A binary operation * on Z defined by a * b = 3a + b for all a, b … - Vidyadip

Question

A binary operation * on Z defined by a * b = 3a + b for all a, b ∈ Z, is:

Commutative.
Associative.
Not commutative.
Commutative and associative.

✓

Answer

Not commutative.

Solution:
Let $\text{a, b}\in\text{Z}$
a * b = 3a + b
b * a = 3b + a
Thus, a * b $\neq$ b * a
If a = 1 and b = 2,
1 * 2 = 3(1) + 2
= 5
2 * 1 = 3(2) + 1
= 7
1 * 2 $\neq$ 2 * 1
Thus, * is not commutative on Z.

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 "M.C.Q (1 Marks)" from RELATIONS AND FUNCTIONS→RELATIONS AND FUNCTIONS — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

If the binary operation $\odot$ is defined on the set $Q^+$ of all positive rational numbers by $\text{a}\odot\text{b}=\frac{\text{ab}}4$. Then, $3\odot\Big(\frac{1}5\odot\frac{1}2\Big)$ is equal to:

if $\text{y}=\text{e}^{{\tan}\text{x}},$ then $(\cos^2\text{x})\text{y}_2=$

$(1-\sin2\text{x})\text{y}_1$
$-(1+\sin2\text{x})\text{y}_1$
$(1+\sin2\text{x})\text{y}_1$
$\text{None of these}$

If OACB is a parallelogram with $\overrightarrow{\text{OC}}=\vec{\text{a}}$ and $\overrightarrow{\text{AB}}=\vec{\text{b}}$, then $\overrightarrow{\text{OA}}=$

$\big(\vec{\text{a}}+\vec{\text{b}}\big)$
$\big(\vec{\text{a}}-\vec{\text{b}}\big)$
$\frac{1}2\big(\vec{\text{b}}-\vec{\text{a}}\big)$
$\frac{1}2\big(\vec{\text{a}}-\vec{\text{b}}\big)$

Evaluate: $\int\sec^2(7-4\text{x})\text{dx}.$

$-\frac{1}{4}\tan(7-4\text{x})+\text{c}$
$\frac{1}{4}\tan(7-4\text{x})+\text{c}$
$\frac{1}{4}\tan(7+4\text{x})+\text{c}$
$-\frac{1}{4}\tan(7\text{x}-4)+\text{c}$

The equation $\sin^{-1}\text{x}-\cos^{-1}\text{x}=\cos^{-1}(\frac{\sqrt3}{2})$ has:

Nique solution.
No solution.
Infinitely many solution.
None of these.

The signum function, $f: R \rightarrow R$ is given by $f(x)=\left\{\begin{array}{ll}1, & x>0 \\ 0, & x=0 \\ -1, & x<0\end{array}\right.$ is

If the events A and B are independent, then $\text{P}(\text{A}\cap\text{B})$ is equal to,

If $A$ is an invertible matrix, then which of the following is not true:

$l = m = n = 1$ represents the direction cosines of:

Two persons $A$ and $B$ take turns in throwing a pair of dice.The first person to throw $9$ from both dice will be awarded the prize. If $A$ throws first, then the probability that $B$ wins the game is.