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CFTRI M.Sc. (Food Technology) Mathematics Flashcards
51 question-and-answer cards covering Mathematics as it is examined in CFTRI M.Sc. (Food Technology). 24 of them are printed below, taken from across the deck — no signup, no paywall on the preview.
24 sample cards from the Mathematics deck
Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.
Solve the first-order equation dy/dx = ky.
y = C e^(kx), where C is an arbitrary constant (exponential growth/decay).
What distinguishes the order from the degree of a differential equation?
Order is the highest derivative present; degree is the power of that highest derivative (after the equation is made polynomial in derivatives).
What is the standard form of a first-order linear differential equation?
dy/dx + P(x) y = Q(x).
What is the integrating factor for dy/dx + P(x)y = Q(x)?
The integrating factor is IF = e^(∫P(x) dx).
State the general solution of a first-order linear differential equation using the integrating factor.
y · (IF) = ∫ Q(x) · (IF) dx + C, where IF = e^(∫P dx).
What is the standard form of a linear equation in two variables, and what does its graph look like?
ax + by + c = 0 (a, b not both zero); its graph is a straight line.
What is the slope-intercept form of a straight line?
y = mx + c, where m is the slope and c is the y-intercept.
For a system of two linear equations, what does it mean to have a unique solution, no solution, or infinitely many solutions?
Unique solution: lines intersect (a1/a2 ≠ b1/b2). No solution: parallel lines (a1/a2 = b1/b2 ≠ c1/c2). Infinitely many: coincident lines (a1/a2 = b1/b2 = c1/c2).
Define a ratio and how it is written.
A ratio compares two quantities of the same kind by division, written a:b or a/b (b ≠ 0).
Define a proportion and state the cross-multiplication property.
A proportion states two ratios are equal, a:b = c:d; then ad = bc (product of extremes = product of means).
What is the duplicate ratio of a:b?
The duplicate ratio of a:b is a^2 : b^2.
What is the sub-duplicate ratio of a:b?
The sub-duplicate ratio of a:b is √a : √b.
What does the componendo and dividendo rule state for a/b = c/d?
If a/b = c/d, then (a+b)/(a-b) = (c+d)/(c-d).
Define the mean proportional (geometric mean) between two quantities a and b.
The mean proportional x satisfies a:x = x:b, so x = √(ab).
In a:b = c:d, identify the means and the extremes.
The extremes are a and d (the outer terms); the means are b and c (the inner terms).
Define sampling in statistics.
Sampling is the process of selecting a subset (sample) from a population to estimate characteristics of the whole population.
What is the difference between a population and a sample?
A population is the entire set of items/individuals under study; a sample is a subset selected from that population for examination.
Define simple random sampling.
A sampling method in which every member of the population has an equal and independent chance of being selected.
Distinguish stratified sampling from cluster sampling.
Stratified: divide the population into homogeneous strata and sample from each. Cluster: divide into heterogeneous clusters and randomly select whole clusters to sample.
What is the difference between a parameter and a statistic?
A parameter is a numerical characteristic of a population (e.g. μ, σ); a statistic is a numerical characteristic computed from a sample (e.g. x̄, s).
What is sampling error?
The difference between a sample statistic and the true population parameter, arising because only a portion of the population is observed.
State the classical (theoretical) definition of the probability of an event.
P(E) = (number of favourable outcomes) / (total number of equally likely outcomes), with 0 ≤ P(E) ≤ 1.
State the addition rule of probability for two events A and B.
P(A ∪ B) = P(A) + P(B) - P(A ∩ B); for mutually exclusive events, P(A ∪ B) = P(A) + P(B).
State the multiplication rule and the condition for independent events.
P(A ∩ B) = P(A) · P(B|A); if A and B are independent, P(A ∩ B) = P(A) · P(B). Conditional: P(B|A) = P(A ∩ B)/P(A).
What this deck covers
The Mathematics deck follows the CFTRI M.Sc. (Food Technology) Mathematics syllabus — 6 chapters and 8 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 8.5 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 92 characters, which is long enough to carry the reasoning and short enough to say out loud.
A deck like this earns its keep on the second and third pass. Read the syllabus first so you know the shape of the subject, then use the cards to find the specific facts that have not stuck.
Mathematics flashcards FAQ
How many Mathematics flashcards are in this CFTRI M.Sc. (Food Technology) deck?
51 cards. This page previews 24 of them, sampled evenly across the deck so you can judge the difficulty before installing anything.
Are these CFTRI M.Sc. (Food Technology) flashcards free?
Yes. The preview here is free to read with no signup, and the full 51-card deck is free inside the Examius app.
What do the Mathematics cards cover?
They follow the CFTRI M.Sc. (Food Technology) Mathematics syllabus — 6 chapters and 8 topics — so the questions track what is actually examinable.
How should I use these flashcards?
Read the syllabus first so you know the shape of the subject, then drill the deck. Examius schedules each card with spaced repetition, so cards you keep missing come back sooner and ones you know drift further apart.