Let R be a relation defined on the set Z of all integers and xRy, when x + 2y is divisible by 3, then
A is not transitive
R is symmetric only
R is an equivalence relation
R is not an equivalence relation
Let f : N R be such that f(1) = 1 and f(1) + 2f(2) + 3f(3) + ... + nf(n) = n(n+ 1) f(n), for all n N, n 2, where N is the set of natural numbers and R is the set of real numbers. Then, the value of f(500) is
1000
500
1/500
1/1000
For the function f(x) = . where [x] denotes the greatest integer less than or equal to x, which of the following statements are true?
The domain is
The range is
The domain is
The range is
If R be the set of all real numbers and f : R ➔ R is given by f(x) = 3x2 + 1. Then, the set f-1([1, 6]) is
Let Xn = for all integers is
a singleton set
not a finite set
an empty set
a finite set with more than one element
If f(x) = 2100x + 1, g(x) = 3100x + 1, then the set ofreal numbers x such that f{g(x)} = x is
empty
a singleton
a finite set with more than one element
infinite
B.
a singleton
Given, f(x) = 2100 . x + 1
and g(x) =3100 . x + 1
Now, f{g(x)} = x
Hence, f{g(x)} = x represent a singleton set.
If A = {x : x2 - 5x + 6 = 0}, B={2, 4}, C = {4, 5}, then A x (B ∩ C) is
{(2, 4), (3, 4)}
{(4, 2), (4, 3)}
{(2, 4), (3, 4), (4, 4)}
{(2, 2), (3, 3), (4, 4), (5, 5)}