Math-Chapter1: Sets, Relations and Functions

If A = {(x, y) : y = e

x

, x ∈ R} and B = {(x, y) : y = e

−x

, x ∈ R} then n(A ∩ B) is

1

If A = {(x, y) : y = sin x, x ∈ R} and B = {(x, y) : y = cos x, x ∈ R} then A ∩ B contains

Infinitely many elements

The relation R defined on a set A = {0, −1, 1, 2} by xRy if |x^2 + y^2| ≤ 2, then which one of the following is true?

(4) Range of R is {0, −1, 1}

If f(x) = |x − 2| + |x + 2|, x ∈ R, then

Let R be the set of all real numbers. Consider the following subsets of the plane R × R:

S = {(x, y) : y = x + 1 and 0 < x < 2} and T = {(x, y) : x − y is an integer }

Then which of the following is true?

T is an equivalence relation but S is not an equivalence relation.

Let A and B be subsets of the universal set N, the set of natural numbers. Then A0∪[(A∩B)∪B0’] is

(4) N

The number of students who take both the subjects Mathematics and Chemistry is 70. This

represents 10% of the enrollment in Mathematics and 14% of the enrollment in Chemistry. The

number of students take at least one of these two subjects, is

(2) 1130

If n((A × B) ∩ (A × C)) = 8 and n(B ∩ C) = 2, then n(A) is

(2) 4

If n(A) = 2 and n(B ∪ C) = 3, then n[(A × B) ∪ (A × C)] is

(3) 6

If two sets A and B have 17 elements in common, then the number of elements common to the

set A × B and B × A is

(2) 17²

For non-empty sets A and B, if A ⊂ B then (A × B) ∩ (B × A) is equal to

(2) A × A

The number of relations on a set containing 3 elements is

(3) 512

Let R be the universal relation on a set X with more than one element. Then R is

(3) transitive

Let X = {1, 2, 3, 4} and R = {(1, 1),(1, 2),(1, 3),(2, 2),(3, 3),(2, 1),(3, 1),(1, 4),(4, 1)}. Then

R is

(2) symmetric

The range of the function 1/ 1-2sinx

(4) (−∞, −1] ∪ [1/3,∞).

The range of the function f(x) = |bxc − x|, x ∈ R is

(3) [0, 1)

The rule f(x) = x² is a bijection if the domain and the co-domain are given by

(4) [0,∞), [0, ∞)

The number of constant functions from a set containing m elements to a set containing n elements

is

(3) n

The function f : [0, 2π] → [−1, 1] defined by f(x) = sin x is

(2) onto

If the function f : [−3, 3] → S defined by f(x) = x² is onto, then S is

(4) [0, 9]

Let X = {1, 2, 3, 4}, Y = {a, b, c, d} and f = {(1, a),(4, b),(2, c),(3, d),(2, d)}. Then f is

(4) not a function

Let f : R → R be defined by f(x) = 1 − |x|. Then the range of f is

(4) (−∞, 1]

The function f : R → R is defined by f(x) = sin x + cos x is

(2) neither an odd function nor an even function

The function f : R → R is defined by

(3) an even function