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 "5 Marks Questions" from Functions→Functions — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Determine if $\text{f(x)}=\begin{cases}\text{x}^2\sin\frac{1}{\text{x}},&\text{ x}\neq0\\0,&\text{x}=0\end{cases}$ is a continuous function?

Find the intervals in which the following functions are increasing or decreasing.
$f(x) = 3x^4 - 4x^3- 12x^2 + 5$

Show that four points whose position vectors are
$6\hat{\text{i}}-7\hat{\text{j}},16\hat{\text{i}}-19\hat{\text{j}}-4\hat{\text{k}},3\hat{\text{i}}-6\hat{\text{k}},2\hat{\text{i}}-5\hat{\text{j}}+10\hat{\text{k}}$ are coplanar.

Let $d_1, d_2, d_3$ be three mutually exclusive diseases. Let $S$ be the set of observable symptoms of these diseases. $A$ doctor has the following information from a random sample of $5000$ patients: 1800 had disease $d_1, 2100$ has disease $d _2$, and others had disease $d _3 .1500$ patients with disease $d _1, 1200$ patients with disease $d _2$, and 900 patients with disease $d _3$ showed the symptom. Which of the diseases is the patient most likely to have?

Evaluate the following:
$\int\frac{\sin^6\text{x}+\cos^6\text{x}}{\sin^2\text{x}\cos^2\text{x}}\text{dx}$

The contents of urns I, II, III are as follows:
Urn I : 1 white, 2 black and 3 red balls
Urn II : 2 white, 1 black and 1 red balls
Urn III : 4 white, 5 black and 3 red balls.
One urn is chosen at random and two balls are drawn. They happen to be white and red. What is the probability that they come from Urns I, II, III?

Using integration find the area of the region bounded by the curve $\text{y}=\sqrt{4-\text{x}^2},\text{ x}^2+\text{y}^2-4\text{x}=0$ and the x-axis.

A manufacturer considers that men and women workers are equally efficient and so he pays them at the same rate. He has 30 and 17 units of workers (male and female) and capital respectively, which he uses to produce two types of goods A and B. To produce one unit of A, 2 workers and 3 units of capital are required while 3 workers and 1 unit of capital is required to produce one unit of B. If A and B are priced at

120 per unit respectively, how should he use his resources to maximise the total revenue? Form the above as an LPP and solve graphically. Do you agree with this view of the manufacturer that men and women workers are equally efficient and so should be paid at the same rate?

Find the value of $\lambda$ such that the line $\frac{\text{x}-2}{6}=\frac{\text{y}-1}{\lambda}=\frac{\text{z}+5}{-4}$ is perpendicular to the plane 3x - y - 2z = 7.

Prove that if a plane has the intercepts a, b, c and is at a distance of p units from the origin, then $\frac{1}{\text{a}^2}+\frac{1}{\text{b}^2}+\frac{1}{\text{c}^2}=\frac{1}{\text{p}^2}.$