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Q. No. 1 – 25 Carry One Mark Each

1. Solution of the linear differential equation

dy π
+ y cot x = 4x cos ecx, if y=0 when x= is
dx 2
⎛ π2 ⎞ ⎛ π2 ⎞
(A) y = ⎜ 2x2 + ⎟ cos ec x (B) y = ⎜ 2x2 + ⎟ cos x
⎝ 2 ⎠ ⎝ 2 ⎠

⎛ π2 ⎞ ⎛ π2 ⎞
(C) y = ⎜ 2x2 − ⎟ cos ec x (D) y = ⎜ 2x2 − ⎟ cos ec x
⎝ 4⎠ ⎝ 2 ⎠

2. If C and D are two events such that C ⊂ D and P (D ) ≠ 0 , then the correct
statement among the following is
P (D )
(A) P ( C | D ) = P ( C ) (B) P ( C | D ) ≥ P ( C ) (C) P ( C | D ) < P ( C ) (D) P ( C | D ) =
P (C )

3. The events A and B are such that P ( A ) = 0.2, P (B ) = 0.6, P ( A / B ) = 0.3 .

Determine P(A’ intersection B’) where A’ determines complement of A.
(A) 0.62 (B) 0.18 (C) 0.06 (D) 0.38

⎡2 1⎤ ⎡ −3 2 ⎤ ⎡1 0⎤
4. If ⎢ ⎥ A⎢ ⎥=⎢ ⎥ , then A =
⎣3 2 ⎦ ⎣ 5 −3⎦ ⎣0 1 ⎦
⎡0 1⎤ ⎡1 0 ⎤ ⎡1 1⎤ ⎡1 1 ⎤
(A) ⎢ ⎥ (B) ⎢ ⎥ (C) ⎢ ⎥ (D) ⎢ ⎥
⎣1 1⎦ ⎣1 1 ⎦ ⎣0 1⎦ ⎣1 0 ⎦

5. The change in enthalpy ΔHo for the reaction CH4 ( g) + 2O2 ( g) → CO2 ( g) + 2H2O
is −802.2 kJ . The enthalpies of formation of CH4 , CO2 and H2O −74.9, − 393.5
and x kJ / mol respectively. Find x.
(A) −241.8 kJ / mol (B) 241.8 kJ / mol
(C) −483.7 kJ / mol (D) 483.7 kJ / mol

6. For a Carnot refrigerator operating between 72ºC and 30ºC, the coefficient of
performance is
(A) 7.2 (B) 6.2 (C) 8.2 (D) 9.2

7. A substance is said to be easily biodegradable, if the ratio of BOD to COD is

(A) <0.3 (B) 0.3 − 0.6 (C) > 0.6 (D) 0

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8. A furnace is made up of red brick wall of thickness 0.5m and conductivity

__________ W/m K, if for same heat loss and temperature drop, this can be
replaced by a layer of diatomite earth of thickness 0.25m and conductivity
0.14 W/m K.
(A) 0.38 (B) 0.18 (C) 0.28 (D) 0.34

9. An equimolar liquid mixture of species 1 and 2 is in equilibrium with its vapour at

400K. At this temperature, the vapour pressure of species P1sat = 172 kPA and
P2sat = 135kPA . Assuming that Roult’s law is valid, the value of y1 is
(A) 0.26 (B) 0.36 (C) 0.46 (D) 0.56

10. A plate 3mm distant from a fixed plate moves at 0.75 m/s and requires a
force/unit area of 2 Pascal to maintain this speed. Viscosity of fluid between the
plates will be
(A) 0.008 Ns / m2 (B) 0.08 Ns / m2 (C) 0.007 Ns / m2 (D) 0.07Ns / m2

11. A piston of diameter 40mm moves inside a cylinder 40.10mm diameter. The
percentage decrease in force necessary to move the piston when the lubricant
warms up from 0 to 100OC will be _______. (Values of μ for the lubricant are
0.01725 Ns / m2 at 0ºC and 0.00312 Ns / m2 at 100ºC).
(A) 80.9% (B) 81.9% (C) 71.9% (D) 70.9%

12. Choose the correct statement(s) regarding agitation.

(1) Agitation is a process, which generally accomplishes chemical change.
(2) A propeller agitator produces mainly axial flow.
(3) Most suitable agitator for handling fibrous & dense slurries is the cone type
agitator.
(4) Paddle agitator is suitable for mixing low viscosity liquids.
(A) 1 & 2 (B) 2 & 3 (C) 3 & 4 (D) All are correct

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13. Match List – I with List – II and choose the correct answers from the codes given
below.
List – I List – II
q
(P) Flow number NQ (1)
nD3α

ρgc
(Q) Power number NP (2)
n3D5αP

6vP
(R) Sphericity ( φ ) for non-spherical particle (3) φS =
DPSP

For given propeller K and β2 is as related as 2K

(S) (4) tan β2 =
1−K
(A) P-1;Q-2;R-3;S-4 (B) P-2;Q-1;R-4;S-3
(C) P-3;Q-4;R-1;S-2 (D) P-4;Q-3;R-2;S-1

14. Convert 15.14 poises of kinematics viscosity into square feet per second. The
liquid has a specific gravity of 0.964.
(A) 1.69 ft2/s (B) 0.169 ft2/s (C) 16.9 ft2/s (D) 0.0169 ft2/s
15. A vertical circular disk 1.1m in diameter has its high point 0.4m below the
surface of a pond. Find the magnitude of the hydrostatic force on one side and
the depth of the center of pressure.
(A) 10.84kN, 10.3m (B) 9.34kN, 0.103m
(C) 8.84kN, 1.03m (D) 5.48kN, 0.0103m

16. Raffinate is defined as

(A) Solution which is to be extracted
(B) Solvent rich product of the operation
(C) Residual liquid from which the solute has been removed
(D) None of these

17. The flooding velocity in a plate column operating at 1 atmospheric pressure is

5m/s. If the column is operated at 3 atmospheric pressures under otherwise
identical conditions, the flooding velocity will be
4 5 7 2
(A) (B) (C) (D)
3 3 3 3

18. The feed to a binary distillation column has 20mol% vapor and 80mol% liquid.
Then the slope of q-line in McCabe-Thiele plot is
(A) -2 (B) -6 (C) -4 (D) -8

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19. Match the list – I (Chemical) with their Applications in List - II

List – I List – II
(P) Potassium Pyrophosphate (1) Greases
(Q) Lithium Stearate (2) Paper
(R) Tert-do decyl mercaptan (3) Modifier
(S) Aluminum Sulphate (4) Buffer
(A) P-4,Q-1,R-3,S-2 (B) P-2,Q-1,R-3,S-4
(C) P-3,Q-2,R-1,S-4 (D) P-1,Q-3,R-2,S-4

20. Choose the wrong statement regarding H2SO4 .

(P) Tower of glover acid produced by nitroso method contains 60% of sulphuric
acid
(Q) Sulphuric acid is used for fin plating
(R) H2SO4 basicity is dibasic
(S) Most recent procedure for manufacture of sulphuric acid is double contact
double adsorption [DCDA]
(A) All are correct (B) Q & R (C) P (D) R & S

Q.No. 21 to 25 are Numerical Answer Type Questions and Carry One Mark
Each. Enter a number as the answer using virtual keyboard.

21. Reaction rate of a first order reaction, which is half completed in 35min, will be
________ min-1.

22. If fluid velocity is 27 m/s and length of reactor is 0.7 cm with dispersion number
as 9, then the axial dispersion coefficient will be ________.

23. A plant has capacity of producing 23000 units per year. The annual fixed cost is
Rs. 75,000. The variable cost per unit is Rs. 12. The price of product is Rs. 18 per
unit. The breakeven point in terms of capacity of the plant will be ________ %.

24. If spring of transducer deflects 0.06m when subjected to a force of 9kN, the
spring sensitivity will be _______m/kN.

25. Accuracy is specified as ± 0.63% of true value. At 9% of full scale, the error of
instrument will be _____%.

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Q. No. 26 – 51 Carry Two Marks Each

Q.No. 26 to 30 are Numerical Answer Type Questions and Carry Two

Marks Each. Enter a number as the answer using virtual keyboard.

26. A saturated liquid at 1500kPa and 500K with an enthalpy 875kJ/kg is throttled to
a liquid vapour mix at 150kPa and 300K. At the exit condition, the enthalpy of
saturated liquid is 600kJ/kg and enthalpy of saturated vapour is 2000kJ/kg. The
percentage of original liquid, which vaporizes, is ________%.

27. A man wants to deposit in a savings bank a certain amount of money annually by
the end of current year and for a total of 30 years. The amount he deposits
annually, so that he will have Rs. 30,000 by the end of 30 years, if the interest
rate is 10%, will be Rs.___________.

28. A 40cm diameter pipe, 6000m long conveys 0.07cm of water, which is to be
pumped through a height of 8m. The horse power required by the pump, if its
efficiency is 75% will be __________HP. (Take, μf = 0.007 )

29. A furnace wall is made up of steel plate 10mm thick

(k = 20 kCal /m.hr. deg) lined on inside with silica bricks 170 mm thick
(k = 2.15 kCal / m.hr. deg) on the outside with magnesia brick 375 mm thick (k
= 5.5 kCal /m.hr. deg). Then the total resistance of composite wall will be
___________ deg-hr/kCal.

30. A package is having 50 similar components and inspection shows that four have
been damaged during transit. If 6 components are randomly drawn from
package, then probability that less than 3 components are damaged is
_____________.

31. Let A and B be two symmetric matrices of order 3.

Statement-1 : A(BA) and (AB)A are symmetric matrices.
Statement-2 : AB is symmetric matrix if matrix multiplication of A and B
is commutative.
Considering both the statements, the correct option among the following is
(A) Statement-1 is true, Statement-2 is true; Statement-2 is correct explanation
for Statement-1.
(B) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct
explanation for Statement-1.
(C) Statement-1 is true, Statement-2 is false
(D) Statement-1 is false, Statement-2 is true

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2z2 + 1
32. By using the residue theorem, evaluation of ∫ ( z + 1) ( z − 2 ) dz
C
2
in the case where

.
C is the circle z =3 gives

(A) πi (B) 2 πi (C) 3 πi (D) 4 πi

33. If a fair coin is tossed 10 times, then probability of getting at most six heads will
be
47 49 51 53
(A) (B) (C) (D)
64 64 64 64

⎛ 8 2⎞
34. The Eigen vectors of A T = ⎜ ⎟ are
⎝ −4 2 ⎠
⎛1⎞ ⎛1 ⎞ ⎛2⎞ ⎛2⎞
(A) ⎜ ⎟ (B) ⎜ ⎟ (C) ⎜ ⎟ (D) ⎜ ⎟
⎝ −2 ⎠ ⎝1 ⎠ ⎝1⎠ ⎝ −1 ⎠

35. A fluid system undergoes a process following the pressure volume relation as
5
P= + 1.5 where P is in bar and V is in m3 . During the process, the volume
V
changes from 0.15 m3 to 0.05 m3 . Determine the work done by the system.

(A) –564 J (B) –564 kJ (C) –5.64 J (D) −5.64 × 10−3 J

36. What drag force is exerted at sea level by a 4.3m breaking parachute when the
speed is 30m/s? CD = 2.2(CD remains constant)
Pair (sea level) = 1.325 kg/m3
Pair (at 2000m) = 1.009 kg/m3
(A) 43.73 m/s (B) 34.37 m/s (C) 44.37 m/s (D) 54.37 m/s

37. The spent acid from a nitrating process contains 33% H2SO4 , 36% HNO3
and 31% water by weight. This acid is to be strengthened by the addition of
concentrated H2SO4 containing 95% H2SO4 and concentrated HNO3 containing
78% HNO3 . The strengthened mixed acid is to contain 40% H2SO4 and 43%
HNO3 . Calculate the quantity of concentrated H2SO4 that should be mixed to
yield 1500 kg desired mixed acid.
(A) 217 kg (B) 727 kg (C) 816 kg (D) 556 kg

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38. According to ZN controller settings:

Type of control KC
I. P (a) 0.6 Ku
II. PI (b) 0.45 Ku
III. PID (c) 0.5 Ku
(A) I − ( a) , II − (b ) , III − ( c ) (B) I − ( c ) , II − (b ) , III − ( a)

(C) I − ( c ) , II − ( a) , III − (b ) (D) I − ( a) , II − ( c ) , III − (b )

39. A production equipment cost is Rs. 1,98,000. Its salvage value is Rs. 16,000. The
expected return is Rs. 43,000 per annum. The corporate taxes are taken as 30%.
The payback period will be
(A) 6yrs (B) 4yrs (C) 2yrs (D) 10yrs

40. In a liquid level measuring system is shown in figure, one leg of U-type is
calibrated. The measured liquid has a density of 900kg/m2. The relative density
of mercury is 13.6. The sensitivity of measuring system is

PS

h
hm

(A) 0.034 (B) 0.0034 (C) 0.4 (D) 34.03

k1 k1 = 5lit / mol ⋅ min

41. ZZZZ
The liquid phase reaction A + B YZZZ X
ZR + S
k2
k 2 = 1lit / mol ⋅ min
is to take place in 0.30 lit steady state mixed reactor. Two feed streams one
containing 2.6 mol/lit and other containing 1.8 mol lit are to be introduced in
equal volumes into the reactor and 75% conversion of limiting component is
desired. What should be the flow rate of each stream? Assume constant density
throughout.
(A) 50 lit/min (B) 53 lit/min (C) 57 lit/min (D) 59 lit/min

42. A thermocouple system has time constant of 20s. It is used to measure a

temperature of surface varying between 300 and 350OC with a periodic time 60s.
The thermocouple will indicate maximum temperature of
(A) 328OC (B) 330OC (C) 336OC (D) 340OC

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43. The specific heats of a gas are given by Cp = a + KT and CV = b + K T , where a, b

and K are constants and T is in K. For an isentropic expansion of this gas.
(A) T a−b Vb eKT = cons tan t (B) T b V a−b eKT = const an t
1 1 1 1
(C) T b V a−b eKT = const an t (D) T a−b V b eKT = const an t

44. 95% of SO2 present in 8% (mole basis) SO2 air mixture is recovered by fresh
water in a packed absorption tower. Hourly rates of gas and water are 7000 kg
and 200000 kg respectively.

% SO2 in solution 0.2 0.3 0.4 0.6 0.8 1.0 1.2

Partial Pressure
3.2 8.5 14.1 26 39 59 92
(mm Hg)
GmHi
HTU can be calculated from HOG (HTU) = Hg + m
Lm
Hg = height of gas film transfer unit = 0.9m
Hi = height of liquid film transfer unit = 0.9m
m = slope of equilibrium relation (may be taken as 35)
Flooding velocity = 0.75 kg / m s
Operating velocity = 56% of flooding
Find the diameter of column.
(A) 2.42m (B) 3.42m (C) 4.42m (D) 5.42m

45. The influence of pressure on chemical potential can be expressed as

⎛ ∂ vi ⎞ ⎛ ∂μi ⎞ ⎛ ∂μi ⎞ ⎛ ∂μi ⎞
(A) ⎜⎜ ⎟⎟ = μi (B ) ⎜ ⎟ = vi (C ) ⎜ ⎟ = vi (D ) ⎜ ⎟ = vi
⎝ ∂P ⎠ T,ni ⎝ ∂ T ⎠P,n: ⎝ ∂P ⎠ T,ni ⎝ ∂ni ⎠ T,P

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46. Identify the end products of following reactions.

NH2 NH2
N
(1) + HCHO ?
N N
CH = CH2
NH2

(2 ) CH2 = CH − CH = CH2 + ?

NH2 NH2 CH3 − CH − CH3

N
(A)
;
N N

NH2 NHCH2OH ( −CH2 − CH = CH − CH2 − CH − CH2 )n

N
(B)
N N

NH2

NH2 CHO − ( CH2 − CH − CH2 )n −

N
;
(C) N N

NH2

N
(D) ; Ph − CH = CH2
N N
N

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47. For the reaction, CO2 ( g) + H2 ( g) → CO ( g) + H2O ( g) , at 298K, equilibrium constant

is 8.685 x 10-6. Estimate the value of ka at 1000K, assuming that ΔHo is constant
in the temperature range of 298K to 1000K.
The data given is

Component ΔH0f (kJ / mole )

CO(g) 110.532
H2O(g) -241.997
CO2(g) -393.978
H2(g) 0

⎛ ∂ ln k a ⎞ ΔHO
Van’t Hoff’s equation is ⎜ ⎟ = , where ΔHO is the standard heat of
⎝ ∂T ⎠ RT2
reaction.
(A) 1.746 x 1027 (B) 1.476 x 1027 (C) 2.41 x 1027 (D) 1.626 x 1027

Common Data Questions: 48 & 49

A binary distillation column separates 100ml/hr of a feed mixture into distillate D

and residue W. The McCabe Thiele diagram for this process is given below.

0.1
(0.07, 0.07 ) (0.92, 0)
0 0.1 0.2 0.9 1

48. The distillate and residue flow rates in mol/hr are

(A) D = 62.35; W = 37.65 (B) D = 37.65; W = 62.35
(C) D = 60; W = 30 (D) D = 30; W = 60

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A binary distillation column separates 100ml/hr of a feed mixture into distillate D

and residue W. The McCabe Thiele diagram for this process is given below.

0.1
(0.07, 0.07 ) (0.92, 0)
0 0.1 0.2 0.9 1
49. The ratio of liquid to vapour molar flow rate in the rectifying section is
(A) 18.83 (B) 0.23 (C) 81.18 (D) None of these

Common Data Questions: 50 & 51

Methane and steam are fed to a reactor in molar ratio 1: 2. The following
reaction takes place
CH4 ( g) + 2H2O ( g) ⎯⎯⎯
→ CO2 ( g) + 4H2 ( g)

CH4 ( g) + H2O ( g) ⎯⎯⎯

→ CO ( g) + 3H2 ( g)

Where CO2 is desired product and CO is undesired product and H2 is by product.

The exit steam has following composition:

Species CH4 H2O CO2 CO H2

Mole % 5.73 11.38 16.46 3.31 70.5

50. The selectivity for desired product relative to undesired product is

(A) 2.97 (B) 3.97 (C) 4.97 (D) 5.97

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Methane and steam are fed to a reactor in molar ratio 1:2. The following reaction
takes place
CH4 ( g) + 2H2O ( g) ⎯⎯⎯
→ CO2 ( g) + 4H2 ( g)

CH4 ( g) + H2O ( g) ⎯⎯⎯

→ CO ( g) + 3H2 ( g)

where CO2 is desired product and CO is undesired product and H2 is by product.

The exit steam has following composition

Species CH4 H2O CO2 CO H2

Mole % 5.73 11.38 16.46 3.31 70.5

51. The fractional yield of CO2 is

(A) 0.57 (B) 0.67 (C) 0.77 (D) 0.83

Linked Answer Questions: Q.52 to Q.55 Carry Two Marks Each

Statement for Linked Answer Questions: 52 & 53

A 0.17m diameter journal runs in a bearing 0.5m long. The lubricant used has
specific gravity of 0.923 and a kinematic viscosity of 1.71 stokes. The radial
clearance may be assumed to be uniform and equal to 0.04m.
52. The torque to overcome viscous resistance of lubricant will be
(A) 161.16N/m (B) 171.16N/m (C) 181.18N/m (D) 151.15N/m

A 0.17m diameter journal runs in a bearing 0.5m long. The lubricant used has
specific gravity of 0.923 and a kinematic viscosity of 1.71 stokes. The radial
clearance may be assumed to be uniform and equal to 0.04m.
53. The power required to overcome the viscous resistance of lubricant journal
rotating at 300 r.p.m will be
(A) 0.506kW (B) 5.060kW (C) 56.04kW (D) 50.46kW

Statement for Linked Answer Questions: 54 & 55

A liquid phase reaction C ⎯⎯⎯→ D is conducted isothermally in CSTR having

residence time 6s. The inlet concentration of species is 6mol/ lit. Outlet
concentration is 20mol/ lit.
kCA
The rate law for the reaction is −rA = .
k + CA

54. If k1 = 7 moles /litre, find k 2 .

(A) 11 (B) 12 (C) 18 (D) 20

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A liquid phase reaction C ⎯⎯⎯→ D is conducted isothermally in CSTR having

residence time 6s. The inlet concentration of species is 6mol/ lit. Outlet
concentration is 20mol/ lit.
kCA
The rate law for the reaction is −rA = .
k + CA
55. If the same reaction conducted in series of two CSTRs with residence time 3s and
0.5s, then the inlet concentration of A is
(A) 4.309 (B) 3.309 (C) 1.309 (D) 2.309

Q. No. 56 – 60 Carry One Mark Each

56. The beneath question has a set of four words. Choose the word that does NOT
belong to the group.
(A) Resurgence (B) Comeback (C) Recovery (D) Regression

57. Given below are four sentences. Which of the following four arrangements is the
best way to express the sentence?
(a) Though the law did not permit it,
(b) After the execution of Ajmal Kasab,
(c) A relative of a 26/11 victim was quoted as saying that,
(d) The mass murderer should “have been hanged in public.”
(A) abcd (B) bacd (C) bcad (D) dabc

58. Which of the following is closest in meaning to the word “Presumptuous”?

(A) Down to earth (B) Behaviour (C) Arrogant (D) Modest

Directions for Question 59: In the following question, identify the pair that
best expresses a similar relationship similar to that expressed in the original.
59. Sleep: Night :: Hibernate : ___________
(A) Ground (B) Cold blooded (C) Summer (D) Winter

60. Jatin remembers that his friend Vinay’s birthday falls after 20th of August but
before the 28th of August, while Amit remembers that Vinay’s birthday falls
before the 22nd of August but after the 12th of August. What is Vinay’s exact date
of birth, if they are both right?
(A) 20th August (B) 21st August (C) 22nd August (D) 23rd August

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Q. No. 61 – 65 Carry Two Marks Each

61. Honour killings continue to occur with alarming frequency in India, particularly in
northern states. One of the primary reasons is the failure of state and police
agencies to protect the victims or prosecute perpetrators of the crime. What’s
deeply worrying is evidence of collusion among powerful community and state
agencies, with the authority of khap panchayats allowed to overrirde the Indian
Penal Code (IPC). Honour killings are endemic in Punjab, Haryana, UP and
Rajasthan.
Which of the following statements best supports the author’s contention?
(A) If India is to emerge as a modern nation, the fundamental rights of citizens
must be given high priority.
(B) According to Punjab Police data, 34 honour killings took place there between
2008 and 2010.
(C) What’s preventing its diligent enforcement is the nexus between the police
and political parties.
(D) The police fail to take honour killings seriously.

62. There are four mixtures (P, Q,R and S) containing liquids X and Y in different
proportions. Mixture P contains X and Y in the ratio 1:2, Q in the ratio 11:13, R in
the ratio 5:3 and S in the ratio 19:5. Which of the following parts, mixed in equal
quantity will have the highest concentration?
(A) Q and R (B) P and R (C) P and S (D) Q and P

63. There are five restaurants in a line. If 4 men go into a restaurant at 11 a.m, what
is the probability that each go into a different restaurant?
124 24 240 48
(A) (B) (C) (D)
125 125 625 625

64. The value of a two-digit number is 6 times the sum of its digits, then find the
difference of the digits.
(A) 1 (B) 2 (C) 3 (D) 4

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Data for Question: 65

The chart shows the production of soft drinks (in thousand tonnes) by three
companies P, Q, and R over the years.

60

50

40

30

20

10

0
2000 2001 2002 2003

P Q R

65. Which of these statements are true?

(i) Average production of P in four years is 27.5.
(ii) Percentage decrease of Q in 2002 from the previous year is 100%.
(iii) Ratio between the production of R in 2002 and Q in 2001 is 3:4.
(iv)Total production of P in four years is equivalent to total production of Q and R
in 2002 and 2003 put together.
(A) (i) and (iii) only (B) (i), (ii) and (iii) only
(C) (i), (ii) and (iv) only (D) (i), (ii), (iii) and (iv)

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