Set, Relation and FunctionHard
Question
The number of elements in the relation $R = \{(x,y)$ : $\left. \ 4x^{2} + y^{2} < 52,x,y \in Z \right\}$ is
Options
A.77
B.89
C.67
D.86
Solution
$4x^{2} + y^{2} < 52,\ x,y \in Z$
↓ ↓
$${0\ \ \ \ \ \ \ \ \ 0, \pm 1, \pm 2, \pm 3, \pm 4, \pm 5, \pm 6, \pm 7\ \rightarrow \ 1 \times 15 = 15 }{\pm 1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0, \pm 1, \pm 2, \pm 3\ldots\ldots\ldots. \pm 6\ \rightarrow \ 2 \times 13 = 26 }{\pm 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0, \pm 1, \pm 2, \pm 3\ldots\ldots\ldots. \pm 5\ \rightarrow \ 2 \times 11 = 22 }{\pm 3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0, \pm 1, \pm 2 \pm 3\ \rightarrow \ 2 \times 7 = 14 }$$Number of elements $= 77$
Create a free account to view solution
View Solution FreeMore Set, Relation and Function Questions
Domain of the definition of functionf(x) = is (where [.] → G.I.F.)...Let f: R → R be a function such that f(2 − x) = f(2 + x) and f(4 − x) = f(4 + x), for all x ∈ R ...Let R be a relation defined on N × N by (a, b) R(c, d) ⇔ a(b + c) = c(a + d). Then R is...Let W denote the words in the English dictionary. Define the relation R by : R = {(x, y) ∈ W × W | the words ...A function f(x) is such that f(x) = 0 has 8 distinct real roots and f(x) = f(6 - x) for x ∈ R. Sum of real roots o...