Understanding Elementary Shapes Test

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Understanding Elementary Shapes Test - 33

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Question 1
1 / -0

In figure, lines $$PQ$$ and $$ST$$ intersect at $$O$$. If $$\angle POR=90^o$$ and $$x:y =3:2$$, then $$z$$ is equal to

A
$$126^o$$

B
$$144^o$$

C
$$136^o$$

D
$$154^o$$

Solution

We can see in the given figure, $$PQ$$ is a straight line
$$\therefore \angle POR +ROT +\angle TOQ =180^o$$
$$\Rightarrow 90^o +x+y=180^o$$
$$\Rightarrow x+y=90^o$$
$$\Rightarrow x+y=90^o$$ ...(1)
Given that, $$\dfrac xy =\dfrac 32$$
Let $$x=3K$$ and $$y=2K$$
From equation (1)
$$\Rightarrow 3K+2K=90^o$$
$$\Rightarrow K=\dfrac{90^o}{5}$$
$$\Rightarrow K=18^o$$
$$\therefore y=2\times 18^o =36^o$$
Now, $$SOT$$ is a straight line
$$\Rightarrow z+y=180^o$$
$$\Rightarrow z+36^o =180^o$$
$$\Rightarrow z=180^o-36^o$$
$$\Rightarrow z=144^o$$
Hence, Option $$(B)$$ is correct.
Question 2
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In Fig. which of the following is a regular polygon?

A
(i)

B
(ii)

C
(iii)

D
(iv)

Solution

Option $$B$$ is right
For a regular polygon, all sides and all angle must be equal to each other.
And, only figure $$(ii)$$ follows this condition.
Question 3
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In a triangle, one angle is of $$90^{o}$$. Then
(i) The other two angles are of $$45^{o}$$ each
(ii) In remaining two angles, one angle is $$90^{o}$$ and other is $$45^{o}$$
(iii) Remaining two angles are complementary

In the given option(s) which is always true?

A
(i) only

B
(ii) only

C
(iii) only

D
(i) and (ii)

Solution

If one angle is right angle then the other both angles are a complementary angle in a triangle.
Question 4
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In figure, the value of $$x$$ is

A
$$110^o$$

B
$$46^o$$

C
$$64^o$$

D
$$150^o$$

Solution

Option (d) is correct.
As we knew, the angle made around a point is $$360$$ degree.
Then,
$$\therefore y+64^o +46^o +100^o -360^o$$
$$\Rightarrow y+210^o =360^o $$
$$\Rightarrow y=360^o -210^o$$
$$\Rightarrow y=150^o$$
Question 5
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The closed curve which is also a polygon is

A

B

C

D

Solution

A polygon is a simple closed curve made up of line segments. Hence, option $$A$$ is correct.
Question 6
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In a solid if $$ F=V = 5$$, then the number of edges in this shape is

A
6

B
4

C
8

D
2

Solution

The correct answer is option $$(c).$$
For any polyhedron, Euler' s formula ;
$$F + V - E = 2$$
Where, $$F$$ = Face and $$V$$ = Vertices and $$E$$ = Edges
Given, $$ F = V = 5$$
On putting the values of $$F$$ and $$V$$ in the about formulae,
$$ 5 + 5 - E = 2$$
$$\Rightarrow 10 - E = 2$$
$$\Rightarrow E = 8$$
Question 7
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Which of the following cannot to be true for a polyhedron ?

A
V = 4, F = 4, E = 6

B
V = 6, F = 8, E = 12

C
V = 10, F = 12, E = 20

D
V = 4, F = 6, E = 6

Solution

The correct answer is option $$(d)$$.
Euler's Formula for any polyhedron$$ = F + V -E = 2$$
Where, F = Faces and V = Vertices and $$E =$$ Edges
Option $$A:$$
$$F+V-E=4+4-6=2$$

Option $$B:$$
$$F+V-E=6+8-12=2$$

Option $$C:$$
$$F+V-E=10+12-20=2$$

Option $$D:$$
$$F+V-E=4+6-6=4\neq2$$
Question 8
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How many diagonals does a hexagon have ?

A
$$ 9 $$

B
$$ 8 $$

C
$$ 2 $$

D
$$ 6 $$

Solution

The polygon of $$ n $$ sides $$ = \dfrac{n(n - 3)}{2} $$

Hexagon has $$ 6 $$ sides $$ = \dfrac{6 (6 - 3)}{2} = 9 $$
Question 9
1 / -0

Which of the following shapes has a vertex:

A

B

C

D

Solution

The correct answer is option $$(c).$$
Because, a vertex is a sharp corner.
Only cone among the given figures has a sharp corner.
Question 10
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How many faces does a die have

A
$$ 1 $$

B
$$ 2 $$

C
$$ 6 $$

D
$$ 4 $$

Solution

Die have six faces $$1,2,3,4,5, 6 $$
$$n(S)=6$$