10 Question MCQ (including Assertion)

Let R be a relation on the set \(\mathbf{N}\) of natural numbers defined by \(n \mathrm{R} m\) if \(n\) divides \(m\). Then R is

Let \(\mathrm{A}=\{1,2,3\}\) and consider the relation
$$ R=\{1,1),(2,2),(3,3),(1,2),(2,3),(1,3)\} . $$
Then \(R\) is

Let \(f: \mathbf{R} \rightarrow \mathbf{R}\) be defined by \(f(x)=3 x^2-5\) and \(g: \mathbf{R} \rightarrow \mathbf{R}\) by \(g(x)=\frac{x}{x^2+1}\). Then \(g o f\) 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 \(f: \mathbf{R} \rightarrow \mathbf{R}\) be defined by \(f(x)=\sin x\) and \(g: \mathbf{R} \rightarrow \mathbf{R}\) be defined by \(g(x)=x^2\), then \(f \circ g\) is

Let \(f: \mathbf{R} \rightarrow \mathbf{R}\) be defined by \(f(x)=3 x-4\). Then \(f^{-1}(x)\) is given by

If a relation \(R\) on the set \(\{1,2,3\}\) be defined by \(R=\{(1,2)\}\), then \(R\) is

Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as \(a \mathrm{R} b\) if \(a\) is congruent to \(b \forall a, b \in \mathrm{~T}\). Then R is

Consider the non-empty set consisting of children in a family and a relation \(R\) defined as \(a \mathrm{R} b\) if \(a\) is brother of \(b\). Then R is