NCERT Exemplar MCQ Quiz

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

Let \(\mathrm{A}=\{1,2,3, \ldots n\}\) and \(\mathrm{B}=\{a, b\}\). Then the number of surjections from A into \(B\) 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 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

Let \(f: \mathbf{R} \rightarrow \mathbf{R}\) be defined by
$$ f(x)=\left\{\begin{array}{c} 2 x: x>3 \\ x^2: 1<x \leq 3 \\ 3 x: x \leq 1 \end{array}\right. $$
Then \(f(-1)+f(2)+f(4)\) is

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