LA

A relation R is defined on Z, the set of integers, as $R = \{(x, y) : |x - y|\text{ is divisible by a prime number 'p', } x, y \in \mathbb{Z}\}$ check whether R is an equivalence relation or not.

LA

Show that the relation $R$ in the set $A$ of points in a plane given by $R = \{(P, Q) : \text{distance of the point } P \text{ from the origin is same as the distance of the point } Q \text{ from the origin}\}$, is an equivalence relation. Further, show that the set of all points related to a point $P \neq (0, 0)$ is the circle passing through $P$ with origin as centre. [Competency]

SA

Show that the function $f:R\rightarrow R$ defined by $f(x)=4x^{3}-5$, $\forall x\in R$ is one-one and onto.

LA

Check whether the relation S in the set of real numbers R defined by $S=\{(a,b)$: where $a-b+\sqrt{2}$ is an irrational number is reflexive, symmetric or transitive.

MCQ_SINGLE

For real x, let \(f(x)=x^{3}+5x+1\). Then:

View All Questions