ICAR AIEEA-PG: Dairy Science (group 16) and Dairy Technology (group 17) · India · NTA for ICAR
Original practice questions written to the published syllabus · not past papersThe calculus, differential equations and statistics that dairy engineering problems, kinetics and quality control need.
In the exams: Supports numerical items across ICAR AICE subject 38 (Dairy Engineering) and GATE XL-U Section 4; statistics recurs in ASRB NET dairy disciplines and in quality-control units
How our questions for ICAR AIEEA-PG spread across the units of Mathematics & Statistics for Dairy Science. Difficulty: 6 easy, 32 medium, 4 hard.
| Ordinary differential equations: first-order kinetics and cooling | 7 | |
| Numerical methods for engineering problems | 7 | |
| Differential and integral calculus | 6 | |
| Matrices and linear equations | 5 | |
| Correlation and regression | 5 | |
| Introduction to response surface methodology for product optimisation | 5 | |
| Sampling theory and confidence intervals | 4 | |
| Descriptive statistics and probability distributions | 2 | |
| Tests of significance: t, chi-square and F | 1 |
Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.
A pasteuriser holding tube is designed with milk in laminar flow at a mean velocity of 0.5 m/s. At what velocity must the fastest particle be assumed to travel when checking the minimum holding time?
B. 1.0 m/s
In laminar flow u_max = 2 × mean = 1.0 m/s, and the fastest particle receives the shortest holding time. 0.61 m/s corresponds to the turbulent ratio (mean ≈ 0.82 u_max); using the mean 0.5 m/s overestimates the holding time.
Further reading: Singh and Heldman, Introduction to Food Engineering
In thermal process calculation, the F value of a process is obtained by:
A. Integrating the lethal rate 10^((T − T_ref)/z) over the heating time
F = ∫10^((T − T_ref)/z) dt accumulates lethality minute by minute. Peak temperature × time ignores that lethality rises tenfold for each z degrees.
Further reading: Singh and Heldman, Introduction to Food Engineering
Vitamin C in a flavoured milk is lost by first-order kinetics with k = 0.05 per day. What is its half-life?
A. 13.9 days
t½ = ln 2/k = 0.693/0.05 = 13.9 days. 1/k = 20 days is the time constant; 2.303/k = 46.1 days is the time for a tenfold fall (the D value).
Further reading: Singh and Heldman, Introduction to Food Engineering
Newton's law of cooling, applied as a lumped-capacity model, is reasonable when the Biot number is:
A. Below about 0.1
Bi = hL/k_solid compares internal to surface resistance. Below about 0.1 the internal temperature is nearly uniform, so a single temperature describes the body. Large blocks of butter or cheese have high Bi and need conduction models.
Further reading: Singh and Heldman, Introduction to Food Engineering
A well-mixed 2,000 litre balance tank is flushed with clean water at 500 litres per minute. What fraction of an initial dissolved residue remains after 12 minutes?
A. 0.050
τ = V/q = 2000/500 = 4 min. C/C₀ = e^(−t/τ) = e^(−3) = 0.050. Plug-flow thinking (three tank volumes = empty) gives 0; e^(−4/12) inverts the ratio.
Further reading: Singh and Heldman, Introduction to Food Engineering
Applying one Newton–Raphson step to f(x) = x³ − 2x − 5 from x₀ = 2 gives:
C. 2.1
f(2) = 8 − 4 − 5 = −1; f′(x) = 3x² − 2, so f′(2) = 10. x₁ = 2 − (−1)/10 = 2.1. Sign slips give 1.9.
Further reading: Chapra and Canale, Numerical Methods for Engineers
Lethal rates logged every 2 min during a heat process are 0.1, 0.6, 0.9, 0.5 and 0.1 (min of reference process per min). What is the F value by the trapezoidal rule?
B. 4.2 min
Trapezoidal: h(½y₀ + y₁ + y₂ + y₃ + ½y₄) = 2(0.05 + 0.6 + 0.9 + 0.5 + 0.05) = 4.2 min. Simpson's rule gives 4.27 min; multiplying the plain sum by h (4.4) counts the end points twice their weight.
Further reading: Chapra and Canale, Numerical Methods for Engineers
A sample is drawn from the top of an unstirred milk tank. The resulting error in fat content is best described as:
C. A non-sampling bias error that more replicate samples from the top would not reduce
Cream rises in unstirred milk, so top samples are systematically high in fat. That is bias, which more samples from the same spot do not remove; only mixing does.
Further reading: Codex CAC/GL 50, General Guidelines on Sampling
A calibration line is A = 0.016 + 0.196C (C in mg/L). A sample reads A = 0.50. What is its concentration?
C. 2.47 mg/L
C = (A − a)/b = (0.50 − 0.016)/0.196 = 2.47 mg/L. Ignoring the intercept gives 2.55; adding it gives 2.63.
Further reading: Snedecor and Cochran, Statistical Methods
Optimising several responses at once, such as creaminess, melt resistance and cost of an ice cream, is commonly done with:
A. A desirability function combining each response on a 0–1 scale
Derringer's desirability approach converts each response to 0 (unacceptable) to 1 (ideal) and maximises their geometric mean. The optimum must then be confirmed experimentally.
Further reading: Myers, Montgomery and Anderson-Cook, Response Surface Methodology
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