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🇮🇳 CBSE Class 12 Board Exam · flashcards
CBSE Class 12 Board Exam Mathematics Flashcards
50 question-and-answer cards covering Mathematics as it is examined in CBSE Class 12 Board Exam. 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 is the integral of 1/x dx?
Integral of 1/x dx = ln|x| + C.
State the integration by parts formula.
Integral of u dv = uv - integral of v du.
In integration by parts, what does the ILATE rule help decide?
It gives the priority order (Inverse, Logarithmic, Algebraic, Trigonometric, Exponential) for choosing the first function u.
State the fundamental theorem of calculus (evaluation part) for a definite integral.
Integral from a to b of f(x) dx = F(b) - F(a), where F is an antiderivative of f.
What is the integral of 1/(x^2 + a^2) dx?
(1/a) tan^(-1)(x/a) + C.
What is the formula for the area between a curve y = f(x) and the x-axis from x = a to x = b (f >= 0)?
Area = integral from a to b of f(x) dx.
What is the order of a differential equation?
The order is the order of the highest derivative appearing in the differential equation.
What is the degree of a differential equation?
The degree is the power of the highest-order derivative, when the equation is polynomial in derivatives and free from radicals/fractions in them.
What is the integrating factor for a linear differential equation dy/dx + Py = Q?
I.F. = e^(integral of P dx).
What is the dot (scalar) product of two vectors a and b in terms of magnitudes and angle?
a . b = |a| |b| cos(theta), where theta is the angle between them.
What is the magnitude of the cross product of vectors a and b?
|a x b| = |a| |b| sin(theta), where theta is the angle between them; it equals the area of the parallelogram they form.
How do you determine if two non-zero vectors a and b are perpendicular?
They are perpendicular if and only if a . b = 0.
What is a unit vector in the direction of vector a?
a-hat = a / |a|, the vector a divided by its magnitude.
What is the formula for the projection of vector a on vector b?
Projection of a on b = (a . b) / |b|.
What are direction cosines of a line?
The cosines (l, m, n) of the angles the line makes with the positive x, y, z axes; they satisfy l^2 + m^2 + n^2 = 1.
State the vector equation of a line through point a parallel to vector b.
r = a + lambda b, where lambda is a scalar parameter.
What is the formula for the angle between two lines with direction ratios (a1,b1,c1) and (a2,b2,c2)?
cos(theta) = |a1a2 + b1b2 + c1c2| / (sqrt(a1^2+b1^2+c1^2) x sqrt(a2^2+b2^2+c2^2)).
State the equation of a plane in normal form (vector).
r . n-hat = d, where n-hat is the unit normal vector and d is the perpendicular distance from the origin.
What is the shortest distance between two skew lines r = a1 + lambda b1 and r = a2 + mu b2?
d = |((a2 - a1) . (b1 x b2))| / |b1 x b2|.
In linear programming, what is the feasible region?
The common region determined by all the constraints (including non-negativity) of a linear programming problem.
State the corner point theorem in linear programming.
If a feasible region is bounded, the optimal value of the objective function occurs at a corner (vertex) of the feasible region.
What is the formula for conditional probability P(A|B)?
P(A|B) = P(A and B) / P(B), provided P(B) > 0.
State Bayes' Theorem for events A and E_i (a partition).
P(E_i | A) = [P(E_i) P(A | E_i)] / [sum over j of P(E_j) P(A | E_j)].
What are the mean and variance of a binomial distribution with n trials and success probability p?
Mean = np; Variance = npq, where q = 1 - p.
What this deck covers
The Mathematics deck follows the CBSE Class 12 Board Exam Mathematics syllabus — 4 chapters and 13 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 12.5 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 72 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 CBSE Class 12 Board Exam deck?
50 cards. This page previews 24 of them, sampled evenly across the deck so you can judge the difficulty before installing anything.
Are these CBSE Class 12 Board Exam flashcards free?
Yes. The preview here is free to read with no signup, and the full 50-card deck is free inside the Examius app.
What do the Mathematics cards cover?
They follow the CBSE Class 12 Board Exam Mathematics syllabus — 4 chapters and 13 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.