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MATHS M.C.Q. [1 Marks Each]

Practical Geometry Symmetry and Visualising Solid Shapes · Bihar Board (BSEB) STD 7 (BSEB - English Medium). 28 questions.

Questions

M.C.Q. [1 Marks Each]

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28 questions · auto-graded multiple-choice test.

MCQ 11 Mark
Out of the following which is a $3-D$ figure?
  • A
    Square
  • ✓
    Sphere
  • C
    Triangle
  • D
    Circle
Answer
Correct option: B.
Sphere
Square, triangle and circle are $2-D$ figures while sphere is the $3-D$ figure.
Hence, $(b)$ is the correct option.
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MCQ 21 Mark
The solid with one circular face, one curved surface and one vertex is known as:
  • ✓
    Cone
  • B
    Sphere
  • C
    Cylinder
  • D
    Prism
Answer
Correct option: A.
Cone
Cone has one circular face, one curved surface and one vertex.
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MCQ 31 Mark
Which of the following are reflections of each other?






 
  • ✓
  • B
  • C
  • D
Answer
Correct option: A.


Since in the figure $(a)$ the image of one side of the figure is exactly same as the figure on the other side of the line of symmetry.
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MCQ 41 Mark
Which of the following has a line of symmetry?
  • A
  • B
  • ✓
  • D
Answer
Correct option: C.



Line of symmetry is the line which divides a figure into two equal halves which are mirror image of each other.
From all the options mentioned, there exists only one figure which when cut by the line of symmetry will be divided in two equal halves.
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MCQ 51 Mark
Which of the following $3$-dimensional figures has the top, side and front as triangles?
  • A
  • B
  • ✓
  • D
Answer
Correct option: C.



$(c)$ will show all (top, side and front) views as triangle.
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MCQ 61 Mark
The number of lines of symmetry in the figure given below is:
  • A
    $4$
  • B
    $8$
  • ✓
    $6$
  • D
    Infinitely many
Answer
Correct option: C.
$6$
Line of symmetry is the line which divides a figure into two equal halves which are mirror image of each other.
So for the given figure, it has six grooves or inside edge through which we can draw three lines of symmetry.
The figure also has six outside edge through which we can draw three lines of symmetry.
So total six lines of symmetry for the figure is six.
The figure is as follows:
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MCQ 71 Mark
Which of the following letters of English alphabets have more than $2$ lines of symmetry?
  • A
  • B
  • ✓
  • D
Answer
Correct option: C.
 


The letter $0$ has more than two lines of symmetry.
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MCQ 81 Mark
The number of lines of symmetry in Fig is:
  • A
    $1$
  • ✓
    $3$
  • C
    $6$
  • D
    Infinitely many
Answer
Correct option: B.
$3$
The given figure has $3$ lines of symmetry.
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MCQ 91 Mark
When a torch is pointed towards one of the vertical edges of a cube, you get a shadow of cube in the shape of:
  • A
    Square
  • ✓
    Rectangle but not a square
  • C
    Circle
  • D
    Triangle
Answer
Correct option: B.
Rectangle but not a square
When a torch is pointed towards one of the vertical edges of a cube, you get a shadow of cube in the shape of rectangle but not a square.
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MCQ 101 Mark
The order of rotational symmetry in the Fig given below is:
  • A
    $4$
  • B
    $8$
  • ✓
    $6$
  • D
    Infinitely many
Answer
Correct option: C.
$6$
Since, the number of times a figure fits onto itself in one full turn is called order of rotational symmetry.
Therefore, the given figure has rotational symmetry of order $6$.
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MCQ 111 Mark
Take a square piece of paper as shown in figure $(1).$ Fold it along its diagonals as shown in figure $(2).$ Again fold it as shown in figure $(3).$ Imagine that you have cut off $3$ pieces of the form of congruent isosceles right$-$angled triangles out of it as shown in figure $4$.
$1.$

$2.$

$3.$

$4.$


On opening the piece of paper which of the following shapes will you get?

  • ✓
  • B
  • C
  • D
Answer
Correct option: A.


As per the given condition, if we open the piece of paper, we will get the figure as shown in option $(a)$.
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MCQ 121 Mark
Total number of edges a cylinder has:
  • A
    $0$
  • B
    $1$
  • ✓
    $2$
  • D
    $3$
Answer
Correct option: C.
$2$
The total number of edges of a cylinder are two.
The figure of cylinder is as follows:

So the correct answer is $C$.
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MCQ 131 Mark
Which of the following sets of triangles could be the lengths of the sides of a right-angled triangle:
  • A
    $3\ cm, 4\ cm, 6\ cm$
  • B
    $9\ cm, 16\ cm, 26\ cm$
  • ✓
    $1.5\ cm, 3.6\ cm, 3.9\ cm$
  • D
    $7\ cm, 24\ cm, 26\ cm$
Answer
Correct option: C.
$1.5\ cm, 3.6\ cm, 3.9\ cm$
The sides of right-angled triangle must satisfy Pythagoras theorem.
$(\text { Hypotenuse })^2=(\text { Base })^2+(\text { Perpendicular })^2$
Note: Hypotenuse is the largest side of all the sides. So, check all options by putting the values in above formula.
Let us check all the options.
a.
$(6)^2=(3)^2+(4)^2$
$36=9+16$
$36 \neq 25$
b.
$(26)^2=(16)^2+(9)^2=676$
$=256+81$
$676 \neq 337$
c.
$(3.9)^2=(1.5)^2+(3.6)^2$
$=15.21$
$=2.25+12.96$
$=15.21$
$=15.21 \text { (satisfied) }$
d.
$(26)^2=(7)^2+(24)^2$
$=676$
$=49+576$
$=676 \neq 625$
Clearly, option $(c)$ is correct.
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MCQ 141 Mark
The name of the solid in Fig is:
  • A
    Triangular pyramid
  • B
    Rectangular prism
  • ✓
    Triangular prism
  • D
    Rectangular pyramid
Answer
Correct option: C.
Triangular prism
It is a combination of triangle and prism.
Hence, $(c)$ is the correct option.
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MCQ 151 Mark
The name of the given solid in Fig is:
  • A
    Triangular pyramid
  • ✓
    Rectangular pyramid
  • C
    Rectangular prism
  • D
    Triangular prism
Answer
Correct option: B.
Rectangular pyramid
It is a combination of rectangle and pyramid.
Hence, $(b)$ is the correct option.
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MCQ 161 Mark
A solid that has only one vertex is:
  • A
    Pyramid
  • B
    Cube
  • ✓
    Cone
  • D
    Cylinder
Answer
Correct option: C.
Cone
The cone is the shape, that has only one vertex.
Hence, $(c)$ is the correct option.
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MCQ 171 Mark
A solid that has two opposite identical faces and other faces as parallelograms is a:
  • ✓
    Prism
  • B
    Pyramid
  • C
    Cone
  • D
    Sphere
Answer
Correct option: A.
Prism

Prism has two opposite identical faces and other faces as parallelograms.
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MCQ 181 Mark
A triangle can be constructed by taking its sides as:
  • ✓
    $1.8\ cm, 2.6\ cm, 4.4\ cm$
  • B
    $2\ cm, 3\ cm, 4\ cm$
  • C
    $2.4\ cm, 2.4\ cm, 6.4\ cm$
  • D
    $3.2\ cm, 2.3\ cm, 5.5\ cm$
Answer
Correct option: A.
$1.8\ cm, 2.6\ cm, 4.4\ cm$
Triangle can be constructed only if they satisfy the given condition. Sum of two sides > Third side Clearly, only option $(b)$ satisfies the given condition.
$(2 + 3)\ cm > 4\ cm$ i.e. $5\ cm > 4\ cm$
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MCQ 191 Mark
In which of the following cases, a unique triangle can be drawn:
  • A
    $\ce{AB = 4\ cm, BC = 8\ cm}$ and $\ce{CA = 2\ cm}$
  • B
    $\ce{BC = 5.2\ cm} , \angle\text{B}=90^\circ$ and $\angle\text{C}=110^\circ$
  • ✓
    $\ce{XY = 5\ cm} , \angle\text{X}=45^\circ$ and $\angle\text{Y}=60^\circ$
  • D
    An isosceles triangle with the length of each equal side $6.2\ \ce{cm}.$
Answer
Correct option: C.
$\ce{XY = 5\ cm} , \angle\text{X}=45^\circ$ and $\angle\text{Y}=60^\circ$
Let us draw the triangle according to measurement given in respective options.
$a.$ As we can see, triangle cannot be drawn.

$b.$ Triangle cannot be formed.

$c.$ Unique triangle can be drawn by these measurements.

$d.$ Using given data, we can from as many triangles as we want.
Hence, option $(C)$ is correct.
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MCQ 201 Mark
If we rotate a right-angled triangle of height $5\ cm$ and base $3\ cm$ about its height a full turn, we get:
  • ✓
    Cone of height $5\ cm$, base $3\ cm$
  • B
    Triangle of height $5\ cm$, base $3\ cm$
  • C
    Cone of height $5\ cm$, base $6\ cm$
  • D
    Triangle of height $5\ cm$, base $6\ cm$
Answer
Correct option: A.
Cone of height $5\ cm$, base $3\ cm$
If we rotate a right-angled triangle of height $5\ cm$ and base $3\ cm$ about its height a full turn, then we get a cone of height $5\ cm$ and base $3\ cm$.
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MCQ 211 Mark
If we rotate a right-angled triangle of height $5\ cm$ and base $3\ cm$ about its base, we get:
  • A
    Cone of height $3\ cm$ and base $3\ cm$
  • B
    Cone of height $5\ cm$ and base $5\ cm$
  • C
    Cone of height $5\ cm$ and base $3\ cm$
  • ✓
    Cone of height $3\ cm$ and base $5cm$
Answer
Correct option: D.
Cone of height $3\ cm$ and base $5cm$
When a right angled triangle of height $5\ cm$ and base $3\ cm$ is rotated about its base in full turn, then we will get a cone of height $3\ cm$ and base of radius $5\ cm$.
So the correct answer is $D$.
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MCQ 221 Mark
All faces of a pyramid are always:
  • A
    Triangular
  • B
    Rectangular
  • C
    Congruent
  • ✓
    None of these
Answer
Correct option: D.
None of these

The faces of pyramid can be triangular or rectangular. But we have to choose only one correct option.

So the correct answer is $D$.
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MCQ 231 Mark
A triangle can be constructed by taking two of its angles as:
  • ✓
    $110^\circ , 40^\circ $
  • B
    $70^\circ , 115^\circ $
  • C
    $135^\circ , 45^\circ$
  • D
    $90^\circ , 90^\circ$
Answer
Correct option: A.
$110^\circ , 40^\circ $
We know that, the sum of all the angles of a triangle is equal to $180^\circ .$
So, sum of any two angles of a triangle should be less than $180^\circ .$
$110^\circ + 40^\circ = 150^\circ $ i.e. less than $180^\circ .$
$70^\circ + 115^\circ = 185^\circ $ i.e. greater than $180^\circ .$
$135^\circ + 45^\circ = 180^\circ $ i.e. equal to $180^\circ .$
$90^\circ + 90^\circ = 180^\circ $ i.e. equal to $180^\circ .$
Hence, $(a)$ is the correct option.
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MCQ 241 Mark
When we cut a corner of a cube as shown in the figure $12.19,$ we get the cutout piece as:
  • A
    Square pyramid
  • B
    Trapezium prism
  • ✓
    Triangular pyramid
  • D
    A triangle
Answer
Correct option: C.
Triangular pyramid
If we cut a corner of a cube, then we get cut-out of a piece in the form of triangular pyramid.
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MCQ 251 Mark
Which of the following nets is a net of a cylinder?
  • A
  • B
  • ✓
  • D
Answer
Correct option: C.




A net is $2-D$ figure which when folded in a particular axis gives a $3-D$ figure.
So for the net to form a cylinder, the shape of the interlinking blocks of nets should contain a rectangle which is present only in option $C$.

So the correct answer is $C$.
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MCQ 271 Mark
The order of rotational symmetry in the figure given below is:
  • A
    $4$
  • ✓
    $2$
  • C
    $1$
  • D
    Infinitely many
Answer
Correct option: B.
$2$
The number of times a figure fits into itself in one full turn is called as order of rotational symmetry.
So for the given figure the order of rotational symmetry is two.
So the correct answer is $B$.
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MCQ 281 Mark
If three cubes each of edge $4\ cm$ are placed end to end, then the dimensions of resulting solid are:
  • ✓
    $12\ cm \times 4\ cm \times 4\ cm$
  • B
    $4\ cm \times 8\ cm \times 4\ cm$
  • C
    $4\ cm \times 8\ cm \times 12\ cm$
  • D
    $4\ cm \times 6\ cm \times 8\ cm$
Answer
Correct option: A.
$12\ cm \times 4\ cm \times 4\ cm$
When three cubes are placed end to end then the dimensions of the resulting solid would be more than the cube.
The new cuboid will be having the following dimensions: $12\ cm \times 4\ cm \times 4\ cm$
So the correct answer is $A$.
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