Relations and Functions Test

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Relations and Functions Test - 15

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Weekly Quiz Competition

Question 1
1 / -0

If $$x$$ and $$y$$ co-ordinate of a point is $$(3, 10)$$, then $$y$$ co-ordinate is

A
$$0$$

B
$$3$$

C
$$10$$

D
None of the above

Solution

$$y$$ coordinate will be second entry in ordered pair.
So, option C is correct.
Question 2
1 / -0

If $$a$$ and $$b$$ are two variables and $$(a, b)=(b, a)$$, then

A
$$a = 0$$

B
$$b = 0$$

C
$$a = b$$

D
$$\displaystyle a\pm b$$

Solution

$$(a, b) = (b, a)$$ only if $$a = b.$$.
So, option C is correct.
Question 3
1 / -0

If $$y$$ is second entry and $$x$$ is first entry then its ordered pair will be ............

A
$$(x, y)$$

B
$$(y, y)$$

C
$$(y, x)$$

D
None of the above

Solution

If $$x$$ is first entry and $$y$$ is second, then its ordered pair will be $$(x, y)$$.

So, option A is correct.
Question 4
1 / -0

Identify the first component of an ordered pair $$(2, 1)$$.

A
$$1$$

B
$$2$$

C
$$-1$$

D
$$0$$

Solution

In an ordered pair $$(x,y)$$, the first component is $$x$$ and the second component is $$y$$.
Therefore, in an ordered pair $$(2,1)$$, the first component is $$2$$.
Question 5
1 / -0

Which of the ordered pair satisfies the relation $$x<y$$?

A
$$(1,2)$$

B
$$(2,1)$$

C
$$(1,1)$$

D
None of these

Solution

$$(A) (1,2)$$
$$x<y$$
$$1<2$$
True , $$x<y$$

$$(B) (2,1)$$
$$2>1$$

$$(C) (1,1)$$
$$x=y$$
Question 6
1 / -0

What is general representation of ordered pair for two variables $$a$$ and $$b$$?

A
$$a, b$$

B
$$(a, b)$$

C
$$(a), b$$

D
$$a, (b)$$

Solution

An ordered pair is written in the form $$(x-$$coordinate, $$y-$$coordinate$$)$$.
Question 7
1 / -0

Identify the first component of an ordered pair $$(0, -1) $$.

A
$$0$$

B
$$-1$$

C
$$2$$

D
$$1$$

Solution

In an ordered pair $$(x,y)$$, the first component is $$x$$ and the second component is $$y$$.
Therefore, in an ordered pair $$(0,-1)$$, the first component is $$0$$.
Question 8
1 / -0

If $$A = \{a, b\}, B=\{1, 2, 3\}$$, find B $$\times$$ A

A
$$B$$ $$\times$$ $$A$$$$ = \{(1, a), (2, a), (3, a), (1, b) (2, b), (3, b)\}$$

B
$$B$$ $$\times$$ $$A$$$$ = \{ (2, a), (3, a), (1, b) (2, b), (3, b)\}$$

C
$$B$$ $$\times$$ $$A$$$$ = \{(1, a), (2, a), (3, a), (1, b) (2, b)\}$$

D
None of these

Solution

To find B × A multiply each element of B with that of A & form an ordered pair.
i.e. ordered pairs are (1,a); (2,a); (3,a); (1,b); (2,b); (3,b)
Therefore B × A = { (1,a), (2,a), (3,a), (1,b), (2,b), (3,b)}
Question 9
1 / -0

Ordered pairs $$(x, y)$$ and $$(-1, -1)$$ are equal if $$y = -1$$ and $$x =$$ _____

A
$$1$$

B
$$-1$$

C
$$0$$

D
$$2$$

Solution

Given , $$(x-y)=(-1,1)$$
$$x=-1, y=-1$$
The value of $$x=-1$$.
Question 10
1 / -0

Let R be the set of real numbers and the mapping $$f:R\rightarrow R$$ and $$g:R\rightarrow R$$ be defined by $$f(x)=5-x^2$$ and $$g(x)=3\lambda-4$$, then the value of $$(fog)(-1)$$ is

A
$$-44$$

B
$$-54$$

C
$$-32$$

D
$$-64$$

Solution

Given, $$f(x)=5-x^2,\,g(x)=3x-4$$
Now, $$(fog)(-1)=f\begin{Bmatrix}g(-1)\end{Bmatrix}$$
$$=f(-7)\;[\because\;g(-1)=3(-1)-4=-7]$$
$$=5-(-7)^2$$
$$=-44$$

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Re-Attempt Weekly Quiz Competition

Relations and Functions Test - 15

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Relations and Functions Test - 15

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SHARING IS CARING

Question 1

$$0$$

$$3$$

$$10$$

None of the above

Solution

Question 2

$$a = 0$$

$$b = 0$$

$$a = b$$

$$\displaystyle a\pm b$$

Solution

Question 3

$$(x, y)$$

$$(y, y)$$

$$(y, x)$$

None of the above

Solution

Question 4

$$1$$

$$2$$

$$-1$$

$$0$$

Solution

Question 5

$$(1,2)$$

$$(2,1)$$

$$(1,1)$$

None of these

Solution

Question 6

$$a, b$$

$$(a, b)$$

$$(a), b$$

$$a, (b)$$

Solution

Question 7

$$0$$

$$-1$$

$$2$$

$$1$$

Solution

Question 8

$$B$$ $$\times$$ $$A$$$$ = \{(1, a), (2, a), (3, a), (1, b) (2, b), (3, b)\}$$

$$B$$ $$\times$$ $$A$$$$ = \{ (2, a), (3, a), (1, b) (2, b), (3, b)\}$$

$$B$$ $$\times$$ $$A$$$$ = \{(1, a), (2, a), (3, a), (1, b) (2, b)\}$$

None of these

Solution

Question 9

$$1$$

$$-1$$

$$0$$

$$2$$

Solution

Question 10

$$-44$$

$$-54$$

$$-32$$

$$-64$$

Solution

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