Instruction
- Total number of questions : 20
- Time allotted : 30:00 Minutes:Seconds.
- Each question carry 1 mark, no negative marks.
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Agricultural Process Engineering [ Question No: 1 To 9 ] :
Consider the following statements about cost estimation:
1. The Lang factor scales equipment cost to fixed capital investment.
2. The six-tenths rule scales cost between capacities.
3. Payback period accounts for the time value of money.
Which of the statements given above is or are correct?
Cold store load breakdown for 40 tonnes of respiring produce.
| Load component | Value (kW) | Share |
|---|---|---|
| Product pull-down over 24 h | 37.0 | 86 per cent |
| Respiration | 1.8 | 4 per cent |
| Transmission | 1.4 | 3 per cent |
| Infiltration | 2.6 | 6 per cent |
Which component dominates during steady holding once the produce is cold?
The equilibrium moisture content of a product is
Assertion (A): Solvent extraction plants are built with stringent fire precautions.
Reason (R): Commercial hexane is highly flammable and its vapour forms explosive mixtures with air.
Select the correct answer from the options below.
Match each wheat mill machine in List I with its duty in List II.
List I
A. Break rolls
B. Purifier
C. Reduction rolls
D. Conditioner
List II
1. Separating bran flakes from semolina
2. Opening the kernel and scraping the bran
3. Adding water and tempering the grain
4. Grinding semolina to flour
Select the correct match.
Paddy separation, following hulling, divides
A groundnut decorticator separates
A cyclone handles \( 1.8 \) m\(^3\)/s of air through an inlet of \( 0.15 \) m\(^2\). The inlet velocity is
Consider the following pairs of term and its definition:
Porosity - Void volume as a fraction of bulk volume
Bulk density - Mass divided by total occupied volume
True density - Mass divided by the volume of solid material
Sphericity - Ratio of the longest to the shortest dimension
How many of the pairs given above are correctly matched?
Engineering Mathematics [ Question No: 10 To 18 ] :
Given \(\int_{-\infty}^{\infty} e^{-x^{2}}\,dx = \sqrt{\pi}\).
If \(a\) and \(b\) are positive integers, the value of \(\int_{-\infty}^{\infty} e^{-a(x+b)^{2}}\,dx\) is ________.
Consider the differential equation \(x^{2}\frac{d^{2}y}{dx^{2}}+x\frac{dy}{dx}-4y=0\) with the boundary conditions of \(y(0)=0\) and \(y(1)=1\). The complete solution of the differential equation is
The differential equation \(\frac{d^{2}y}{dx^{2}} + 16y = 0\) for \(y(x)\) with the two boundary conditions \(\left.\frac{dy}{dx}\right|_{x=0} = 1\) and \(\left.\frac{dy}{dx}\right|_{x=\frac{\pi}{2}} = -1\) has
Just one of these four quantities is a scalar. Which?
The mean value of \( f(x) = x^{2} \) over \( [0, 3] \) is
Revolving \( y = x \) from \( x = 0 \) to \( x = 3 \) about the \( x \)-axis gives a volume of
Consider the following statements about determinants.
1. Interchanging two rows changes the sign 2. Adding a multiple of one row to another leaves the value unchanged 3. For a matrix of order n, the determinant of kA is k times that of A
A system of 4 equations in 3 unknowns has coefficient matrix of rank 3 and augmented matrix of rank 3. The system has
Consider the following statements about partial derivatives. 1. The mixed derivatives commute whenever they are continuous 2. Euler's theorem weights each first derivative by its own variable 3. A vanishing Jacobian means the functions are independent
Farm Machinery and Equipment [ Question No: 19 To 19 ] :
For a two-wheel drive tractor, use of differential lock in adverse field condition ensures
Food Processing Technology [ Question No: 20 To 20 ] :
The temperature for thermal processing of food materials depends upon the heat sensitivity of-
Total number of questions : 20
Number of answered questions : 0
Number of unanswered questions : 20
Agricultural Process Engineering [ Question No: 1 To 9 ] :
Consider the following statements about cost estimation:
1. The Lang factor scales equipment cost to fixed capital investment.
2. The six-tenths rule scales cost between capacities.
3. Payback period accounts for the time value of money.
Which of the statements given above is or are correct?
Your Answer : (Not Answered)
Correct Answer : D
Correct answer: 1 and 2 only
Statements 1 and 2 describe the two scaling tools correctly. Statement 3 is false: payback uses undiscounted cash flows and takes no account of the time value of money - which, with its blindness to everything after the payback point, is its central weakness.
Cold store load breakdown for 40 tonnes of respiring produce.
| Load component | Value (kW) | Share |
|---|---|---|
| Product pull-down over 24 h | 37.0 | 86 per cent |
| Respiration | 1.8 | 4 per cent |
| Transmission | 1.4 | 3 per cent |
| Infiltration | 2.6 | 6 per cent |
Which component dominates during steady holding once the produce is cold?
Your Answer : (Not Answered)
Correct Answer : C
Correct answer: The three continuous loads
Once the produce is at temperature the product pull-down load ceases entirely - it is a transient, present only while the produce is being cooled. What remains is respiration at \( 1.8 \) kW, transmission at \( 1.4 \) kW and infiltration at \( 2.6 \) kW, a continuous total of about \( 5.8 \) kW.
The table therefore describes two quite different duties: a peak of \( 42.8 \) kW during pull-down and a holding load of \( 5.8 \) kW thereafter. Sizing on the holding load alone would leave the plant unable to pull down; sizing on the peak alone leaves it cycling inefficiently for most of its life.
The equilibrium moisture content of a product is
Your Answer : (Not Answered)
Correct Answer : A
Correct answer: The moisture in balance with the air
The equilibrium moisture content is the value a product reaches when it is left long enough in air of a given temperature and relative humidity: at that point it neither gains nor loses moisture, because its vapour pressure equals that of the air.
It sets the floor for any drying operation - no dryer can take a product below the equilibrium value for its exhaust air, however long it runs. It varies with the air's relative humidity and with the material, and it is a property of the product, not of the air alone.
Assertion (A): Solvent extraction plants are built with stringent fire precautions.
Reason (R): Commercial hexane is highly flammable and its vapour forms explosive mixtures with air.
Select the correct answer from the options below.
Your Answer : (Not Answered)
Correct Answer : C
Correct answer: Both A and R are true, and R is the correct explanation of A
Both are true and the reason is the whole basis of the precautions. Commercial hexane has a flash point around minus 22 degrees Celsius and forms explosive mixtures with air over a wide range of concentrations.
Everything in the plant follows from that: electrical equipment is flameproof, the building is designed to vent an explosion, vapour is recovered rather than released, and hot work is tightly controlled. It is also why hexane loss per tonne is watched as a safety figure and not merely as a cost.
Match each wheat mill machine in List I with its duty in List II.
List I
A. Break rolls
B. Purifier
C. Reduction rolls
D. Conditioner
List II
1. Separating bran flakes from semolina
2. Opening the kernel and scraping the bran
3. Adding water and tempering the grain
4. Grinding semolina to flour
Select the correct match.
Your Answer : (Not Answered)
Correct Answer : D
Correct answer: A-2, B-1, C-4, D-3
Each machine has one duty in the flow. The conditioner adds water and tempers the grain before anything else happens. The break rolls open the kernel and scrape the bran. The purifier then separates bran flakes from the semolina by air current. And the reduction rolls grind the purified semolina down to flour.
Paddy separation, following hulling, divides
Your Answer : (Not Answered)
Correct Answer : C
Correct answer: Unhulled paddy from brown rice
Hulling is never complete in one pass - a proportion of grains escape the rolls unhulled - so the discharge is a mixture of brown rice and paddy. The paddy separator divides the two, using their difference in density and surface texture on an oscillating tray or compartment separator, and returns the unhulled grains to the huller.
Separating them matters because paddy passing into the whitening machine would be abraded pointlessly, wearing the equipment and producing brokens. Bran removal is whitening's job, and broken separation is grading's.
A groundnut decorticator separates
Your Answer : (Not Answered)
Correct Answer : C
The pods are cracked between a beater and a screen sized so that the freed kernels pass through while the shell fragments are carried on. Detaching the pods from the plant is a separate operation, done by a stripper or picker.
A cyclone handles \( 1.8 \) m\(^3\)/s of air through an inlet of \( 0.15 \) m\(^2\). The inlet velocity is
Your Answer : (Not Answered)
Correct Answer : C
Correct answer: 12.0 m/s
Velocity is volumetric flow divided by area:
\[ v = \frac{1.8}{0.15} = 12.0\ \mathrm{m/s} \]
Inlet velocity governs cyclone performance directly, since the centrifugal force separating the dust from the air rises with its square. Too low and fine material escapes with the exhaust; too high and pressure drop and erosion rise steeply. Design velocities for grain dust cyclones typically fall in the range of 12 to 20 m/s, so this machine sits at the gentle end.
Consider the following pairs of term and its definition:
Porosity - Void volume as a fraction of bulk volume
Bulk density - Mass divided by total occupied volume
True density - Mass divided by the volume of solid material
Sphericity - Ratio of the longest to the shortest dimension
How many of the pairs given above are correctly matched?
Your Answer : (Not Answered)
Correct Answer : A
Correct answer: Only three
Porosity, bulk density and true density are all defined correctly: void volume as a fraction of bulk volume, mass over total occupied volume, and mass over solid volume respectively.
The sphericity definition is the odd one out. The ratio of longest to shortest dimension is an aspect ratio; sphericity is the surface area of the equal-volume sphere divided by the particle's own surface area, computed in practice as \( (LWT)^{1/3}/L \). The distinction matters because sphericity is bounded at one and an aspect ratio is not. Three pairs are correct.
Engineering Mathematics [ Question No: 10 To 18 ] :
Given \(\int_{-\infty}^{\infty} e^{-x^{2}}\,dx = \sqrt{\pi}\).
If \(a\) and \(b\) are positive integers, the value of \(\int_{-\infty}^{\infty} e^{-a(x+b)^{2}}\,dx\) is ________.
Your Answer : (Not Answered)
Correct Answer : B
The value is \(\sqrt{\pi/a}\).
Substitute \(u = \sqrt{a}\,(x + b)\), so \(du = \sqrt{a}\,dx\). The limits stay \(-\infty\) to \(\infty\), because shifting by \(b\) and scaling by a positive \(\sqrt{a}\) does not change an infinite range:
\[ \begin{aligned} \int_{-\infty}^{\infty} e^{-a(x+b)^{2}}\,dx &= \frac{1}{\sqrt{a}}\int_{-\infty}^{\infty} e^{-u^{2}}\,du \\ &= \frac{\sqrt{\pi}}{\sqrt{a}} = \sqrt{\frac{\pi}{a}} \end{aligned} \]
The shift \(b\) only slides the bell curve along the axis, so it cannot change the area: both options with a factor \(b\) are wrong. \(\sqrt{\pi a}\) multiplies by \(\sqrt{a}\) where it should divide; a larger \(a\) makes the curve narrower, so the area must shrink.
Consider the differential equation \(x^{2}\frac{d^{2}y}{dx^{2}}+x\frac{dy}{dx}-4y=0\) with the boundary conditions of \(y(0)=0\) and \(y(1)=1\). The complete solution of the differential equation is
Your Answer : (Not Answered)
Correct Answer : A
The solution is \(y = x^{2}\).
This is a Cauchy-Euler equation. Try \(y = x^{m}\):
\[ \begin{aligned} m(m-1)+m-4 &= 0 \\ m^{2} &= 4,\ m = \pm 2 \\ y &= c_{1}x^{2}+c_{2}x^{-2} \end{aligned} \]
The condition y(0) = 0 needs \(c_{2}=0\), since \(x^{-2}\) is unbounded at the origin, and y(1) = 1 then gives \(c_{1}=1\).
The three sine options satisfy both boundary values but not the equation: substituting \(\sin(\pi x/2)\), for example, leaves terms in \(x^{2}\sin\) and \(x\cos\) that do not cancel.
The differential equation \(\frac{d^{2}y}{dx^{2}} + 16y = 0\) for \(y(x)\) with the two boundary conditions \(\left.\frac{dy}{dx}\right|_{x=0} = 1\) and \(\left.\frac{dy}{dx}\right|_{x=\frac{\pi}{2}} = -1\) has
Your Answer : (Not Answered)
Correct Answer : A
The problem has no solution.
The general solution is \(y = A\cos 4x + B\sin 4x\), so \(y' = -4A\sin 4x + 4B\cos 4x\).
\[ \begin{aligned} y'(0) &= 4B = 1 \Rightarrow B = \tfrac{1}{4} \\ y'(\pi/2) &= -4A\sin 2\pi + 4B\cos 2\pi = 4B = 1 \end{aligned} \]
The second condition demands -1, but every solution gives y'(\(\pi\)/2) = 1, so the two conditions contradict each other.
If the second condition had been +1, A would be free and there would be infinitely many solutions; a linear problem like this can never have exactly two.
Just one of these four quantities is a scalar. Which?
Your Answer : (Not Answered)
Correct Answer : B
The divergence contracts the operator with the field and returns a scalar rate of outflow per unit volume. The curl and the gradient both return vectors, and the curl of a gradient is a vector too, albeit the zero vector. Keeping track of which operations change the rank is what stops ill-formed identities being written
The mean value of \( f(x) = x^{2} \) over \( [0, 3] \) is
Your Answer : (Not Answered)
Correct Answer : C
Divide the integral by the length of the interval:
\[ \bar{f} \;=\; \frac{1}{3}\int_{0}^{3} x^{2}dx \;=\; \frac{1}{3}\left[\frac{x^{3}}{3}\right]_{0}^{3} \;=\; \frac{1}{3}(9) \;=\; 3. \]
The mean exceeds the midpoint value \( f(1.5) = 2.25 \), as it must for a convex function, and falls well below the maximum of nine at the right-hand end
Revolving \( y = x \) from \( x = 0 \) to \( x = 3 \) about the \( x \)-axis gives a volume of
Your Answer : (Not Answered)
Correct Answer : B
Apply the disc formula with \( y = x \):
\[ V \;=\; \pi\int_{0}^{3} x^{2}\,dx \;=\; \pi\left[\frac{x^{3}}{3}\right]_{0}^{3} \;=\; 9\pi. \]
The solid is a cone of radius three and height three, and the elementary formula \( \tfrac{1}{3}\pi r^{2}h = \tfrac{1}{3}\pi(9)(3) = 9\pi \) agrees
Consider the following statements about determinants.
1. Interchanging two rows changes the sign 2. Adding a multiple of one row to another leaves the value unchanged 3. For a matrix of order n, the determinant of kA is k times that of A
Your Answer : (Not Answered)
Correct Answer : C
Correct answer: 1 and 2 only are correct
Statements 1 and 2 are standard properties: a row interchange reverses the sign, and adding a multiple of one row to another leaves the value unchanged, which is what makes elimination safe. Statement 3 is wrong - scaling the whole matrix scales every row, so \( |kA| = k^{n}|A| \), not \( k|A| \).
A system of 4 equations in 3 unknowns has coefficient matrix of rank 3 and augmented matrix of rank 3. The system has
Your Answer : (Not Answered)
Correct Answer : B
Correct answer: a unique solution
The two ranks are equal, so the system is consistent, and their common value 3 equals the number of unknowns, so there are no free variables. The fourth equation is therefore not an extra constraint but a consequence of the other three - more equations than unknowns does not imply inconsistency, only that some are redundant.
Consider the following statements about partial derivatives. 1. The mixed derivatives commute whenever they are continuous 2. Euler's theorem weights each first derivative by its own variable 3. A vanishing Jacobian means the functions are independent
Your Answer : (Not Answered)
Correct Answer : B
Clairaut's theorem gives the first, and Euler's theorem \( x f_{x} + y f_{y} = n f \) the second. The third reverses the truth: a vanishing Jacobian marks functional *dependence*, a relation \( \phi(u,v) = 0 \) tying the two together, and independence is what a non-zero Jacobian certifies
Farm Machinery and Equipment [ Question No: 19 To 19 ] :
For a two-wheel drive tractor, use of differential lock in adverse field condition ensures
Your Answer : (Not Answered)
Correct Answer : D
The differential lock ensures distribution of higher amount of torque to the wheel under better traction.
An open differential always sends equal torque to both wheels, and that torque is limited by the wheel with the poorer grip: when one wheel slips, it spins and the other gets little. Locking the differential makes both wheels turn together, so the wheel on firm ground can now take as much torque as its traction allows, far more than the slipping wheel.
Equal torque is what the open differential gives, the condition the lock is meant to escape. Equal power is not a design feature of either. Sending more torque to the wheel with poor traction would only make it spin faster.
Food Processing Technology [ Question No: 20 To 20 ] :
The temperature for thermal processing of food materials depends upon the heat sensitivity of-
Your Answer : (Not Answered)
Correct Answer : B
It depends on the heat sensitivity of Bacteria.
Thermal processes such as pasteurization and canning are designed around the heat resistance of the target bacteria and their spores, because they are the most heat-resistant organisms of concern in food. Low-acid canned foods, for example, are processed to destroy spores of Clostridium botulinum, using its D and z values to set time and temperature.
Protozoa, fungi (yeasts and moulds) and most viruses are destroyed at lower temperatures, so a process that kills the target bacteria also takes care of them.
Marks
Total number of questions : 20
Number of answered questions : 0
Number of unanswered questions : 20