Indian Institute of Technology Madras (IIT-M) 2010 M.Tech Agricultural Engg Agricultural Process&Food Engg. Agricultural engineering gate- - Question Paper
2010 AG
Duration Three Hours Maximum MarKv. 100
Read the following Instruction? carefully.
J. Tliis question paper contains 16 pages including blank pages for rough work. Please check all pages and report discrepancy, if any
2. Write your registration number, your name and name of the examination centre at the specified locations on the right half of the Optical Response Sheet (ORS).
3. Using HB pencil, darken the appropriate bubble under each digit of your registration number and (he letters corresponding lo your paper code.
4. All questions in this paper are of objective type.
5. Questions must be answered on the ORS by darkening the appropriate bubble (marked A, B, C. D) using HB pencil against the question number on the left hand side of the ORS. For each question darken the bubble of the correct answer. In case you wish to change an answer, erase the old answer completely. More than one answer bubbled against a question will be treated as an incorrect response.
6. There are a total of 65 questions carrying 100 marte.
SEAL
7. Questions Q.l - Q.25 will carry 1 -mark each, and questions Q.26 -Q.55 will cany 2-marks each.
8. Questions Q.48 - Q.51 (2 pairs) are common data questions and question pain (Q.52, Q.53) and (Q.54, Q.55) are linked answer questions. The answer to the second question of the linked answer questions depends on the answer to the first question of the pair If (he first question in the linked pair is wrongly answered or is un-attempted, then the answer to the second question in the pair will not be evaluated,
9. Questions Q.56 - Q,65 belong to Genera) Aptitude (GA), Questions Q.56 - Q.60 will carry 1-mark each, and questions Q.61 - Q.65 will cany 2-roarks each. The GA questions will begin on a fresh page starting from page 10.
10. Un-attempted questions will carry zero marks.
11. Wrong answers will carry NEGATIVE marks. For Q.l - Q.25 and Q.56 - Q.60. *A mark will be deducted for each wrong answer. For Q.26 - Q.51 and Q.61 - Q.65, % mark will be deducted for each wrong answer. The question pairs (Q.52, Q.53), and (Q.54, Q.55) are questions with linked answers. There will be negative marks only for wrong answer to the first question of the linked answer question puir i.e. for Q.52 and Q.54, % mark will be deducted for each wrong answer. There is no negative marking for Q.53 and Q.55.
12. Calculator (without data connectivity) is allowed in the examination hall.
13. Charts, graph sheets or tables are NOT allowed in the examination hall-
14. Rough work can be done chi the question paper itself. Additionally, blank pages are provided ai the end of the question paper for rough work.
im
Q'l - Q.25 carry one mark each.
d'y dy
Q. 1 A particular solution of t* + 5--3 v = 6 is
dx dx
(A) 2.0 (B)0.5 (C) -0.5 (D) -2.0
d~u
Q.2 The partial differential equation r - 7 + 2 7- = 0 is said to be
oU dxoy py"
(A) parabolic (B) hyperbolic (C) elliptic (D) eccentric
Q 3 While carrying out tillage operations, negative slip is sometimes experienced with
(A) front wheels of two-wheel drive iracior
(B) front wheels of fom-wheel drive tractor
(C) front wheels of front wheel assisted tractor
(D) wheels of power tiller pulling a mould board plough
Q.4 A two-wheel drive tiactor has a PTO speed of 540 rpm and it produces 35 kW net engine power. Corresponding torque available at PTO in N m will be
(A) 435-457
(B) 465 -485
(C) 495-505
(D) 535-558
Q.5 Raising the hitch on the implement frame of a puJI type offset disk harrow without gauge wheel helps in
(A) increasing the depth of penetration for the rear gang <B) increasing the depth of penetration for the front gang
(C) decreasing the depth of penetration for the front gang
(D) maintaining (he same depth of penetration for both the gangs
Q.6 While deriving the Chezy formula for uniform flow, it is assumed that there is a balance between
(A) gravity and inertial forces
(B) inertial and viscous forces
(C) frictional and gravity forces
(D) frictional and inertial forces
Q.7 A cross regulator is usually provided
(A) at the head of the off-taking channel
(B) in the main channel upstream of the off-taking channel
(C) in the main channel downstream of the off-taking channel
(D) in the watercourse to regulate the outlet*
Q.8 An effective rainfall of 20 mm h_> occurs for 2 hours in a catchment. The time of concentration of the catchment is 1.5 hour. The peak of the resulting direct runoff hydrograph, in mm h'\ is
(A) 10 (B) 20
(C) 30 (D)40
Q 9 The dimensionless number in heat transfer corresponding to Sherwood Number in mass transfer is
(A) Biot Number (B) Schmidt Number
(C) Nusselt Number (D) (iraetz Number
Q. 10 The imerrclaiionship between thermal conductivity, dynamic viscosity and temperature of gas can be described as
fA) dynamic viscosity and thermal conductivity decrease as temperature increases
(B) dynamic viscosity decreases and thermal conductivity increases as temperature increases
(C) dynamic viscosity and thermal conductivity decrease as temperature decreases
(D) dynamic viscosity and thermal conductivity increase as temperature decreases
Q.J 1 A system of equations represented as
2
~4
1
1 -1 2 1 I 3
is
(B) inconsistent and has no solution
(A) consistent and has unique solution (C) consistent and has infinite solutions
(D) inconsistent and has unique solution
There is a significant difference between scores from two groups if
Q.J2
(A) the means are large compared to the standard error
(B) the difference between the means is large compared to the standard error
(C) the means are small compared to the standard error
(D) the difference between the standard deviation is large compared to the means
Q.13 The error in using trapezoidal rule for finding the value of
dx
IS
1 + x
(A) 0.0368 (B) 0.0468 (C) 0.0568 (D) 0.0668
A fanner constructed a 2 40 days HRT (hydraulic retention time) Deenbandhu model biogas plant. The gas will be solely used for cooking in a stove with a burner efficiency of 45%. If the density of biogas is 0 94 kg mJ with a heating value of 21 MJ kg"1, the total effective energy available per day in Mi will be
Q.J 4
(A) 17.77
(B) 18.91
(C) 24.47
(D) 39.48
A 2 x 0.3 m tractor drawn mould board plough while operating at a depth of 0.15 m has a draft of
Q 15
Q.16
2.5 kN at a forward speed of 3 km h_l with a field efficiency of 75%. When the speed of operation is increased by 20%, draft increased by 10%. Assuming field efficiency, soil pulverization and soil inversion to be the same at both the speeds, the performance index of the plough increases by
(A) 0% (B)9% iC) 20% (D) 30%
While evaluating a stationary power thresher for threshing wheai having a grain to straw ratio of 45% and at a moisture content (dry basis) of 14%. the following observations were recorded for a duration of 5 min:
Quantity of grain (clean and broken) collccted at main grain outlet = 16 kg, quantity of clean grain collected at bhusa outlet = 0.3 kg, quantity of clean grain obtained at sieve underflow and overflow = 0.2 kg and quantity of unthreshed grain from all outlets = 0.5 kg.
Percentage of blown and spilled grain are
(A) J-18,3.03 (B) 1.25. 1.82 (C) J.76, 1.18 <D) 1.88.1.25
Q.I7 The Local Apparent Time (LAT) corresponding to 14 h 30 Indian Standard Time (1ST) at a place in India (19 07'N. 72 5lE) in the month of April with a time correction of zero min will be
(A) 13 h 51' 24 (B) 14 h 9 39"
(C) 14 h 30' (D) 15 h 8 36
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Q.18 The following figure shows two advance curves for surface irrigation. |
 |
|
Distance across field |
The advance represented by curve M is slower than N. This could be attributed to
P. the inflow rate to the field is Lower
Q. the intake rate of the soil is Lower
R. the field slope is flatter
S. the hydraulic roughness is greater for curve N than for curve M
(A)P,Q (B)P,R
<C)Q,S (D) R, S
Q. 19 A land survey is conducted on 40 m x 40 m grids and the elevations of grids in m from mean sea level are as follows.
|
A |
B |
C | |
|
1 |
102.3 |
103.0 |
103.7 |
|
2 |
1015 |
102.4 |
102.3 |
|
3 |
101,2 |
103.5 |
102.6 |
Assuming that cut is equal to fill, the volume of earthwork required to level the area in m3 is (A) 4480 (B) 4840 (C) 5480 (D) 6480
Q.20 For hydrologic design, the entire runoff hydrograph should be known in case of
(A) Drop spillway
(B) Chute spillway
(C) Drop inlet spillway
(D) Ogee spillway
Q.21 For a given watershed, the rainfall erosivity index is 1000 Mi mm ha-1 h_l year*1, soil credibility index is 0.25 Mg ha h ha-1 MJl nun-1, crop management factor is 0 75. conservation practice factor is 1.0 and slope length factor is 0 2. If by certain conservation practices, the conservation practice factor is reduced to 0.7, then the reduction in soil loss, in Mg ha-1 year'1 is
(A) 9.75 (B) 11.25 ((') 11.75 (D) 12.25
AG
Q 22 Eighl log cycle reduction of Clostridium botulinum having z-value of 9*C needs a process time of
1.5 minute at 12 PC temperature. The same degree of reduction at 130C temperature will require a proccss lime of
(A)72s (B)54 s (C)18 s (D>9s
Q.23 Let m, n and p be the numbers of carbon, hydrogen and fluorine atoms in a refrigerant. The identification number of the refrigerant is
(A) R(m+l)(n-l)p (B) R(m-l)(n+l)p (C) R(m-l)(n-l)p (D) R(m+l)(n+l)p
Q.24 A household refrigerator of 1 TR capacity operates half the time during 13-hour long days and 30% time during the nights. If coefficient of performance is 4.7 then at Rs. 3 per kWh, monthly (30 days) electricity bill in Rupees for the refrigerator is
(A) 110 (B) 220 (C) 440 (D) 660
Q 25 Air at 40*C temperature has partial vapour pressure of 2.4 kPa. If universal gas constant is
8.314 Id kg mole'1 K1 and total pressure is 101.325 kPa then humid volume of air in m3 (kg dry air) is
(A) 0.809 (B) 0.908 (C) 1.089 (D) L09S
Q.26 - Q.55 carry two marks each.
Q.26 The curl of the vector A = xyi + yj + zxk (i. j and k represent unit vectors along the three orthogonal axes) is
(A)xl + yj + zk (B)-xi-yj-zk (C) yi + zj + xk (D) - yi- y - xk
Q 27 The angle of intersection between the planes x - 3y + 2z = 10 and 2x + 4y + 52 = 0 is (A) 30 (B) 60 (C)75 (D) 90
Q 28 The Laplace transformation of is
4! 3! 3T 41
(A) ---7 (B) --rr (C) --rr (D)
U-3)4 (s-4Y (j-4)1 (s-A)?
Q. 29 The deri vat ive of
- yjx + >/t +Jx + ... with respect to x al y = 0 is
y
(A)-I (B)0 (C) I (D) 2
X y.
Q 30 The value of J j xy dx dy is
0 0
(A) 0.5 (B) 1.0 (C) 2.0 (D) 4.0
Q.31 A thresher requires a torque of (5000 + 500 sin a) N m lo drive, where a is the angle of rotation of shaft measured from certain datum. The thresher is directly coupled to an engine which produces a torque of (5000 + 600 sin 2a) N m. The fly wheel and the rotary parts attached to (he engine have a mass of 500 kg at a radius of gyration 0.4 rtv The maximum angular acceleration of the flywheel in rad sec'' will be
(A) 3.46 (B) 5.46 (C) 7.46 (D) 9.46
AG
Q.32 The iractor seat vibrates with a frequency of J Hz when there is no damping. When damping is provided, the frequency of damped vibration is reduccd by 10%. The damping factor is
(A) 0.21 (B) 0.39 (C) 0 44 (D) 0.93
Q.33 A disk type mower, operated by a tractor PTO. has six discs with a swath of 0.4 m per disk. The specific energy required for cutting is 2. i kJ m"~ and specific power losses due to air, stubble and gear train friction are 2 kW m 1 of cutting width. If the mower with tractor requires a propelling force of 2 kN, the total power requirement for carrying out mowing in kW at a forward speed of 3 km h1 is
(A) 6.47 (B) 7.57 <C) 8.33 (D) 10.67
Q.34 In a tractor differential, the pinion on the propeller shaft has 12 teeth and the crown gear has 60 teeth. The propeller shaft rotates at 1000 rpm and the right rear axle rotates at 210 rpm while taking a left turn. The rotation of the left rear axle in rpm w ill be
(A) 170 (B)180 (C) 190 (D)200
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Q.35 Match all items in Group I with correct options from those in Group II | ||||||||||||||||||||||||
| ||||||||||||||||||||||||
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(C) i - d . ii - c, iii - a, iv - b (D) i - b, ii - d, iii - a. iv- c |
Q.36 The mass of a 3.0 mm crumbled soil thread is 17.5 x 10"3 kg. On oven-drying, the mass of the soil thread reduces to 14.9 * 10"3 kg. The liquid limit of the soil sample is 35.4%. The plasticity index of lhe soil sample is
(A) 14.9 (B) IS O <C) 318 (D) 35.4
Q 37 A pipeline carrying a discharge of 500 litres per minute branches into two parallel pipes, X and Y, as shown in the following figure, The length and diameter of pipes X and Y are shown in the figure.
|
L = 500 ill D = 0,2m |
 |
|
D = 03 m |
The friction factor, f. for all pipes is 0 030. The ratio of flow in pipes X and Y is
(A) 0.36 (B) 0.44 (C) 0.67 (D) 1.00
Q.38 A pump installed m an existing irrigation system delivers 3200 litres per minute flow at a total head of 60.0 m. The impeller diameter is 0 26 m and it is rotated at 1800 rpm. A motor with an output shaft power of 54 kW is required to drive the pump. The existing irrigation system, however, is modified in such a way that the discharge pressure requirement is reduced to 52 0 m while keeping the flow rate unchanged. If the existing pump is to be utilized, then to meet the new system requirement, the impeller diameter in m will be
(A) 0.24 (B) 0.25 (O 0.26 (D) 0.27
In order to evaluate irrigation distribution, an irrigator estimates the depth of infiltration, in mm, around a field as given below.
|
42 |
36 |
32 |
38 |
|
40 |
32 |
35 |
34 |
|
25 |
28 |
29 |
31 |
|
36 |
30 |
32 |
28 |
|
40 |
38 |
34 |
44 |
The distribution uniformity for the irrigation is
2010
Q.39
(A) 80.4 (B) SI -9 (C) 87.9 (D) 88.1
A parabolic shaped grassed waterway has a lop width of 4 m, a maximum depth of 0.40 m, and a slope of 2.5%. The Manning's V value is 0.035 and there is no provision of freeboard. The discharge carrying capacity of the waterway in m3 s~l is
Q 40
Q.41
(A) 1.38 (B) 1.52 (0 1.76 (D) 1.96
In an irrigation command area, the irrigation interval, gross application in an irrigation and the application efficiency are 20 days, 75 mm and 60%. respectively. The soil is homogeneous with K = 0.9 m day'1. The impermeable layer is at a depth of 7 m from the ground surface. The area is to be tile drained with tiles at a depth of 2 m below ihc ground surface. The maximum permissible steady state water table height mid way between the drains, from the plane of the drain, is 1.2 hl Using the steady slate approach of Hooghoudt, assuming an equivalent depth of 4.12 m, the drain spacing in m will be
(A) 115 25 (B) 131.75
(C) 146.25 (D) 186J5
A tubewell in a confined aquifer has a diameter of 0.30 rtv For a certain yield, the radius of influence is 400 m. AH conditions remaining the same, if Ihe diameter of the well is doubled, then the percentage increase in the yield is
Q.42
Q.43
(A) 9.28 (B) 9 63 (O 10.00 (D) 10.23
The heating surface of an oven has an emis&ivity of 0.7 with 0.1 m2 surface area and is maintained at 280*C. The view factor of this surface with respect to a piece of bread of 0,01 m3 surface area is
0 05. If bread has emissivity of 0.3 and receives 10 W of energy through radiation from the heating surface with Stephan - Boltzman constant of 5.67 x 10* W nrf21C\ the steady state bread surface temperature in is
(A) 137.2 (B) 118-5 (097 3 (D) 84.5
In parboiling operation water to paddy ratio is 1.2, Water of specific heat capacity of 4.2 kJ kg-1 K' is heated from 25eC to 85C by condensation of steam supplying 2114 kJ kg1 latent heat across a tubular heat exchanger. When 1 ion paddy at 30 C is poured into the hot water the mixture temperature stabilizes at 75C. Assuming no heat loss to the surrounding this implies:
Q.44
P. steam supplied is 431 kg.
Q. specific heat capacity of paddy is 1,12 kJ kg"1 K"1.
R. steam supplied is 143 kg.
S. specific heat capacity of paddy is 2.11 kJ kg"1 K l.
(A) P, Q (B)Q, R (OR. $ (D) P, S
Q.45 Density, specific heat capacity and thermal conductivity of air are 0.99 kg m"3, 1 kJ kg"] K1 and
0 03 W rn"1 K'\ respectively. Convective heat transfer coefficient of air medium awl equimolar countered iffusion mass transfer coefficient of water vapour into air are 35 W m": K1 and (1.32 m s', respectively. The mass diffusivity of water vapour into the air in m' s'1 is
(A) 2.46 x 10"3 (B) 4.62 x lO-1 (C) 8.25 x lO'* (D) 2.85 x HT
Q.46 20% sucrose solution is boiled and frozen separately. Jf latent heat of vapourization at 100C and the latent heat of crystallization at 0C are 2257 and 334 kJ kg*1, respectively, then the ratio of freezing point depression to boiling point elevation is
{A) 6.3 (B) 4.2 CQ 3.6 (D)2.4
Q.47 Carre# slices of 2 mm thickness are freeze dried from initial free moisture content of 80% {wet basis) to a final free moisture content of 2% (wet basis). Mass density of fresh carrot is 1100 kg m'3. Thermal conductivity of dried layer is 0.005 W m"1 K"1. Latent heat of sublimation at -35C is 2840 kJ kg1 and product surface temperature is -5C. The total drying time in hour is
{A) 1.2 (B) 2.3 (C) 3.2 (D) 5.4
Common Data Questions Common Data for Questions 48 and 49:
A field sprayer having 16 fan type spray nozzles spaced 0.5 m apart is moving at a forward speed of
3.5 km h~ with an application rale of I rtv ha'1. At a deposition level 430 mm below the lip of the nozzle, the discharge rate across a 0 2 m width at the centre of (he sprayed tip is essentially constant at 15 ml min'1 per 10 mm of lateral distance. On each side of this 0.2 m centre strip, the discharge rale per mm of width decreases uniformly to zero at a lateral distance of 0.36 m from the nozzle centre line.
Q.48 The discharge rate per nozzle in m3 h3 will be
(A) 0.175 (B) 0.215 (C) 0.350 (D) 0.430
Q.49 The nozzle tip height in mm above the deposition level that would give uniform coverage will be
(A) 602 (B) 546 (C) 501 (D) 477
Common Data for Questions 50 and 51:
In a drying experiment on potato slices of 5 mm thickness the initial moisture content of 4.2 kg water (kg dry matter)'1 got reduced to 0.03 kg water (kg dry matter)'1 by (he application of hot airat 65CC having absolute humidity of 0.02 kg water vapour (kg dry air)*1 with saturation water vapour pressure of 6 kPa. Critical moisture content of 2.5 kg water (kg dry matter)-1 was reached after 3 hour of drying time. The dry matter concentration in the drying chamber was 5 kg per m* of surface area.
Q.50 The mass transfer coefficient in kg mole m"2 s"1 during drying is
(A) 1.43 xUT* (8)3-14x10-' <04.31 xlG (D) 7.87 x 10*
Q.51 Mass diffusivity of water vapour in rn2 sl during the falling rate phase of drying is
(A) 7.01 x OT* (B) 5-07 x 10 (C) 3 71 x 10-5 (D) 1.07 x 10"3
Statement for Linked Answer Questions 52 and 53:
A 37 kW two-wheel drive tractor weighing 20 kN with a wheel base of 2.1 m is having ihe option to be fined with either 12.4 - 28 12PR or 13.6-28 12 PR at the rear axle. The ratio of section height and section width for all tyres is 0.75. On a level ground, the weight distribution on the front and rear axles is 35 and 65% of the total tractor weight, respectively. Cone index of soil is 1200 kPa.
Q.52 The motion resistance ratio of each of the rear wheels when fitted with the above-mentioned tyres at normal tyre inflation pressure while moving on a level ground will be
(B) 0.047,0.055 (C) 0.051,0.049 (D) 0.057, 0.055
(A) 0.04.0.04
Q.53 Net traction developed in kN by the rear wheels when fitted with 13.6 28 12 PR tyre at normal inflation pressure on a level ground with 15% wheel slip will be
(A) 8.79
(B) 9.18
(C) 9.78
(D) 10.32
Statement for Linked Answer Questions 54 and 55:
The peak of a flood hydrograph due to a 1 - h duration isolated storm in a catchment of area 13.5 km2 is 135 m7 s~. The total depth of rainfall is 54 mm. Assume a constant base flow of 10 m' s'1 and phi - index equal to 4 mmh"1.
Q.54 The peak of I - h unit hydrograph foe the catchment in mJ s"1 is
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(A) 15 (C) 25 (D) 30 |
 |
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(A) 13.25 (B) 18.75 (C) 21.25 (D) 26 75 |
(8)20
General Aptitude (GA) Questions Q56 - Q.60 carry one mark each.
Q.56 Choose the most appropriate *ord from the options given below to complete the following sentence:
His rather casual remarks on politics_bis lack of seriousness about the subject
(A) masked <B) belied
(C) betrayed
(D) suppressed
Q.57 Which of the following options is the closest wi meaning to the word below:
Circuitous
(A) cyclic
(B) indirect
(C) confusing
(D) crooked
Q.58 Choose the most appropriate word from the options given below to complete the following sentence:
If we manage to____our natural resources, we would leave a better planet for
our children.
(A) uphold
(B) restrain
(C) cherish (D> conserve
Q.59 25 persons are in a room. 15 of them play hockey, 17 of them play football and 10 of them play both hockey and football. Then the number of persons playing neither hockey nor football is:
(A) 2 (B) 17 (C) 13 (D) 3
Q.60 The question below consists of a pair of related words followed by four pairs of words, Select the pair that best expresses the relation in the original pair.
Unemployed : Worker
(A) fallow : land
(B) unaware: sleeper
(C) wit; jester
(D) renovated : house
Q.61 - Q.65 carry two marks each.
Q.61 If 137 + 276 = 435 how much is 731 + 672?
(A) 534 (B) 1403 (C) 1623 (D) 1513
Q.62 Hari (H), Gita (G), Irfan (1) and Saira (S) are siblings (i.e. brothers and sisters) All were bom on 1>1 January The age difference between any iwo succcssive siblings (thai is bom one after another) is less than 3 years. Given (he following facts:
i Han's age + Gila's age > Irfans age + Sairas age.
ii. The age difference between Gita and Saira is I year. However, Gita is not the oldest and Saira is not the youngest.
iii. There are no twins.
In whai order were they bom (oldesi first)?
(A) HS1G (B)SGHl (C) IGSH (D) IHSG
Q.63 Modern warfare has changed from large scale dashes of armies to suppression of civilian populations. Chemical agents that do their work silently appear to be suited to such warfare; and regretfully tthere exist people In military establishments who think that chemical agents are useful tools for their cause.
Which of the following statements best sums up the meaning of the above passage;
(A) Modem warfare has resulted in civil strife.
(B) Chemical agents are useful in modem warfare.
(C) Use of chemical agents in warfare would be undesirable.
(D) People in military establishments like to use chemical agents in war.
Q.64 5 skilled workers can build a wall in 20 days; 8 semi-skilled workers can build a wall in 25 days; 10 unskilled workers can butJd a wall in 30 days. If a team has 2 skilled. 6 semi-skilled and 5 unskilled workers, how long will it take to build the wait?
(A) 20 days (B) 18 days (C) 16 days (D) 15 days
Q 65 Given digits 2, 2, 3, 3, 3. 4, 4t 4, 4 how many distinct 4 digit numbers greater than 3000 can be formed?
(A) 50 (B) 51 (C) 52 <0) 54
I l/kft
A< i
Space for Rough Work
AO 16/16
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