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Maths M.C.Q

Introduction to Euclid Geometry · Gujarat Board (GSEB) STD 9 (GSEB - English Medium). 174 questions.

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MCQ 11 Mark
Which of the following is not a rectilinear figure?
  • A
    Circle.
  • B
    Square.
  • C
    Rectangle.
  • D
    Rhombus.
Answer
  1. Circle.
    Solution:
    A rectilinear figure is a figure all of whose edges meet at right angles. A circle has no edge.
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MCQ 31 Mark
The number of lines passing through two distinct points.
  • A
    4
  • B
    1
  • C
    3
  • D
    2
Answer
  1. 1
    Solution:
    Only one line can pass through two given distinct points.
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MCQ 41 Mark
Write the correct answer in the following:
The side faces of a pyramid are:
  • A
    Triangles.
  • B
    Squares.
  • C
    Polygons.
  • D
    Trapeziums.
Answer
  1. Triangles.
    Solution:
    The side faces of a pyramid are always triangles.
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MCQ 51 Mark
Euclid belongs to the country:
  • A
    India.
  • B
    Greece.
  • C
    Japan.
  • D
    Egypt.
Answer
  1. Greece.
    Solution:
    Euclid belongs to the country, Greece.
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MCQ 71 Mark
‘Lines are parallel if they do not intersect’ – is stated in the form of:
  • A
    A postulate
  • B
    An axiom
  • C
    A definition
  • D
    A proof
Answer
  1. A postulate
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MCQ 81 Mark
The whole is _______ the part.
  • A
    Equal.
  • B
    Greater than.
  • C
    Less than.
  • D
    Double.
Answer
  1. Greater than.
    Solution:
    The whole is made up of its parts, hence, it will always be greater than the part.
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MCQ 111 Mark
Which of the following is a true statement?
  • A
    The floor and a wall of a room are parallel planes.
  • B
    The ceiling and a wall of a room are parallel planes.
  • C
    The floor and the ceiling of a room are parallel planes.
  • D
    Two adjacent walls of a room are parallel planes.
Answer
  1. The floor and the ceiling of a room are parallel planes.
    Solution:
    Two lines are said to be parallel, if they have no point in common.
    Options (a), (b) and (d) have a common point, hence they are not parallel.
    In option (c), the floor and the ceiling of a room are parallel to each other is a true statement.
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MCQ 121 Mark
The boundaries of the solids are:
  • A
    Curves.
  • B
    Points.
  • C
    Surfaces.
  • D
    Lines.
Answer
  1. Surfaces.
    Solution:
    A solid has shape, size, position and can be moved from one place to another. Its boundaries are called surfaces. They separate one part of the space from the other.
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MCQ 131 Mark
Which of the following is a solid?
  • A
    Rectangle.
  • B
    Circle.
  • C
    Cylinder.
  • D
    Square.
Answer
  1. Cylinder.
    Solution:
    All the other figures are 2D except cylinder which is 3D. Any 3D figure is considered to be a solid.
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MCQ 151 Mark
Which of the following is not a solid?
  • A
    Cube.
  • B
    Cone.
  • C
    Cylinder.
  • D
    Circle.
Answer
  1. Circle.
    Solution:
    Any 3D figure is considered to be a solid. A circle is a 2D figure, so, it cannot be considered as a solid.
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MCQ 161 Mark
A _______ is an exact location in space.
  • A
    Line.
  • B
    Solid.
  • C
    Surface.
  • D
    Point.
Answer
  1. Point.
    Solution:
    Point is the basic building block of Geometry. Every shape is made through combining the points. A small dot marked by a pencil is a point. A point has no length or width. It has no thickness. Point is a mark of position. A point specifies the exact location. Point is denoted by a dot (.) and is named by an alphabet.
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MCQ 171 Mark
Which of the following is a true statement?
  • A
    Only a unique line can be drawn through a given point.
  • B
    Infinitely many lines can be drawn through two given points.
  • C
    If two circles are equal, then their radii are equal.
  • D
    A line has a definite length.
Answer
  1. If two circles are equal, then their radii are equal.
    Solution:
    In option (a), infinite number of line can be drawn to pass through a given point. So, it is not a true statement.
    In option (b), only one line can be drawn to pass through two given points. So, it is not a true statement.
    In option (c),
    'If two circles are equal, then their radii are equal' is the true statement.
    In option (d), A line has no end points. A line has an indefinite length. So, it is not a true statement.
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MCQ 191 Mark
Two intersecting lines cannot be parallel to the same line is stated in the form of:
  • A
    A theorem.
  • B
    A postulate.
  • C
    A definition.
  • D
    None of these.
Answer
  1. A postulate.
    Solution:
    Euclid's fifth postulate can also be stated in the following form: Two distinct intersecting lines cannot be parallel to the same line.
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MCQ 201 Mark
“Lines are parallel if they do not intersect” is stated in the form of:
  • A
    A proof.
  • B
    A postulate.
  • C
    A definition.
  • D
    An axiom.
Answer
  1. A definition.
    Solution:
    Euclid gave the definition of parallel lines in Book I, Definition 23 just before the five postulates.
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MCQ 211 Mark
Two lines are said to be ________ if they intersect at right angles.
  • A
    Concurrent.
  • B
    Parallel.
  • C
    Perpendicular.
  • D
    None of these.
Answer
  1. Perpendicular.
    Solution:
    A line is perpendicular to another if it meets or crosses it at right angles (90º).
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MCQ 221 Mark
Write the correct answer in the following:
The total number of propositions in the Elements are:
  • A
    465
  • B
    460
  • C
    13
  • D
    55
Answer
  1. 465
    Solution:
    The total number of propositions in the Elements are 465.
    Note: The statements that can be proved are called propositions or theorems. Euclid deduced 465 propositions in a logical chain using his axioms, postulates, definitions and theorems.
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MCQ 231 Mark
Write the correct answer in the following:
The three steps from solids to points are:
  • A
    Solids - surfaces - lines - points.
  • B
    Solids - lines - surfaces - points.
  • C
    Lines - points - surfaces - solids.
  • D
    Lines - surfaces - points - solids.
Answer
  1. Solids - surfaces - lines - points.
    Solution:
    The three steps from solids to points are solids-surface-lines-points.
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MCQ 241 Mark
Write the correct answer in the following:
Boundaries of surfaces are:
  • A
    Surfaces.
  • B
    Curves.
  • C
    Lines.
  • D
    Points.
Answer
  1. Curves.
    Solution:
     The boundaries of surfaces are curves.
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MCQ 251 Mark
In ancient India, the shapes of altars used for household rituals were:
  • A
    Squares and rectangles.
  • B
    Squares and circles.
  • C
    Triangles and rectangles.
  • D
    Trapeziums and pyramids.
Answer
  1. Squares and circles.
    Solution:
    Squares and circular altars were used for household rituals.
    Whereas altars having shapes as combinatiotanglens of recs, triangles and trapeziums were used for public worship.
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MCQ 261 Mark
The total number of propositions in the Euclid’s Elements is:
  • A
    First Axiom
  • B
    Second Axiom
  • C
    Third axiom
  • D
    Fourth Axiom
Answer
  1. Second Axiom
    Solution:
    By using Euclid’s second axiom, if equals are added to equals then wholes are equal.
    Hence, if z has been added to both the sides of equation x + y = 10, then it becomes x + y + z = 10 + z.
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MCQ 271 Mark
Write the correct answer in the following:
The number of interwoven isosceles triangles in Sriyantra (in the Atharvaveda) is:
  • A
    Seven.
  • B
    Eight.
  • C
    Nine.
  • D
    Eleven.
Answer
  1. Nine.
    Solution:
    The number of interwoven isosceles triangle in Sriyantra (in the Atharva Veda) is nine.
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MCQ 281 Mark
Write the correct answer in the following:
Thales belongs to the country:
  • A
    Babylonia.
  • B
    Egypt.
  • C
    Greece.
  • D
    Rome.
Answer
  1. Greece.
    Solution:
    Thales belongs to the country Greece. The Greeks were interested in establishing the truth of the statements they discovered using deductive reasoning. Thales, a Greeks mathematician, is credited with giving the first known proof.
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MCQ 291 Mark
Three or more lines intersecting at the same point are said to be:
  • A
    Intersecting.
  • B
    Concurrent.
  • C
    Collinear.
  • D
    None of these.
Answer
  1. Concurrent.
    Solution:
    When three or more lines intersect in one point, they are concurrent. The point at which they intersect is the point of concurrency.
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MCQ 301 Mark
A line segment has definite:
  • A
    Breadth.
  • B
    Volume.
  • C
    Length.
  • D
    Area.
Answer
  1. Length.
    Solution:
    A line segment is a piece, or part, of a line in geometry. A line segment is represented by endpoints on each end of the line segment. A line in geometry is represented by a line with arrows at each end. A line segment and a line are different because a line goes on forever while a line segment has a distinct beginning and end.
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MCQ 311 Mark
Euclid stated that 'all right angles are equal to each other', in the form of:
  • A
    A definition.
  • B
    An axiom.
  • C
    A postulate.
  • D
    A proof.
Answer
  1. An axiom.
    Solution:
    Euclid stated that 'All right angles are equal to each other' in the form of a postulate.
    This is Euclid's Postulate 4.
    Note: The answer in the book is option (a). But if you have a look at the Euclid's postulate, the answer is a postulate.
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MCQ 321 Mark
Axioms are assumed:
  • A
    Theorems
  • B
    Definitions
  • C
    Universal truths specific to geometry
  • D
    Universal truths in all branches of mathematics
Answer
  1. Universal truths in all branches of mathematics
    Solution:
    Axioms are assumed universal truths in all branches of mathematics and no mathematical deduction is needed to prove them.
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MCQ 331 Mark
A polygon is a closed figure made up of:
  • A
    Three line segments only.
  • B
    Two line segments.
  • C
    Three or more line segments.
  • D
    None of these.
Answer
  1. Three or more line segments.
    Solution:
    Polygons are 2-dimensional shapes. They are made of straight lines, and the shape is "closed" (all the lines connect up). Polygon comes from the Greek words, Poly-means "many" and gon means "angle".
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MCQ 341 Mark
Write the correct answer in the following:
The number of dimension, a point has:
  • A
    0
  • B
    1
  • C
    2
  • D
    3
Answer
  1. 0
    Solution:
    A point is that which has no part i.e., no length, no breadth and no height. So, it has no dimension.
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MCQ 351 Mark
Write the correct answer in the following:
In ancient India, the shapes of altars used for house hold rituals were:
  • A
    Squares and circles.
  • B
    Triangles and rectangles.
  • C
    Trapeziums and pyramids.
  • D
    Rectangles and squares.
Answer
  1. Squares and circles.
    Solution:
    In ancient India, squares and circular altars were used for household rituals.
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MCQ 361 Mark
Given four distinct points in a plane. How many line segments can be drawn using them when no three of them are collinear?
  • A
    8
  • B
    4
  • C
    6
  • D
    1
Answer
  1. 6
    Solution:
    If the four points are A, B, C and D, we can draw the lines: A-B, A-C, A-D, B-C, B-D, C-D.
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MCQ 371 Mark
Euclid first postulates is:
  • A
    A straight line may be drawn from any point to any other point.
  • B
    A terminated line can be produced indefinitely.
  • C
    All right angles are equal to one another.
  • D
    None of these
Answer
  1. A straight line may be drawn from any point to any other point.
    Solution:
    Euclid first postulates is:
    A straight line may be drawn from any point to any other point
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MCQ 381 Mark
Write the correct answer in the following:
Pythagoras was a student of:
  • A
    Thales.
  • B
    Euclid.
  • C
    Both A and B.
  • D
    Archimedes.
Answer
  1. Thales.
    Solution:
    Pythagoras (572 BC) was a student of Thales. Pythagoras and his group discovered many geometric properties and developed the theory of geometry to a great extent. This process continued till 300 BC. At that time, Euclid, a teacher of mathematics at Alexandria in Egypt, collected all the known work and arranged it in his famous treatise.
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MCQ 391 Mark
It is known that if a + b = 4 then $\frac{1}{2}$(a + b) = 2. The Euclid’s axiom that illustrates this statement is:
  • A
    VI axiom.
  • B
    V axiom.
  • C
    VII axiom.
  • D
    IV axiom.
Answer
  1. VII axiom.
    Solution:
    Things which are halves of the same things are equal to each other.
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MCQ 401 Mark
Boundaries of surfaces are:
  • A
    Lines.
  • B
    Curves.
  • C
    Polygons.
  • D
    None of these.
Answer
  1. Curves.
    Solution:
    Boundaries of surfaces are curves.
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MCQ 411 Mark
Into how many chapters was the famous treatise, 'The Elements' divided by Euclid?
  • A
    13
  • B
    12
  • C
    11
  • D
    9
Answer
  1. 13
    Solution:
    The famous treatise 'The Elements' was divided into 13 chapters by Euclid.
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MCQ 421 Mark
Euclid divided his famous treatise “The Elements” into:
  • A
    12 chapters.
  • B
    11 chapters.
  • C
    9 chapters.
  • D
    13 chapters.
Answer
  1. 13 chapters.
    Solution:
  • Book 1 contains Euclid's 10 axioms.
  • Book 2 is commonly called the "book of geometric algebra".
  • Book 3 deals with circles and their properties.
  • Book 4 constructs the incircle and circumcircle of a triangle.
  • Book 5 is a treatise on proportions of magnitudes.
  • Book 6 applies proportions to geometry: similar figures.
  • Book 7 deals with elementary number theory.
  • Book 8 deals with proportions in number theory and geometric sequences.
  • Book 9 applies the results of the preceding two books and gives the infinitude of prime numbers.
  • Book 10 attempts to classify incommensurable (in modern language, irrational).
  • Book 11 generalizes the results of books 1-6.
  • Book 12 studies volumes of cones, pyramids, and cylinders.
  • Book 13 constructs the five regular Platonic solids.
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MCQ 451 Mark
If a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than 180∘, then the two straight lines, if produced indefinitely, meet on that side on which the angles taken together are:
  • A
    180º
  • B
    < 180º
  • C
    = 180º
  • D
    None of these
Answer
  1. < 180º
    Solution:
    According to Euclid's fifth postulate, if a straight line crossing two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if extended indefinitely, meet on that side on which are the angles less than the two right angles.
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MCQ 461 Mark
In Ancient India, Altars with combination of shapes like rectangles, triangles and trapeziums were used for:
  • A
    Household rituals.
  • B
    Public worship.
  • C
    Both Public worship and Household rituals.
  • D
    None of these.
Answer
  1. Public worship.
    Solution:
    In ancient India altars whose shapes were combinations of rectangles, triangles and trapeziums were used for public worship.
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MCQ 471 Mark
Write the correct answer in the following:
Euclid divided his famous treatise “The Elements” into:
  • A
    13 chapters.
  • B
    12 chapters.
  • C
    11 chapters.
  • D
    9 chapters.
Answer
  1. 13 chapters.
    Solution:
    Euclid divided his famous treatise 'The Elements' into 13 chapters.
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MCQ 481 Mark
Pythagoras was influenced by:
  • A
    Archimedes.
  • B
    Thales.
  • C
    Euclid.
  • D
    None of these.
Answer
  1. Thales.
    Solution:
    Pythagoras of Samos is one of the most famous names in the history of mathematics and is recognized as the first true mathematician. When Pythagoras was 18, he visited Miletus - an ancient Greek city on the western coast of Anatolia, where he met Thales - the first known Greek philosopher and scientist. By that time Thales was very old and is not believed to have taught Pythagoras a great deal. However, it was this meeting which triggered his interest in the science of mathematics and astronomy.
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MCQ 501 Mark
The edges of a surface are:
  • A
    Points.
  • B
    Curves.
  • C
    Lines.
  • D
    None of these.
Answer
  1. Lines.
    Solution:
    Edge is a line or border at which a surface terminates.
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