CBSE Class 12 · 2024 · Relations And Functions XIIMultiple Choice

Students of a school are taken to a railway museum to learn about railways heritage and its history. An exhibit in the museum depicted many rail lines on the track near the railway station. Let $L$ be the set of all rail lines on the railway track and $R$ be the relation on $L$ d …

Let $S$ be the relation defined by $S=\{({\ell }_1,{\ell }_2):{\ell }_1\text{ is perpendicular to }{\ell }_2\}$. Check whether the relation $S$ is symmetric and transitive.

A function $f:[-4,4]\to [0,4]$ is given by $f(x)=\sqrt{16-x^2}$. Show that $f$ is an onto function but not a one-one function. Further, find all possible values of $\alpha$ for which $f(\alpha )=\sqrt{7}$.

A relation $R$ in a set $A$ is called ____, if $(a_1,a_2)\in R$ implies $(a_2,a_1)\in R$, for all $a_1,a_2\in A$.

Consider a bijective function $f:R_{+}\to (7,\infty )$ given by $f(x)=16x^2+24x+7$, where $R_{+}$ is the set of all positive real numbers. Find the inverse function of $f$.

Let $N$ be the set of natural numbers and $R$ be the relation on $N\times N$ defined by $(a,b)R(c,d)$ iff $ad=bc$ for all $a,b,c,d\in N$. Show that $R$ is an equivalence relation.