Which of the following is true? 1. * defined by a*b= a + b 2 is a… - Vidyadip

Question

Which of the following is true?

* defined by $\text{a}*\text{b}=\frac{\text{a + b}}2$ is a binary operation on Z.
* defined by $\text{a}*\text{b}=\frac{\text{a + b}}2$ is a binary operation on Q.
All binary commutative operations are associative.
Subtraction is a binary operation on N.

✓

Answer

* defined by $\text{a}*\text{b}=\frac{\text{a + b}}2$ is a binary operation on Q.

Solution:
For option a, if we take 3 and 2 then
$3*2=\frac{5}2\in\text{Z}$. So, option a is not true.
For option b, if we take any two numbers a and b
then $\frac{\text{a + b}}2$ belongs to Q for $\text{a, b}\in\text{Q}$.
So, option b is correct.
For option d, if we take 2, 3 then $2-3=-1\in\text{N}$.
So, option d is not true.
Option c is not true.

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

Find the equation of the line which passes through the point (1, 2, 3) and is parallel to the vector $3 \hat{i}+2 \hat{j}-2 \hat{k}$

The point on the curve $y = x^2 - 3x + 2$ where tangent is perpendicular to $y = x$ is:

The set points where the function f(x) given by $\text{f(x)=}|\text{x}-3|\cos\text{x}$ is diffrentiable, is:

R
R - {3}
$(0,\infty)$
None of these.

The value of $\hat{i} \cdot(\hat{j} \times \hat{k})+\hat{j} \cdot(\hat{i} \times \hat{k})+\hat{k}(\hat{i} \times \hat{j})$ is

The area of the region bounded by $y = (x - 4)^2, y = 16 - x^2$ and the $x$ axis, is:

Choose the correct answer from the given four options: The area of the region bounded by the curve $x^2 = 4y$ and the straight line $x = 4y - 2$ is:

Choose the correct answer from the given four options.
The probability distribution of a discrete random variable X is given below:

$\text{X}$	$2$	$3$	$4$	$5$
$\text{P}(\text{X})$	$\frac{5}{\text{k}}$	$\frac{7}{\text{k}}$	$\frac{9}{\text{k}}$	$\frac{11}{\text{k}}$

The value of k is:

The maximum number of equivalence relations on the set A = {1, 2, 3} are:

1
2
3
5

Choose the correct answer from the given four options.
The vector in the direction of the vector $\hat{\text{i}}-2\hat{\text{j}}+2\hat{\text{k}}$ that has magnitude 9 is:

$\hat{\text{i}}-2\hat{\text{j}}+2\hat{\text{k}}$
$\frac{\hat{\text{i}}-2\hat{\text{j}}+2\hat{\text{k}}}{3}$
$3(\hat{\text{i}}-2\hat{\text{j}}+2\hat{\text{k}})$
$9(\hat{\text{i}}-2\hat{\text{j}}+2\hat{\text{k}})$

If $\hat{\text{i}},\hat{\text{j}},\hat{\text{k}}$ are unit vectors, then

$\hat{\text{i}}.\hat{\text{j}}=1$
$\hat{\text{i}}.\hat{\text{i}}=1$
$\hat{\text{i}}\times\hat{\text{j}}=1$
$\hat{\text{i}}\times\big(\hat{\text{j}}\times\hat{\text{k}}\big)=1$