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IPU CET Mathematics Flashcards
57 question-and-answer cards covering Mathematics as it is examined in IPU 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.
State the conditions for two lines to be parallel and perpendicular in terms of slopes.
Parallel: m₁ = m₂; perpendicular: m₁·m₂ = −1.
Give the standard equation of a circle with centre (h, k) and radius r, and the general form.
(x−h)² + (y−k)² = r²; general form x² + y² + 2gx + 2fy + c = 0 with centre (−g, −f) and radius √(g²+f²−c).
For an ellipse x²/a² + y²/b² = 1 (a > b), give eccentricity and foci.
e = √(1 − b²/a²); foci at (±ae, 0); b² = a²(1 − e²).
For the parabola y² = 4ax, give the focus, directrix, and length of latus rectum.
Focus (a, 0); directrix x = −a; latus rectum = 4a.
For a hyperbola x²/a² − y²/b² = 1, give eccentricity and the asymptotes.
e = √(1 + b²/a²) > 1; asymptotes y = ±(b/a)x.
Give the distance formula and section formula (internal) in 3D.
Distance = √[(x₂−x₁)²+(y₂−y₁)²+(z₂−z₁)²]; point dividing in ratio m:n: ((mx₂+nx₁)/(m+n), …).
What is the relation among direction cosines l, m, n of a line in 3D?
l² + m² + n² = 1, where l, m, n are cosines of the angles the line makes with the axes.
State the standard limits lim_{x→0} (sin x)/x and lim_{x→0} (1+x)^{1/x}.
lim_{x→0} (sin x)/x = 1; lim_{x→0} (1+x)^{1/x} = e.
State the conditions for a function f to be continuous at x = a.
f(a) is defined, lim_{x→a} f(x) exists, and lim_{x→a} f(x) = f(a).
State the product rule and quotient rule of differentiation.
(uv)' = u'v + uv'; (u/v)' = (u'v − uv')/v².
State the chain rule and the derivatives of sin x, eˣ, and ln x.
dy/dx = (dy/du)(du/dx); d(sin x)/dx = cos x; d(eˣ)/dx = eˣ; d(ln x)/dx = 1/x.
How are increasing/decreasing intervals and maxima/minima found using derivatives?
f increasing where f'(x) > 0, decreasing where f'(x) < 0; critical points at f'(x) = 0; local max if f''<0, local min if f''>0 (second-derivative test).
State the power rule for integration and the integral of 1/x.
∫xⁿ dx = x^{n+1}/(n+1) + C (n ≠ −1); ∫(1/x) dx = ln|x| + C.
State the Fundamental Theorem of Calculus (definite integral evaluation).
∫ₐᵇ f(x) dx = F(b) − F(a), where F is an antiderivative of f.
Give the formula for area under a curve and area between two curves.
Area under y=f(x) from a to b: ∫ₐᵇ f(x) dx; between curves: ∫ₐᵇ [f(x) − g(x)] dx where f ≥ g.
What is the order and degree of a differential equation, and the general solution form of dy/dx = ky?
Order = highest derivative present; degree = power of the highest derivative (when polynomial in derivatives); solution of dy/dx = ky is y = C e^{kx}.
State the solution method for a linear first-order ODE dy/dx + Py = Q.
Use integrating factor IF = e^{∫P dx}; solution: y·(IF) = ∫ Q·(IF) dx + C.
Give the dot product and cross product magnitudes of vectors a and b.
a·b = |a||b|cosθ (scalar); |a×b| = |a||b|sinθ (vector perpendicular to both).
State conditional probability, the multiplication rule, and independence of events.
P(A|B) = P(A∩B)/P(B); P(A∩B) = P(A)P(B|A); A, B independent iff P(A∩B) = P(A)P(B).
State Bayes' theorem.
P(Aᵢ|B) = [P(Aᵢ)P(B|Aᵢ)] / Σⱼ P(Aⱼ)P(B|Aⱼ).
Give the binomial probability distribution formula and its mean and variance.
P(X=r) = nCr pʳ q^{n−r} (q = 1−p); mean = np, variance = npq.
Give the formulas for mean, variance, and standard deviation of a data set.
Mean x̄ = Σxᵢ/n; variance σ² = Σ(xᵢ − x̄)²/n; standard deviation σ = √(variance).
In mathematical reasoning, what are the converse, inverse, and contrapositive of 'if p then q'?
Converse: if q then p; Inverse: if ¬p then ¬q; Contrapositive: if ¬q then ¬p (logically equivalent to the original).
State De Morgan's laws for negation of compound statements.
¬(p ∧ q) ≡ ¬p ∨ ¬q; ¬(p ∨ q) ≡ ¬p ∧ ¬q.
What this deck covers
The Mathematics deck follows the IPU CET Mathematics syllabus — 5 chapters and 24 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 11.4 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 75 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 IPU CET deck?
57 cards. This page previews 24 of them, sampled evenly across the deck so you can judge the difficulty before installing anything.
Are these IPU CET flashcards free?
Yes. The preview here is free to read with no signup, and the full 57-card deck is free inside the Examius app.
What do the Mathematics cards cover?
They follow the IPU CET Mathematics syllabus — 5 chapters and 24 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.