GATE — Life Sciences (XL) with Section U Food Technology · India · IITs and IISc on rotation (2026: IIT Guwahati)
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 GATE spread across the units of Mathematics & Statistics for Dairy Science. Difficulty: 5 easy, 27 medium, 2 hard.
| Numerical methods for engineering problems | 6 | |
| Matrices and linear equations | 5 | |
| Ordinary differential equations: first-order kinetics and cooling | 5 | |
| Correlation and regression | 5 | |
| Introduction to response surface methodology for product optimisation | 5 | |
| Differential and integral calculus | 3 | |
| Sampling theory and confidence intervals | 3 | |
| Descriptive statistics and probability distributions | 2 |
Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.
The cost per metre of insulating a pipe is C(t) = 50t + 2/t (t in m). At what thickness is the total cost a minimum?
C. 0.2 m
dC/dt = 50 − 2/t² = 0 gives t² = 0.04, t = 0.2 m. d²C/dt² = 4/t³ > 0, so it is a minimum. 0.04 m is t², not t.
Further reading: Kreyszig, Advanced Engineering Mathematics
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
For first-order inactivation, the decimal reduction time D and the rate constant k (per min) are related by:
A. D = 2.303/k
log₁₀(N₀/N) = kt/2.303, so one log cycle (tenfold) takes D = 2.303/k. 0.693/k is the half-life.
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
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
Pouches are defective with probability 0.02, independently. What is the probability that a sample of 20 contains no defective pouch?
C. 0.668
Binomial with x = 0: (1 − 0.02)²⁰ = 0.98²⁰ = 0.668. 0.980 is for a single pouch; 0.332 is the probability of at least one defective.
Further reading: Snedecor and Cochran, Statistical Methods
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
Ten here, 34 in the app. The Laisha app has every practice question we have written to GATE in this subject, marked as you go, with timed papers, a jump-to-unanswered list and a certificate when you pass at 70 per cent.
Free for ten days, then one subscription of US$10 a month. We would rather say so here than have you find it later.
An AI operating system for agriculture: free guides, manuals and tools written for every country.