Download App

RELATIONS AND FUNCTIONS — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSRELATIONS AND FUNCTIONS2 Marks
Question
For each binary operation * defined below, determine whether * is commutative or associative.
On Q, define $\text{a} * \text{b} =\frac{\text{ab}}{2}$
✓

Answer

For commutativity: $\text{a}*\text{b}=\frac{\text{ab}}{2}\ \text{and}\ \text{b}*\text{a}=\frac{\text{ba}}{2}=\frac{\text{ab}}{2}=\text{a}*\text{b}$
For associativity: $\text{a}*(\text{b}*\text{c})=\text{a}*\Big(\frac{\text{bc}}{2}\Big)=\frac{\text{abc/2}}{2}=\frac{\text{abc}}{4}$
Also, $(\text{a}*\text{b})*\text{c}=\Big(\frac{\text{ab}}{2}\Big)*\text{c}=\frac{\text{abc}/2}{2}=\frac{\text{abc}}{4}$
$\therefore$ a * (b * c) = (a * b) * c
Therefore, the operation * is commutative and associative.

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 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

For each binary operation * defined below, determine whether * is commutative or associative.
On R - {-1}, define $\text{a}*\text{b}=\frac{\text{a}}{\text{b}+1}$
→
In each of the form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.
$\frac{\text{x}}{\text{a}}+\frac{\text{y}}{\text{b} }=1$
→
The volume of a cube is increasing at the rate of $9 \ cm^3 / \sec$. How fast is the surface area increasing when the length of an edge is $10 \ cm$ ?
→
Evaluate the following integrals:
$\int\limits^{\frac{\pi}{2}}_0\sqrt{1-\cos2\text{x}}\text{ dx}$
→
If $\vec{\text{a}},\vec{\text{b}}$ are two vectors, then write the truth value of the following statement:$\vec{\text{a}}=-\vec{\text{b}}\Rightarrow\big|\vec{\text{a}}\big|=\big|\vec{\text{b}}\big|$
→
Find the equation of a line parallel to x-axis and passing through the origin.
→
Evaluate the following integrals:
$\int\limits^{\text{e}^2}_\text{e}\frac{1}{\text{x}\log\text{x}}\text{ dx}$
→
Evaluate the following determinant: $\begin{vmatrix}67&19&21\\39&13&14\\81&24&26 \end{vmatrix}$
→
If $\vec{\text{a}}=\text{x}\hat{\text{i}}+2\hat{\text{j}}-\text{z}\hat{\text{k}}$ and $\vec{\text{b}}=3\hat{\text{i}}-\text{y}\hat{\text{j}}+\hat{\text{k}}$ are two equal vectors, then write the value of x + y + z.
→
Determine the order and degree of the following differential equations. state also whether they are linear or non linear.
$2\frac{\text{d}^2\text{y}}{\text{dx}^2}+3\sqrt{1-\Big(\frac{\text{dy}}{\text{dx}}\Big)^2-\text{y}}=0$
→