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
B.
The range is
C.
The domain is
We have,
Domain = R - {f(x) = 0}
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
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)}