Let A = \{0, 1, 2, 3\} and define a relation R on A as follows R = {(0, 0), (0, 1), (0, 3), (1, 0), (1, 1), (2, 2), (3, 0), (3, 3)\} then R is

If f = {(5, 2), (6, 3)} and g = {(2, 5), (3, 6)}, then the range of ƒ and g respectively.

Let R be a relation on the set N of natural numbers defined by nRm, if n divides m. Then, R

is

Relation R in set N of natural numbers defined as R={(𝑥, 𝑦) : 𝑦 = 𝑥 + 5 and 𝑥 < 4) are

Relation R in the set A= {1, 2, 3, 4, 5, 6} as

R={(𝑥, 𝑦) : 𝑦 is divisible by 𝑥) are

Relation 𝑅 in the set 𝑍 of all integers defined as R={(𝑥, 𝑦) : 𝑥 − 𝑦 is an integer) is/are

The relation 𝑅 defined in the set {1, 2, 3, 4, 5, 6} as R={(𝑎, 𝑏) : 𝑏 = 𝑎 + 1} is

The relation 𝑅 in 𝑅 defined by R={(𝑎, 𝑏) : 𝑏 = 𝑎 ≤ 𝑏³} } is

The relation 𝑅 in the set 𝐴 of all the books in a library of a college, given by R={(𝑥, 𝑦) :

𝑥 𝑎𝑛𝑑 𝑦 have same number of pages } is a/an

The relation 𝑅 in the set 𝐴 = {1, 2, 3, 4, 5} is given by R={(𝑎, 𝑏) : |𝑎 − 𝑏|, is even } is a/an

The relation 𝑅 in the set 𝐴 = {(𝑥 ∈ 𝑍 ∶ 0 ≤ 𝑥 ≤)} Given by, R={(𝑎, 𝑏) : |𝑎 − 𝑏|,

 a multiple 4} is a/an 

The example of relation which are reflexive and transitive but not symmetric is

The relation 𝑅 in the set 𝐴 of points in a plane, given by R = {(𝑃,𝑄)) : distance of the point

𝑃 from the origin is same as the distance of the point 𝑄 from the origin}, is a/an

The relation 𝑅, defined in the set of 𝐴 all triangles as R = {(𝑇1, 𝑇2) : 𝑇1 is similar to 𝑇2 ) . is a/an

Let 𝐿 be the set of all lines in xy-plane and 𝑅 be the relation in 𝐿 defined as R = {(𝐿1, 𝐿2)

: 𝐿1 is parallel to 𝐿2} ] , then 𝑅 is a/an

Let 𝑅 be the relation in the set (1, 2, 3, 4) given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3,2)}. Choose the correct answer.

Given a non-empty set 𝑋. Consider 𝑃(𝑋), which is the set of all subset of 𝑋. Defined the relation 𝑅 in 𝑃(𝑋) as follows. For subsets 𝐴 and 𝐵 in 𝑃(𝑋), 𝐴𝑅𝐵 if and only if 𝐴 ⊂ 𝐵, then 𝑅 is

Let A=(1, 2, 3). Then, number of relations (1, 2) and (1, 3) which are reflexive and

symmetric but not transitive is 

Let A=(1,2,3). Then, number of equivalence relations containing (1, 2)

If 𝐷 is the domain of the function 𝑠𝑒𝑐 ¹(𝑙𝑜𝑔 𝑥), then 𝐷 contains

The function 𝑓(𝑥) is defined in [0,1], then the domain of definition of the function 𝑓[𝑙𝑜𝑔(1 − 𝑥²)] is

The domain of definition of 𝑓(𝑥) = 𝑙𝑜𝑔2(𝑥+3)/𝑥²+3𝑥+2 is

The domain of the function 𝑓(𝑥) = 𝑙𝑜𝑔0.2𝑙𝑜𝑔0.5𝑙𝑜𝑔0.25 𝑋 is equal to

The domain of the function f(x)= 1/1−𝑡𝑎𝑛𝑥 is

Domain of the function 𝑓(𝑥) = √ 1/𝑠𝑖𝑛 𝑥 -1 is

Domain of 𝑓(𝑥) = sin [2-4x²] ([] denotes the greatest integer function) is

The domain of definition of the function 𝑦(𝑥) given by equation 2 𝑥+2 𝑦=2 is

The domain of the function 𝐹(𝑥) = 1/[𝑥] +√2𝑥 − 𝑥 2 is

Range of the function 𝑓(𝑥) = 𝑥²+𝑥+2 /𝑥² +𝑥+1 ,x∈ 𝑅 𝑖𝑠

Domain and Range of 𝑓(𝑥) = x+3x+20x-sin x

are respectively 

If f(x)= [x2]-[xf, where [] denotes the greatest integer function and x∈ [0,2], then the set of values of f(x) is

Let 𝑓(𝑥)=(1+𝑏²)𝑥 2+2bx+1 and let m(b) be the minimum value of 𝑓(𝑥). As b varies, the range of 𝑚(𝑏) is

If 0<x< 𝜋/2 and 𝑙𝑜𝑔 𝑠𝑖𝑛𝑥 tanx≥0, then range of x is equal to 

If f(x)=(x+1)²-1,(x-1). Then, the set S=(x:f(x) = 𝑓 −1 (x)) is

The function f:R→R defined by 𝑓(𝑥)= 𝑥 𝑥 2+1 , ∀𝑥 ∈ 𝑅 𝑖𝑠

Let R be the set of real numbers and 𝑓: 𝑅 → 𝑅 be the function defined by 𝑓(𝑥) = 4x+5, then f is

Set A has 3 elements and the set B has 4 elements. Then, the number of injective mappings that can be defined from A to B is

Let 𝑓: 𝑅 → 𝑅 be defined by 𝑓(𝑥) = 𝑥² + 1. Then, pre-images of 17 and -3, respectively are

The greatest integer function 𝑓: 𝑅 → 𝑅, given by 𝑓(𝑥) = [𝑥], where [x] denotes the greatest integer less than or equal to x, is

The modulus function 𝑓: 𝑅 → 𝑅, given by 𝑓(𝑥) = [𝑥]. where [x] is x, if x is non-negative and 1x lis-x, if x is negative is

Let A=(1,2,3), B (4,5,6,7) and let f={(1, 4), (2,5), (3, 6)) be a function from A to B, then f is

Let 𝑓: 𝑁 → −𝑁 be defined by 𝑓(𝑛) = { 𝑛+1/2 , if 𝑛 𝑖𝑠 𝑜𝑑𝑑 , n/2 if 𝑛 𝑖𝑠 𝑒𝑣𝑒𝑛 for all n∈ 𝑁 then the function f is

Let 𝐴 = 𝑅 − (3) and 𝐵 = 𝑅 − (1). Consider the function f: A→B defined by f(x) = (𝑥−2 /𝑥−3) is

Let the function 𝑓: 𝑅 → 𝑅 be defined by 𝑓(𝑥) = 𝑐𝑜𝑠 𝑥, 𝑉𝑥𝐸 𝑅, then f is

Which of the following is a bijective function on their ranges?

let E = (1, 2, 3, 4) and F = (1,2). Then, the number of onto functions from E to F is

If f:[0,𝜋/2] → [0,∞) be a function defined by y=sin(𝑥 /2),then f is 

Let A be a set containing m distinct elements, then the total number of distinct functions from A to itself is 

The function 𝑓: 𝑅 → 𝑅 defined by 𝑓(𝑥) = 1(𝑥 − 1)(𝑥 − 2)] is

Let 𝑓: (𝑒, ∞) → 𝑅 be defined 𝑏𝑦 𝑓(𝑥) = 𝑙𝑜𝑔[𝑙𝑜𝑔(𝑙𝑜𝑔 𝑥)], then f is