displacement x of a particle varies with time according to the relation

1 btax eb

. Then

1) At 1/t b , the displacement of the particle is nearly 4 / 3 /a b

2) The velocity and acceleration of the particle at 0t are a and ab respectively.

3) The particle cannot reach a point at a distance ' 'x from its starting position if

/x a b

4) The particle will come back to its starting point as t

32. The horizontal distance x and the vertical distance y of a projectile at time t w.r.t

point of projection are given by x at and 2y bt ct where a, b and c are constants.

Then

1) The speed of the projectile 1 second after it is fired is 1/22 2 2a b c

2) The angle with the horizontal at which the projectile is fired is 1sin ca

3) The acceleration due to gravity is 2c

4) The initial speed of the projectile is 1/22 2a c


33. Two blocks A and B are connected to each other by a string and a spring of force

constant k , as shown in fig. The string passes over a frictionless pulley as shown. The

block B slides over the horizontal top surface of a stationary block C and the block A

slides along the vertical side of C both with the same uniform speed. The coefficient

of friction between the surfaces of the blocks is . If the mass of block A is m . The

mass of block B is

1) m

2) m

3) m 4) m

34. Which one of the following waves cannot be polarized ?

1) radio waves 2) X – rays

3) transverse waves in a string 4) longitudinal waves in a gas


35. A smooth uniform rod of length L and mass M has two identical beads of the

negligible size, each of mass m , which can slide freely along the rod. Initially the two

beads are at the centre of the rod and the system is rotating with angular velocity 0

about its axis perpendicular to the rod and passing through its mid point (see Fig).

There are no external forces. When the beads reach the ends of the rod, the angular

velocity of the system is

1) 0

3M

M m

2) 0

6M

M m

3) 06M mM

4) 0


36. The track shown in Fig ends in a circular track of radius r with centre at O. A small

solid sphere of mass m rolls from rest without slipping from a point A at a height

6h r from the level ground. The speed of the sphere when it reaches a point B at

height r above the level ground in the circular track is

6h r

O Br

ASphere

m

1) 10gr 2) 507

gr 3) 227

gr 4) Zero

37. A ball is dropped downwards to hit the ground at time t=0. After 1 second another ball

is dropped downwards from the same point. The distance between them after 3

seconds is

1) 25 m 2) 20 m 3) 50 m 4) 9.8 m


38. A J – tube , shown in the figure, contains a volume V of dry air trapped in arm A of

the tube. The atmospheric pressure is H cm of mercury. When more mercury is poured

in arm B, the volume of the enclosed air and its pressure undergo a change. What

should be the difference ‘h’ in mercury levels in the two arms so as to reduce the

volume of air to / 2V ? (See Fig)

1) H cm 2) / 2H cm 3) 2H cm 4) / 3H cm

39. A liquid is kept in a vertical cylindrical vessel with upper end is open to atmosphere.

When the vessel is rotated about its axis, the liquid rises at its sides. If the radius of the

vessel is 0.05 m and the speed of rotation is 2 revolutions per second, the difference in

the heights of the liquid at the centre and at the sides of the vessel will be (take 210g ms and 2 10 )

1) 2 cm 2) 4 cm 3) 1 cm 4) 8 cm


40. The centre of a ring of mass m and a sphere of mass M of equal radius R, are at a

distance 8 R apart as shown in Fig. The force of attraction between the ring and the

sphere is

RR

Mm

8 RA B

1) 22 227

GmMR

2) 28GmM

R 3) 29

GmMR

4) 22

9 9GmM

R

41. If the energy , p q rE G h c , where G is universal gravitational constant , h is the

Plank’s constant and c is the speed of light, then the values of p, q and r are,

respectively

1) 1/ 2, 1/ 2 and 5 / 2 2) 1/ 2, 1/ 2 and 5 / 2

3) 1/ 2, 1/ 2 and 3 / 2 4) 1/ 2, 1/ 2 and 3 / 2


42. The ends of a rod of length l and mass m are attached to two identical springs as

shown in fig. The rod is free to rotate about its centre O. The rod is depressed slightly

at end A and released. The time period of the resulting oscillations is

O B

k

2l

A

k

2l

1) 22mk

2) 22 mk

3) 23mk

4) 32mk

43. A cube of wood supporting 200 g mass just floats in water. When the mass is

removed , the cube rises by 2 cm. What is the side of the cube ?(Given density of

water= 31 /g cm )

1) 10 cm 2) 20 cm 3) 30 cm 4) 40 cm


44. Three infinite long plane sheets carrying uniform charge densities 1 2, 2

and 3 3 are placed parallel to the x z plane at y a , 3y a and 4y a as shown

in fig. The electric field at point P is

3 3

2 2

1

4y a

3y a

y aP

x

y

O

1) Zero 2) 0

2 j

3) 0

3 j

4) 0

3 j

45. A photon and electron have same de-Broglie wavelength. Given that v is the speed of

electron and c is the speed of light; , peE E are the kinetic energies of electron and

photon respectively. , hep p are the momenta of electron and photon respectively.

Then which of the following relation is correct.

1) 2p

eE vE c

2) 2

p

eE cE v

3) 2h

ep cp v

4) 2

h

ep cp v


46. The density of a liquid of coefficient of cubical expansion is at 00 C . When the

liquid is heated to a temperature T , the change in density will be

1) 1

TT

2) 1

TT

3) 1 TT

4) 1 TT

47. A thermally insulated rigid container contains an ideal gas at 027 C . It is fitted with a

heating coil of resistance 50 . A current is passed through the coil for 10 minutes by

connecting it to a d.c source of 10 V. The change in the internal energy of the gas is

1) Zero 2) 300 J 3) 600 J 4) 1200 J

48. The electric field in a region is given by 3 12 3 10E i j NC

The electric flux through a rectangular surface 10 20cm cm held parallel to the

y z plane is

1) 1 240 NC m 2) 1 250 NC m 3) 1 260 NC m 4) Zero

49. A metal wire of sonometer is held on two knife edges with tension 100N. The wire

vibrating with its fundamental frequency and a vibrating tuning fork together produce

5 beats per second. The tension in the wire is then reduced to 81N. When the two are

excited, beats are heard at the same rate. What is the frequency of the fork ?

1) 90 Hz 2) 95 Hz 3) 100 Hz 4) 105 Hz


50. For the circuit shown in fig., which of the following statements is true ?

+ + 1S 3S 2S

1 30V V

1 2C pF2 20V V

2 3C pF 1) With 1S closed, 1 215 , 20V V V V

2) With 3S closed, 1 2 25V V V

3) With 1S and 2S closed 1 2 0V V

4) With 1S and 3S closed, 1 30V V and 2 20V V

51. Two pendulums of length 121 cm and 100 cm start vibrating. At some instant the two

are at their respective mean positions and in the same phase. After how many

vibrations of the shorter pendulum, the two will be again in phase at their mean

positions for the first time?

1) 10 2) 11 3) 20 4) 21

52. A potential difference of 600 V is applied across the plates of a parallel plate capacitor. The separation between the plates is 3 mm. An electron projected into the space between the plate and parallel to the plates, with a velocity of 6 12 10 ms moves undeflected between the plates. The magnitude of the magnetic field between the capacitor plates is

1) 0.1 T 2) 0.2 T 3) 0.3 T 4) 0.4 T


53. For a certain thermocouple, if the temperature of the cold junction is 00 C , the neutral

temperature and temperature of inversion are 0285 C and 0570 C respectively. If the

cold junction is brought to 010 C , then the new neutral and inversion temperature are

respectively

1) 0285 C and 0560 C 2) 0285 C and 0570 C

3) 0295 C and 0560 C 4) 0275 C and 0560 C

54. When an electron jumps from the fourth orbit to the second orbit, one gets the

1) second line of Paschen series 2) second line of Balmer series

3) first line of Pfund series 4) second line of Lyman series

55. A coil having n turns and resistance R ohm is connected with a galvanometer of

resistance 4R ohm. This combination is moved in a region where magnetic flux

changes from 1W weber to 2W weber per each turn in t second. The induced current in

the circuit is

1) 2 1

5W W

Rnt

2) 2 1

5n W W

Rt

3) 2 1W WRnt

4) 2 1n W WRt

56. An electron moves in a circular orbit of radius r with an angular velocity in a singly ionized sodium atom. The magnetic induction (in tesla) at the centre of the nucleus will be (here e is the charge of electron).

1) 710er 2) 710

2e

r 3) 7

2 10er 4) 7

2

2 10er


57. An illuminated object is placed at a distance D from a screen. When a convex lens is

placed at position A, a sharp magnified image is obtained on the screen. When the lens

is shifted by a distance d to another position B, a sharp but diminished image is

obtained on the screen. The ratio between the sizes of the two images will be

1) Dd

2) 2

2

Dd

3) D dD d

4)

2

2

D dD d

58. For a transistor, the current amplification factor 0.9 . This transistor is connected in

common emitter configuration. When the base current changes by 0.4 mA , the change

in collector current will be

1) 36 mA 2) 9 mA 3) 4 mA 4) 3.6 mA

59. Interference pattern is obtained with two coherent light sources of intensity ratio n . In

the interference pattern, the ratio max min

max min

I II I

will be

1) 1

nn

2) 2

1n

n 3)

21

n

n 4)

2

2

1

n

n

60. The kinetic energy of the most energetic photo electrons emitted from a metal surface is doubled when the wavelength of the incident radiation is reduced from 1 to 2 . The work function of the metal is

1) 2 11 2

2hc

2) 1 21 2

2hc

3) 1 21 2

hc

4) 1 21 2

hc


MATHEMATICS

61. If the algebraic sum of the perpendicular distances from the points (3, 1), (-1, 2) and

(1, 3) to a variable line is zero, and 2

4 3 2

1 1 22 3 3 2 4

4 4 3 2 5

x x xx x x mx nx px qx r

x x x

be an

identity in x then the variable line always passes through the point:

1). (m, r) 2). (-r, m) 3). (r, m) 4). (2r, m)

62. If ][, xx are the modulus and integral part of ‘x’ respectively and

nx

nx

xxxf

1;0

1;1)(

where ,Nn Then

1) )(xf is discontinuous every where

2) )(xf is non derivable every where

3) )(xf is non-periodic

4) )(xf is a periodic and every where derivable


63. A variable line ‘L’ is drawn through O(0, 0) to meet the lines 1 : 10 0,L y x

2 : 20 0L y x at the points A and B respectively. A point P is taken on ‘L’ such that

OA, OP, OB are in H.P. Locus of P is

1) 3 3 40x y 2) 3 3 40 0x y 3) 3 3 40x y 4) 3 3 40y x

64. The number of ordered pairs (x,y) satisfying the equation sin sin sin( )x y x y and

1x y is

1) 4 2) 6 3) 8 4) 2

65. In the figure, OABC is a square of side 8 cm, then the equation of the smallest circle is:

1) 2 2( 4) ( 4) 4x y 2) 22 2( 4) ( 4) 2 1x y

3) 22 2( 4) ( 4) 2 1x y 4) 22 2( 4) ( 4) 2 2 2x y

66. If [cot1x]2 + (cot1x)2 2[cot1x]2 (cot1x) 2, where [.] denotes greatest integer x

& (.) denotes least integer x, the value of ‘x’ satisfying will be

1) 4

2) Cot1 3) cot 1 4) cot 2


67. The value of n

2n k 1

n k 4kLt cosnn

equals

1) 1 1 1sin 4 cos44 16 16

2) 1 1 1sin 4 cos44 16 16

3) 1 1 sin 416

4) 1 1 cos416

68. Two 8 faced dice (numbered from 1 to 8) are tossed. The probability that the product

of two counts is a square number, is

1) 18

2) 732

3) 316

4) 38

69. General solution of the differential equation 22 x ysin 2x dx 3y cos2x dy 0 is

1) 2 3x y ysin 2x C 2) 2 3x y ycos2x C

3) 2 2x y ysin 2x C 4) 2 2x y ycos2x C

70 The probability that a randomly chosen 3 digit in number has exactly 3 factors is

1). 2225

2). 7900

3). 7300

4). 3500

71. If z satisfies the condition 4

amp z i . Then minimum value of 1 2 3z i z i is

1) 4 2) 5 3) 5 1 4) 0


72. Let 2 21 1g x f 2x 1 f 1 x x R,4 2

where f " x 0 x R , g(x) is necessarily

increasing in the interval.

1) 2 2,3 3

2) 2 2,0 ,3 3

3) 1,1 4) [ 1,1]

73. If the graph of 3 2f x 2x ax bx, where a, b N cuts the x-axis at three distinct

points, then minimum value of a b is

1) 2 2) 3 3) 4 4) 5

74. 3 3 matrices are formed using the elements from the set

{ 2013, 2012, 2011,0,2011,2012,2013} . Number of matrices whose trace is at least

6037 is

1) 9 37 7 2) 65(7 ) 3) 610(7 ) 4) 77

75. If be non-real complex cube roots of unity, then the value of

4

17

2

1

( )

( )

p

p

q

q

is equal to

1) 1 32i 2) 1 3

2i 3) 1 3

2i 4) 1 3

2i


76. If 1Z and 2Z are complex numbers such that 2 2 2 21 2 1 2 1 215 13 13 15Z Z Z Z Z Z ,

then the value of .......... is equal to

1) 394 2) 934 3) 439 4) 943

77. If log log

x y z x y z x y z x y zx log y z

then . 2 . 3 .

. .

y x z y x z

z y x z y x

x y y z z xy z z x x y

1) –1 2) 3 3) 1 4) 0

78. If 1 11 1a tan cos ,b tan cos4 2 m 4 2 m

then

1) 2ma b

2) 2 22 ma b

3) 2a b

m

4) 2 22 ma b

79. A point P is selected inside an equilateral triangle. If sum of lengths of perpendiculars

dropped on to three sides from P is 10 then the length of altitude of triangle is

1) 5 2) 5 32

3) 10 3 4) 10

80. If the function 2f x 2x 3x 5 satisfies LMVT at x = 3 on the closed interval [1,a]

then the value of ‘a’ is equal to

1) 3 2) 4 3) 5 4) 1


81. The figure shows two regions in the first quadrant. A t is the area under the curve y =

2sin x from 0 to t and B(t) is the area of the triangle with vertices O, P and M(t,0).

t 0

A tLt

B t equals.

XO

Y

M

2P t,sin t

II

B t

1) 13

2) 12

3) 23

4) 35

82. The slope of the tangent at the point of inflection of 3 2y x 3x 6x 2009 is equal to

1) 1 2) 2 3) 3 4) 4

83. Consider the curve Max x y , x y 2 . Let f(x) be given by the part of the curve

which lies above the x-axis, then the value of 1/2

1/2f x dx

is equal to

1) 4 2) 14

3) 32

4) 148


84. The sum 1 11

63 2 3 2

k

k k k kk

1) 1 2) 2 3) 3 4) 4

85. If

2

2x 20I dx

x sin x 5cos x

, then ‘ I ’ equals

1)

x tan x ccos x xsin x 5cos x

2) x cot x c

sin x(xsin x 5cos x)

3)

x tan x ccos x x sin x 5cos x

4)

x cot x csin x 5xsin x cos x

86. If x 10 8cos ycos zcos3 3

then xy + yz + zx is equal to

1) 1 2) 2 3) -1 4) 0

87. Let P(x) be a polynomial with degree 2012 and leading co-efficient unity such that

P(0)=2011, P(1)=2010, P(2)=2009,….P(2011)=0 then the value of P(2012)= n a

where n and a are natural numbers then value of n a

1) 2013 2) 2012 3) 2011 4) 2010


88. Let n ' 2n ' 3nS S S are the sums of n, 2n, 3n terms of an arithmetic progression, then

3n

2n n

SS S

is equal to

1) 1 2) 3/2 3) 2 4) 3

89. A plane is such that the foot of perpendicular drawn from the origin to it is (2, -1, 1).

The perpendicular distance of the point (1,2,3) from the plane is (in units)

1) 32

2) 12

3) 32

4) 32

90. The equation 1/2 1/21/2 1/23 4 1 8 6 1 1x x x x

1). no solution 2). only 1 solution

3). only 2 solutions 4). more than 2solutions

CHEMISTRY · The equivalent conductivity of a monobasic acid at infinite dilution is 348ohm cm eq 1...

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