A relation from C to R is defined by x y |x|=y. Which one is corr… - Vidyadip

Question

A relation $\phi$ from C to R is defined by $\text{x }\phi\text{ y}\Leftrightarrow|\text{x}|=\text{y.}$ Which one is correct?

$(2+3\text{i})\phi13$
$3\phi(-3)$
$(1+\text{i})\phi2$
$\text{i}\phi1$

✓

Answer

$\text{i}\phi1$

Solution:
$\because\ |2+3\text{i}|=\sqrt{13}\neq13$
$|3|\neq-3$
$|1+\text{i}|=\sqrt{2}\neq2$
and $|\text{i}|=1$
So, $(\text{i, }1)\in\phi$

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→Relations — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Choose the correct answer from the given four options.
Let f : R → R be defined by $\text{f}(\text{x})=\frac{1}{\text{x}}\ \forall\ \text{x}\in\text{R}.$ Then f is:

one-one.
onto.
bijective.
f is not defined.

The probability distribution of a discrete random variable $X$ is given below:

$\text{X}:$	$1$	$2$	$3$	$4$
$\text{P}(\text{X}):$	$\frac{1}{10}$	$\frac{1}{5}$	$\frac{3}{10}$	$\frac{2}{5}$

The value of $E(X^2)$ is:

Let $\text{U}=\sin^{-1}\Big(\frac{2\text{x}}{1+\text{x}^2}\Big)$ and $\text{V}=\tan^{-1}\Big(\frac{2\text{x}}{1-\text{x}^2}\Big),$ then $\frac{\text{dU}}{\text{dV}}=$

$\frac{1}{2}$
$\text{x}$
$\frac{1-\text{x}^2}{\text{x}^2-4}$
$1$

$\cos^{-1}[\cos(2\cot^{-1}(\sqrt2-1))]=$ ______.

$\sqrt2-1$
$1+\sqrt2$
$\frac{\pi}{4}$
$\frac{3\pi}{4}$

If from Lagrange's mean value theorem, we have
$\text{f}'(\text{x}_1)=\frac{\text{f}(\text{b})-\text{f}(\text{a})}{\text{b}-\text{a}},$ then:

A person travels 12km in the southward direction and then travels 5km to the right and then travels 15km toward the right and finally travels 5km towards the east, how far is he from his starting place?

5.5kms
3km
13km
6.4km

The distance of the line $\vec{\text{r}}=2\hat{\text{i}}-2\hat{\text{j}}+3\hat{\text{k}}+\lambda(\hat{\text{i}}-\hat{\text{j}}+4\hat{\text{k}})$ from the plane $\vec{\text{r}}.(\hat{\text{i}}+5\hat{\text{j}}+\hat{\text{k}})=5$ is:

$\frac{5}{3\sqrt{3}}$
$\frac{10}{3\sqrt{3}}$
$\frac{25}{3\sqrt{3}}$
$\text{None of these}$

Choose the correct answer: Area of the region bounded by the curve $y^2 = 4x, y-$ axis and the line $y = 3$ is :

Choose the correct answer from the given four options.
Let F = 3x - 4y be the objective function.
Minimum value of F is:

If a line makes angles of $90^{\circ}, 135^{\circ}, 45^{\circ}$ with $x, y$ and $z$ axes, then its direction cosines will be :