MCQ
Let $A = N \times N$ and $\times $ be the binary operation on $A$ defined by $(a, b) \times (c, d) = (a + c, b + d).$ Then $\times $ is:
  • A
    Commutative.
  • B
    Associative.
  • Both $(a)$ and $(b).$
  • D
    None of these.

Answer

Correct option: C.
Both $(a)$ and $(b).$

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

Similar questions

Number of triplets $(x, y, z)$ satisfying $ \sin ^{-1}\text{x}+\sin ^{-1}\text{y}+\cos ^{-1}\text{z}=2\pi$ is:
Let $f$ be a real valued function, defined on $R -\{-1,1\}$ and given by

$f(x)=3 \log _{e}\left|\frac{x-1}{x+1}\right|-\frac{2}{x-1}$

Then in which of the following intervals, function $f ( x )$ is increasing?

let $S = \{1, 2, … 20\}$. A subset $B$ of $S$ is said to be $“nice”$, if the sum of the elements of $B$ is $203$. Then the probability that a randomly chosen subset of $S$ is $‘nice’$ is
Let $\mathrm{F}:[3,5] \rightarrow \mathrm{R}$ be a twice differentiable function on $(3,5)$ such that $\mathrm{F}(\mathrm{x})=\mathrm{e}^{-\mathrm{x}}$ $\int_{3}^{x}\left(3 t^{2}+2 t+4 F^{\prime}(t)\right) \,d t$

If $F^{\prime}(4)=\frac{\alpha e^{\beta}-224}{\left(e^{\beta}-4\right)^{2}}$, then $\alpha+\beta$ is equal to $....$

What is integrating factor of $\frac{\text{dy}}{\text{dx}}+\text{y}\sec\text{x}=\tan\text{x}?$
The distance of the point (-1, -5, -10) from the point of intersection of the line $\vec{\text{r}}.=2\hat{\text{i}}-\hat{\text{j}}+2\hat{\text{k}}+\lambda(3\hat{\text{i}}+4\hat{\text{j}}+12\hat{\text{k}})$ and the plane $\vec{\text{r}}.=(\hat{\text{i}}-\hat{\text{j}}+\hat{\text{k}})=5$ is:
The vector $a + b$ bisects the angle between the vectors $ a $ and $ b,$  if
A box contains 3 orange balls, 3 green balls and 2 blue balls. Three balls are drawn at random from the box without replacement. The probability of drawing 22 green balls and one blue ball is
If in a triangle $\overrightarrow {AB} = a,\,\,\overrightarrow {AC} = b$ and  $ D, E $ are the mid-points of  $ AB $ and  $ AC$  respectively, then $\overrightarrow {DE} $ is equal to
Choose the correct answer from the given four options.
Projection vector of $\vec{\text{a}}$ on $\vec{\text{b}}$ is: