M.C.Q. [1 Marks Each]

MCQ 11 Mark

Which of the following will not form a polyhedron?

✓
$3$ triangles.
B
$2$ triangles and $3$ parallelogram.
C
$8$ triangles.
D
$1$ pentagon and $5$ triangles.

Answer

Correct option: A.

$3$ triangles.

A polyhedron is bounded by more than four polygonal faces. But in case of $3$ triangles, it is not possible. So, option $(a)$ does not form a polyhedron.

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MCQ 21 Mark

The net shown below can be folded into the shape of a cube. The face marked with the letter L is opposite to the face marked with which letter?

✓
$M$
B
$N$
C
$Q$
D
$O$

Answer

Correct option: A.

$M$

Clearly, the given net is a cube. If we fold it into a cube, then $N$ will face opposite to $R Q$ on the top and $0$ on the bottom. So, $L$ faces opposite to $M.$

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MCQ 31 Mark

Side of a square garden is 30m. If the scale used to draw its picture is $1\ cm: 5\ m$, the perimeter of the square in the picture is

A
$20\ cm$
✓
$24\ cm$
C
$28\ cm$
D
$30\ cm$

Answer

Correct option: B.

$24\ cm$

Given, side of a square garden $= 30m$
$\therefore$ Perimeter of square $= 4 \times $ Side
$\therefore$ Perimeter of a square garden $= 4 \times 30m = 120m$
Scale used to draw its picture $= 1cm: 5cm$
Hence, the perimeter of a square in the picture $=\frac{120}{5}=24\text{cm}$

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MCQ 41 Mark

In the given map, the distance between the places is shown using the scale $1\ cm : 0.5\ km.$ Then the actual distance $($in $km)$ between school and the book shop is:

A
$1.25$
B
$2.5$
C
$2$
✓
$1.1$

Answer

Correct option: D.

$1.1$

Given, scale $1cm = 0.5km.$
The distance between school and the book shop shown in map is equal to $2.2cm.$ So, the actual distance between them will be $= 2.2 \times 0.5km.$
$= 1.1km$

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MCQ 51 Mark

We have $4$ congruent equilateral triangles. What do we need more to make a pyramid?

A
An equilateral triangle.
✓
A square with same side length as of triangle.
C
$2$ equilateral triangles with side length same as triangle.
D
$2$ squares with side length same as triangle.

Answer

Correct option: B.

A square with same side length as of triangle.

We know that, a pyramid is a polyhedron, whose base is a polygon and lateral faces are triangles. But in the question, we have only $4$ congruent equilateral triangles. Thus, we have to add a polygon in the base of atleast a four-sided figure.
Hence, option $(b)$ is required to make a pyramid.

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MCQ 61 Mark

Which of the following is a regular polyhedron?

A
Cuboid.
B
Triangular prism.
✓
Cube.
D
Square prism.

Answer

Correct option: C.

Cube.

A polyhedron is regular if its faces are congruent regular polygons and the same number of faces meet at each vertex. Hence, a cube satisfies-all the properties for a regular polyhedron.

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MCQ 71 Mark

Which of the following shapes has a vertex.

Answer

Correct option: C.

Figures given in options $(a), (b)$ and $(d)$ have no vertex but figure given in option $(c)$, is a cone having a vertex. Since, vertex is a point where two or more edges meet.

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MCQ 81 Mark

Which of the following cannot be true for a polyhedron?

A
$V = 4, F = 4, E = 6.$
B
$V = 6, F = 8, E = 12.$
C
$V = 20, F = 12, E = 30.$
✓
$V = 4, F = 6, E = 6.$

Answer

Correct option: D.

$V = 4, F = 6, E = 6.$

We know that, Euler’s formula for any polyhedron is $\text{F + V - E} = 2$
Where, $F =$ faces, $V =$ vertices
$E =$ edges
$a. V = 4, F = 4$ and $E = 6$
$\text{LHS = F + V - E}$
$= 4 + 4 - 6$
$= 8 - 6 = 2$
$= \text{RHS}$
$\therefore $ Option $(a)$ is true for a polyhedron.
$b. V = 6, F = 8 $and $E = 12$
$\text{LHS = F + V - E}$
$= 8 + 8 -12$
$= 14 - 12 = 2$
$= \text{RHS}$
$\therefore$ Option $(b)$ isyrue for a polyhedron.
$c. V = 20, F = 12$ and $E = 30.$
$\text{LHS = F + V - E.}$
$= 12 + 20 - 30.$
$= 32 - 30 = 2.$
$= \text{RHS}..$
$\therefore$ Option $(c)$ is true for a polyhedron.
$d. V = 4, F = 6$ and $E = 6.$
$\text{LHS = F + V - E.}$
$= 6 + 4 - 6.$
$=10-6=4\neq\text{RHS}$.
$\therefore$ Option $(d)$ is not true a polyhedron.

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MCQ 91 Mark

Which of the following is a two Dimensional figure?

✓
Rectangle.
B
Rectangular Prism.
C
Square Pyramid.
D
Square Prism.

Answer

Correct option: A.

Rectangle.

A two dimensional figure have two dimensions (measurements) like length and breadth. In the given options, only rectangle has two dimensions, i.e. length and breadth.

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MCQ 101 Mark

Which of the following is not a prism?

Answer

Correct option: B.

We know that, a prism is a polyhedron whose bottom and top faces are congruent polygons and faces known as lateral faces are parallelograms. Clearly in option (b) figure, bottom and top faces are not congruent polygons and also lateral faces are not parallelograms.

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MCQ 111 Mark

Which of the nets given below will generate a cone?

Answer

Correct option: A.

Option (a) net diagram gives a cone because other options has no circular base.
Since, a cone is a solid figure which has a circular base and it tapers from a circular base to a point called vertex.

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MCQ 121 Mark

Which of the following $3D$ shapes does not have a vertex?

A
Pyramid.
B
Prism.
C
Cone.
✓
Sphere.

Answer

Correct option: D.

Sphere.

As we kndw that, a vertex is a meeting point of two or more edges. Since, a sphre has only one curved face, so it has no vertex and no edges.

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MCQ 131 Mark

In a blueprint of a room, an architect has shown the height of the room as $33cm.$ If the actual height of the room is $330cm,$ then the scale used by her is:

A
$1:11$
✓
$1:10$
C
$1:100$
D
$1:3$

Answer

Correct option: B.

$1:10$

Given, in a blueprint height of the room $= 33\ cm$, and actual height of the room $= 330\ cm$
We know that,
$\text{Scale of map}=\frac{\text{Size drawn}}{\text{Actual size}}$
$=\frac{33}{330}=\frac{1}{10}$

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MCQ 141 Mark

Which of the following can be the base of a pyramid?

A
Line segment.
B
Circle.
✓
Octagon.
D
Oval.

Answer

Correct option: C.

Octagon.

Since, a pyramid is a polyhedron base a polygon and lateral faces are triangles.
Hence, octagon can be the base of a pyarmid.

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MCQ 151 Mark

Which amongst the following is not a polyhedron?

Answer

Correct option: C.

According to the definition of a polyhedron, option (c) figure does not satisfies the condition of a polyhedron.
Since, a solid is a polyhedron if it is made up of only polygonal-faces, the faces meet at edges with one line segment and the edges meeting at a point. The point is generally called as vertex. But all the faces of option (c) are not polygons, there is a circular base, so the figure is not a polyhedron

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MCQ 161 Mark

The ratio of the number of general stores and that of the ground is:

A
$1 : 2$
B
$2 : 1$
C
$2 : 3$
✓
$3 : 2$

Answer

Correct option: D.

$3 : 2$

Clearly,

represent genral stores and

represent ground in the given map.
$\therefore$ Total number

is $6$ and total number

is $4.$
Hence, ratio of the number of general stres and that of the ground is $\frac{6}{4}=\frac{3}{2}=3:2$

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MCQ 171 Mark

In a solid if $F = V = 5$, then the number of edges in this shape is

A
$6$
B
$4$
✓
$8$
D
$2$

Answer

Correct option: C.

$8$

Euler formula for any polyhedron is
$F + V - E = 2$
Given, $F = V = 5$
On puttting the values of $F$ and $V$ in the Euler's formula, we get
$5 + 5 - E = 2$
$\Rightarrow 10 - E = 2 \Rightarrow E - 8$
Note: $F =$ fraces, $V =$ vertices and $E =$ edges.

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MCQ 181 Mark

According to the map, the number of schools in the town is:

A
$4$
B
$3$
✓
$5$
D
$2$

Answer

Correct option: C.

$5$

Clearly,

represent school. So we count

in the given map.
Hence, the number of

in the map is $5.$

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MCQ 191 Mark

Solid having only line segments as its edges is a:

✓
Polyhedron.
B
Cone.
C
Cylinder.
D
Polygon.

Answer

Correct option: A.

Polyhedron.

in polyhedrin, the faces meet at edges which are line segments and edges meet at vertes.

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MCQ 201 Mark

Which of the following is the top view of the given shape?

Answer

Correct option: A.

Since, top view is the picture of the solid which is seen from the top of the given figure. Therefore, the option (a) figure will be the top view, i.e.,

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MCQ 211 Mark

The following is the map of a town. Based on it answer question $19 - 21$
.