Bihar Board Class 12 (Science) Relations and Functions — practice questions
85 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice Bihar Board Class 12 (Science) Relations and Functions in the app →A card is drawn from a deck of 52. Given that the card is RED, what is the probability that it's a KING?If P(A) = 0.5, P(B) = 0.6, and P(A ∩ B) = 0.2, then P(A ∪ B) is:Two dice are rolled. The probability of getting AT LEAST ONE SIX is:Bayes' theorem is essentially used to:For a discrete random variable X with values 0, 1, 2 and probabilities 0.3, 0.5, 0.2 respectively, the mean E(In a binomial distribution B(n=10, p=0.5), the probability of EXACTLY 6 successes is:For a binomial distribution B(n, p), the MEAN and VARIANCE are:The number of ways to choose 3 books out of 5 (order does NOT matter) is:Which relation in a set A contains no ordered pair at all?Which relation on a set A equals the whole product A × A?In a boys' school, 'a is sister of b' on its students is a(n)A relation R on A is reflexive when which pairs lie in R?(a1, a2) in R forcing (a2, a1) in R for all pairs defines which property?(a1, a2) and (a2, a3) in R forcing (a1, a3) in R defines a relation that isA relation that is reflexive, symmetric and transitive is called a(n)On triangles in a plane, 'T1 is congruent to T2' isLines in a plane: 'L1 is perpendicular to L2' isR = {(1,1),(2,2),(3,3),(1,2),(2,3)} on {1,2,3} isFor 'a R b if 2 divides a - b' on Z, the class [0] isWith 'a R b if 3 divides a - b' on Z, how many distinct classes arise?An equivalence relation on X splits X into subsets that areOn {1,...,7}, a R b if a, b are both odd or both even. Largest class size isHow many ordered pairs does R = {(x, y): 3x - y = 0} on {1,...,14} have?In {1,...,6}, R = {(x, y): y is divisible by x} isIn Z, the relation R = {(x, y): x - y is an integer} isOn the real numbers, R = {(a, b): a <= b} isFor R = {(a, b): a <= b^2} on R, which a fails (a, a) in R?On books in a library, 'x and y have the same number of pages' isIn {0,...,12}, a R b if |a - b| is a multiple of 4. Elements related to 1:Points are related if equally far from the origin. The class of P isUnder similarity, with triangles T1 (3,4,5), T2 (5,12,13), T3 (6,8,10), which are related?Polygons are related if they have the same number of sides. The class of a 3-4-5 triangle isLines parallel to y = 2x + 4 are all lines of the formIn N, R = {(a, b): a = b - 2, b > 6}. Which pair is in R?On {1,2,3}, how many relations containing (1,2) and (2,3) are reflexive and transitive but not symmetric?How many equivalence relations on {1,2,3} contain both (1,2) and (2,1)?If f(x1) = f(x2) always implies x1 = x2, then f isA function f: X to Y with range equal to Y is calledf maps each of 50 students to their roll number in N. Then f isf: N to N, f(x) = 2x isf: N to N with f(1) = f(2) = 1 and f(x) = x - 1 for x > 2 isf: N to N, f(x) = x + 1 for odd x and x - 1 for even x, isFor a finite set X, a one-one function f: X to X must beThe greatest integer function [x] from R to R isWhy is f: R to R, f(x) = |x| not onto?The range of f: R to R, f(x) = 1 + x^2 isf(x) = 1/x from N to the non-zero reals isf: N to N, f(n) = (n+1)/2 for odd n and n/2 for even n. Which equality breaks one-one?f(x) = (x - 2)/(x - 3) from R - {3} to R - {1} isFor f: A to B and g: B to C, gof(x) is defined asf(2)=3, f(3)=4, f(4)=f(5)=5; g(3)=g(4)=7, g(5)=g(9)=11. Then gof(4) isIf f(x) = cos x and g(x) = 3x^2, then gof(x) equalsIf g is the inverse of f: X to Y, then gof and fog areFor f(x) = 4x + 3 on N, the inverse g satisfies g(15) =On pairs of positive integers, (x, y) R (u, v) iff xv = yu. Which pair is related to (2, 3)?For any function f: X to Y, R = {(a, b): f(a) = f(b)} on X isHow many one-one functions map {1, 2, 3} onto itself?Why is x to 2x (that is, I_N + I_N) from N to N not onto?On [0, pi/2], f = sin x and g = cos x. f + g takes the value 1 atOn subsets of X, 'A is a subset of B' fails to be an equivalence because it is notA relation from A to B is defined as an arbitrary subset ofHow many different relations can be defined on a 3 element set?On {0,...,12}, with R = {(a, b): a = b}, the set of elements related to 1 isIn N, R = {(x, y): y = x + 5 and x < 4} isIn set theory, a relation R from set A to set B is defined as what?On A = {1, 2, 3, 4}, the relation R = {(a, b): a − b = 10} is which type?A relation R in a set A is called universal when it equals which set?On {1, 2, 3}, R = {(1,1), (2,2), (3,3), (1,2), (2,3)} has which property?Triangles T1 and T2 are related when T1 is congruent to T2. This relation is what?Which properties together make an equivalence relation?On Z, a R b means 2 divides a − b. Which integers are related to 0?A function f : X → Y is one-one when f(x1) = f(x2) implies what?A function f : X → Y is onto exactly when which condition holds?A function that is both injective and surjective is called what?The function f : N → N given by f(x) = 2x is classified as which of these?What is the condition for a function f to be invertible?Is gof = fog for f = cos x, g = 3x², judged at x = 0?For f : N → Y with f(x) = 4x + 3 onto Y, which formula gives the inverse g(y)?The inverse g of an invertible f : X → Y satisfies which pair of equations?The empty relation and the universal relation are together known as what?A relation R is transitive when (a1, a2) and (a2, a3) in R imply what?How are functions related to the general idea of a relation?A function that is not one-one is described by which term?If f(4) = 5 and g(5) = 11, what is gof(4)?Which two relations on a set A are called the extreme relations?