Relations Test 2

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Relations Test 2

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Weekly Quiz Competition

Question 1
1 / -0

If X is brother of the son of Y's son. How is X related to Y?

A
Son

B
Brother

C
Cousin

D
Grandson

E
Uncle

Solution

Son of Y's Son- Grandson, Brother of Y's Grandson- Y's Grandson
Option D is correct.
Question 2
1 / -0

If $$A=\left \{x:x^2-3x+2=0\right \}$$ and $$B=\left \{x:x^2+4x-5=0\right \}$$ then the value of A-B is

A
$$\left \{1, 2\right \}$$

B
$$\left \{2\right \}$$

C
$$\left \{1\right \}$$

D
$$\left \{5, 2\right \}$$

Solution

$$A=\left \{x:x^2-3x+2=0\right \}\Rightarrow A=\left \{1, 2\right \}$$
$$B=\left \{x:x^2+4x-5=0\right \}\Rightarrow A=\left \{1, -5\right \}$$
$$\therefore A-B=\left \{2\right \}$$
Question 3
1 / -0

Suppose y is equal to the sum of two quantities of which one varies directly as x and the other inversely as x If y = 6 when x = 4 and $$\displaystyle y=\frac{10}{3}$$ when x = 3 then what is the relation between x and y?

A
$$\displaystyle y=x+\frac{4}{x}$$

B
$$\displaystyle y+2x=\frac{4}{x}$$

C
$$\displaystyle y=2x+\frac{8}{x}$$

D
$$\displaystyle y=2x-\frac{8}{z}$$

Solution

(A)If$$y=X+\frac{4}{x}\Rightarrow 4+\frac{4}{4}=3 \neq 6=6$$
(B)$$y+2x=\frac{4}{x}\Rightarrow 6+2(4)=\frac{4}{4}\Rightarrow 6+8\neq 1$$
(C)$$y=2x+\frac{8}{x}\Rightarrow 6=2(4)+\frac{8}{4}\Rightarrow 6\neq 8+2$$
(D)$$y=2x-\frac{8}{x}\Rightarrow 6=2(4)-\frac{8}{4}=8-2=6$$ If x=4 and y=6
$$y=2x-\frac{8}{x}\Rightarrow \frac{10}{3}=2\times 3-\frac{8}{3}\Rightarrow \frac{10}{3}=\frac{10}{3}$$ If x=3 and y=$$y=\frac{10}{3}$$
Then option (D) $$Y=2x-\frac{8}{x}$$
Question 4
1 / -0

x varies directly as y and inversely as the square of z. When y = 4 and z is 14 x = 10. If y = 16 and z = 7 what is x?

A
180

B
160

C
280

D
200

Solution

Given x varies directly as y and inversely as the square of z. When y = 4 and z is 14 x = 10. If y = 16 and z = 7
Then $$x=k\frac{y}{z^{2}}$$
$$\Rightarrow 10=k\times \frac{4}{14\times14}$$
$$\Rightarrow k=490$$
Thus $$x=490\times \frac{16}{7\times 7}=160$$
Question 5
1 / -0

The number of reflexive relations of a set with four elements is equal to

A
2$$^{16}$$

B
2$$^{12}$$

C
2$$^{8}$$

D
2$$^{4}$$

Solution

Total number of reflexive relations in a set with n elements = 2$$^n$$ Therefore, total number of reflexive relations set with 4 elements = 2$$^4$$
Question 6
1 / -0

If R={$$(x,y)/3x+2y=15$$ and x,y $$\displaystyle \epsilon $$ N}, the range of the relation R is________

A
$$\{1,2\}$$

B
$$\{1,2,..,5\}$$

C
$$\{1,2,.,7\}$$

D
$$\{3,6\}$$

Solution

Given, $$ 3x + 2y = 15 $$

$$ => y = \dfrac {15-3x}{2} $$
As both $$ x , y $$ are natural numbers, we should find $$ x $$ such that $$ 15-3x $$ is divisible by $$ 2 $$

We can see that when $$ x =1$$ or $$3 $$, we get $$ y = 6$$ or $$3 $$

Hence, the range is $$ {3,6} $$
Question 7
1 / -0

Let $$R$$ be the relation in the set $$N$$ given by $$R=\left\{(a, b): a=b-2, b>6\right\}$$. Choose the correct answer.

A
$$(2, 4)\in R$$

B
$$(3, 8)\in R$$

C
$$(6, 8)\in R$$

D
$$(8, 7)\in R$$

Solution

$$R=\left\{(a, b):a=b-2, b>6\right\}$$
Now, since $$b>6, (2, 4)\notin R$$
Also, as $$3\neq 8-2, (3, 8)\notin R$$
And, as $$8\neq 7-2$$
$$\therefore (8, 7)\notin R$$
Now, consider $$(6, 8)$$.
We have $$8 > 6$$ and also, $$6=8-2$$.
$$\therefore (6, 8)\in R$$
Hence the correct answer is C.
Question 8
1 / -0

If ordered pair $$(a, b)$$ is given as $$(-2, 0)$$, then $$a =$$

A
$$-2$$

B
$$0$$

C
$$2$$

D
None of the above

Solution

$$a$$ will be first entry in ordered pair $$(a, b).$$
So, option A is correct.
Question 9
1 / -0

If $$x$$ co-ordinate of a point is $$2$$ and $$y$$ co-ordinate is $$0$$, then ordered pair for its coordinate on $$XY$$ plane is

A
$$(0, 0)$$

B
$$(2, 2)$$

C
$$(0, 2)$$

D
$$(2, 0)$$

Solution

Ordered pair for co-ordinate of a point in $$XY$$ plane is written as $$(x, y).$$
So, option D is correct.
Question 10
1 / -0

What are the ways of representing a relation?

A
Set builder form

B
Roster form

C
Arrow diagram

D
All of these

Solution

Relation can be represented in set builder form, roster form and Arrow diagram.

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Re-Attempt Weekly Quiz Competition

Relations Test 2

Result

Relations Test 2

Score

-

Rank

-

SHARING IS CARING

Question 1

Son

Brother

Cousin

Grandson

Uncle

Solution

Question 2

$$\left \{1, 2\right \}$$

$$\left \{2\right \}$$

$$\left \{1\right \}$$

$$\left \{5, 2\right \}$$

Solution

Question 3

$$\displaystyle y=x+\frac{4}{x}$$

$$\displaystyle y+2x=\frac{4}{x}$$

$$\displaystyle y=2x+\frac{8}{x}$$

$$\displaystyle y=2x-\frac{8}{z}$$

Solution

Question 4

180

160

280

200

Solution

Question 5

2$$^{16}$$

2$$^{12}$$

2$$^{8}$$

2$$^{4}$$

Solution

Question 6

$$\{1,2\}$$

$$\{1,2,..,5\}$$

$$\{1,2,.,7\}$$

$$\{3,6\}$$

Solution

Question 7

$$(2, 4)\in R$$

$$(3, 8)\in R$$

$$(6, 8)\in R$$

$$(8, 7)\in R$$

Solution

Question 8

$$-2$$

$$0$$

$$2$$

None of the above

Solution

Question 9

$$(0, 0)$$

$$(2, 2)$$

$$(0, 2)$$

$$(2, 0)$$

Solution

Question 10

Set builder form

Roster form

Arrow diagram

All of these

Solution

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