Question Statement:
Mycobacterium tuberculosis is having decimal reduction time of 13.5 s at 72 °C. The count of the organism is to be reduced by eight logarithmic cycles in milk pasteurization with adequate holding at a temperature of 85 °C. If Q₁₀ value for the organism is 7.5, the minimum holding time for the desired sterility of this particular organism at 85 °C is _________ seconds.
Step-by-Step Solution & Explanation
Q₁₀ definition: the rate increases by a factor Q₁₀ for every 10 °C rise, i.e. D decreases by that factor.
Temperature rise ΔT = 85 − 72 = 13 °C.
D₈₅ = D₇₂ / Q₁₀^{ΔT/10} = 13.5 / 7.5^{1.3}
7.5^{1.3} = e^{1.3 ln 7.5} = e^{1.3 × 2.0149} = e^{2.6194} = 13.73
D₈₅ = 13.5/13.73 = 0.9833 s.
Holding time t = n × D₈₅ = 8 × 0.9833 = 7.87 s — within the official range 7.80–8.00.
Common error: using ΔT/10 = 1.3 as a multiplier rather than an exponent (gives 1.38 s).
Appendix A — Consolidated question index
Appendix B — Section-wise weightage
Since the paper totals 100 marks, the marks column and the percentage column are numerically identical.
Preparation observations
Irrigation and Drainage Engineering is the single heaviest subject section (10 questions, 15 marks), tied on marks with Farm Power. Groundwater/well hydraulics, drip emission uniformity, lysimeter water balance and furrow hydraulics all appeared — this section alone repays systematic revision.
Farm Power and Agricultural Process Engineering follow closely (9 questions each). Farm Power was almost entirely numerical: weight transfer, drawbar power, clutch design, Otto-cycle exponent and biogas digester sizing.
Engineering Mathematics (9 questions, 13 marks) was standard and fully scoring: second-order ODE, rank, work done by a resultant force, Simpson's 1/3 rule and elementary probability. This is the cheapest block of marks in the paper.
Of the 55 AG questions, 30 are NAT. NAT carries no negative marking, so every numerical must be attempted — but the accepted ranges are often tight (e.g. −3924 to −3924, 1.00 to 1.00), so rounding must be carried only at the last step.
Three questions needed care in reconciling the textbook route with the official key: AG Q.43 (unit hydrograph peak — the key corresponds to a direct sum of peaks rather than lagged superposition), AG Q.45 (chute blocks — the key uses E = 0.8H, with the inlet head excluded) and AG Q.37 (drawbar power — the wide 18–21 band accommodates both the slip-corrected and theoretical speeds). Each is flagged in its explanation.
Recurring formula families worth memorising: Bond's law, D-value/Q₁₀ kinetics, uniform-wear clutch torque, Thiem's equation, φ-index, emission uniformity, threshing versus cleaning efficiency, and the porosity–void ratio pair.