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MHT CET Mathematics Flashcards
60 question-and-answer cards covering Mathematics as it is examined in MHT CET. 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.
What does the scalar triple product [a b c] = a·(b × c) represent geometrically and when is it zero?
Its absolute value is the volume of the parallelepiped with edges a, b, c. It is zero when the three vectors are coplanar.
Give the section formula for the point dividing the segment joining vectors a and b in ratio m:n internally.
Position vector = (m·b + n·a)/(m + n). Midpoint (1:1) = (a + b)/2.
What are the direction cosines of a line, and what relation do they satisfy?
Direction cosines l, m, n are the cosines of the angles the line makes with the x, y, z axes; they satisfy l² + m² + n² = 1.
State the angle between two lines in 3D with direction ratios (a₁,b₁,c₁) and (a₂,b₂,c₂).
cosθ = |a₁a₂ + b₁b₂ + c₁c₂| / [√(a₁²+b₁²+c₁²)·√(a₂²+b₂²+c₂²)].
What is the perpendicular distance from point (x₁,y₁,z₁) to the plane ax + by + cz + d = 0?
Distance = |a x₁ + b y₁ + c z₁ + d| / √(a² + b² + c²).
State the conditions for a function f to be continuous at x = a.
f is continuous at a if: (1) f(a) is defined, (2) lim(x→a) f(x) exists (left = right limit), and (3) lim(x→a) f(x) = f(a).
State two standard limits: lim(x→0) sinx/x and lim(x→0) (e^x - 1)/x.
lim(x→0) sinx/x = 1; lim(x→0) (e^x - 1)/x = 1. Also lim(x→0) (1 + x)^(1/x) = e.
State the product rule and quotient rule for differentiation.
Product: (uv)' = u'v + uv'. Quotient: (u/v)' = (u'v - uv')/v².
Give the derivatives of sin x, tan x, ln x, and e^x.
d/dx(sinx) = cosx; d/dx(tanx) = sec²x; d/dx(lnx) = 1/x; d/dx(e^x) = e^x.
What is the geometric meaning of the first derivative being zero, and the second derivative test for maxima/minima?
f'(x)=0 gives stationary (critical) points. If f''(x) < 0 it's a local maximum; if f''(x) > 0 it's a local minimum; if f''(x)=0 the test is inconclusive.
State the power rule for integration ∫xⁿ dx and ∫(1/x) dx.
∫xⁿ dx = x^(n+1)/(n+1) + C (n ≠ -1); ∫(1/x) dx = ln|x| + C.
State the formula for integration by parts.
∫u dv = uv - ∫v du, i.e. ∫u·v' dx = u·v - ∫u'·v dx (choose u by ILATE order).
What is the formula for the area bounded by the curve y = f(x), the x-axis, and lines x = a, x = b?
Area = ∫(from a to b) |f(x)| dx (take f(x) ≥ 0 over the interval, or split where it changes sign).
Define the order and degree of a differential equation.
Order = the order of the highest derivative present. Degree = the power of the highest-order derivative when the equation is polynomial in derivatives (free of radicals/fractions).
What is the integrating factor method for a linear differential equation dy/dx + Py = Q?
Integrating Factor IF = e^(∫P dx); solution: y·(IF) = ∫Q·(IF) dx + C.
State the conditional probability formula and the multiplication rule.
P(A|B) = P(A∩B)/P(B), P(B) ≠ 0. Multiplication: P(A∩B) = P(B)·P(A|B) = P(A)·P(B|A).
State Bayes' Theorem.
P(A_i | B) = [P(A_i)·P(B|A_i)] / Σ[P(A_j)·P(B|A_j)], where the A_j form a partition of the sample space.
For a binomial distribution with n trials and success probability p, what is P(X = r), and the mean and variance?
P(X=r) = nCr · p^r · q^(n-r), where q = 1-p. Mean = np; variance = npq.
In mathematical logic, what is the truth value of a conditional p → q, and when is it false?
p → q is false only when p is true and q is false; it is true in all other cases (T→T, F→T, F→F are all true).
What is the contrapositive of p → q, and how does its truth value relate to the original?
The contrapositive is ~q → ~p; it is logically equivalent to p → q (same truth value).
State De Morgan's Laws in logic for the negation of a conjunction and a disjunction.
~(p ∧ q) ≡ ~p ∨ ~q; ~(p ∨ q) ≡ ~p ∧ ~q.
Distinguish a tautology, a contradiction, and a contingency in logic.
Tautology: a statement true for all truth values. Contradiction: false for all truth values. Contingency: true for some and false for others.
In Linear Programming, where does the optimal value of the objective function occur?
At a vertex (corner point) of the feasible region; for a bounded feasible region the optimum always occurs at one of its corner points.
Define the feasible region and the objective function in a Linear Programming Problem.
Feasible region: the set of all points satisfying every constraint (including non-negativity). Objective function: the linear expression (e.g. Z = ax + by) to be maximized or minimized over that region.
What this deck covers
The Mathematics deck follows the MHT CET Mathematics syllabus — 5 chapters and 18 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 12.0 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 99 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 MHT CET deck?
60 cards. This page previews 24 of them, sampled evenly across the deck so you can judge the difficulty before installing anything.
Are these MHT CET flashcards free?
Yes. The preview here is free to read with no signup, and the full 60-card deck is free inside the Examius app.
What do the Mathematics cards cover?
They follow the MHT CET Mathematics syllabus — 5 chapters and 18 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.