Download App

Binary Operations — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSBinary Operations2 Marks
Question
Write the composition table for the binary operation $\times _5 ($multiplication modulo $5)$ on the set $S = {0, 1, 2, 3, 4}.$
✓

Answer

Here,
$1 \times _51 =$ Remainder obtained by dividing $1 \times 1$ by $5 = 1$
$3 \times _54 =$ Remainder obtained by dividing $3 \times 4$ by $5 = 2$
$4 \times _54 =$ Remainder obtained by dividing $4 \times 4$ by $5 = 1$
So, the composition table is as follows$:$
$\times _5$ $0$ $1$ $2$ $3$ $4$
$0$ $0$ $0$ $0$ $0$ $0$
$1$ $0$ $1$ $2$ $3$ $4$
$2$ $0$ $2$ $4$ $1$ $3$
$3$ $0$ $3$ $1$ $4$ $2$
$4$ $0$ $4$ $3$ $2$ $1$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks Questions" from Binary Operations→Binary Operations — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Evaluate:
$\sin\Big(\tan^{-1}\text{x}+\tan^{-1}\frac{1}{\text{x}}\Big)\text{ for }\text{x}>0$
→
Check the injectivity and surjectivity of the below function:
$f : R \rightarrow R$ given by $f(x) = x^2$
→
If $A$ is $2\times 3$ matrix and $B$ is a matrix such that $A^T B$ and $BA^T$ both are defined, then what is the order of $B?$
→
If $\begin{bmatrix}\text{a+b}&2\\5&\text{b} \end{bmatrix}=\begin{bmatrix}6&5\\2&2 \end{bmatrix}$, then find a.
→
Prove that the function $\text{f}(\text{x})=\cos\text{x}$ is:
Strictly decreasing in $(0,\pi).$
→
If A = {1, 2, 3, 4} define relations on A which have properties of being:
Symmetric but neither reflexive nor transitive.
→
If A = {1, 2, 3, 4} define relations on A which have properties of being:
Reflexive, symmetric and transitive.
→
Let C be the set of complex numbers. Prove that the mapping f : C → R given by f(z) = |z|, ∀ z ∈ C, is neither one-one nor onto.
→
Compute the indicated product $\left[\begin{array}{ccc} {2} & {3} & {4} \\ {3} & {4} & {5} \\ {4} & {5} & {6} \end{array}\right]\left[\begin{array}{rrr} {1} & {-3} & {5} \\ {0} & {2} & {4} \\ {3} & {0} & {5} \end{array}\right]$
→
Find $\frac{{dy}}{{dx}}$ if  $xy + {y^2} = \tan x + y$
→