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Maths M.C.Q

Introduction to Euclid Geometry · Bihar Board (BSEB) STD 9 (BSEB - English Medium). 188 questions.

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M.C.Q

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MCQ 11 Mark
The boundaries of the solids are:
  • A
    Curves.
  • B
    Points.
  • ✓
    Surfaces.
  • D
    Lines.
Answer
Correct option: C.
Surfaces.
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 21 Mark
The basic facts which are taken for granted, without proof, are called:
  • A
    Theorems.
  • B
    Propositions.
  • C
    Lemmas.
  • ✓
    Axioms.
Answer
Correct option: D.
Axioms.
An axiom is a proposition regarded as self-evidently true without proof​​​​​​.
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MCQ 31 Mark
A point has:
  • A
    One part
  • B
    Two parts
  • C
    More than two parts
  • ✓
    No parts
Answer
Correct option: D.
No parts
A point has no length and no breadth.
A point is that which has no part.
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MCQ 41 Mark
The number of end points a ray has:
  • A
    $0$
  • B
    $2$
  • ✓
    $1$
  • D
    None of these
Answer
Correct option: C.
$1$
A ray starts at a given point and goes off in a certain direction to infinity. The point where the ray starts is called the endpoint.
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MCQ 51 Mark
Write the correct answer in the following:
It is known that if $x + y = 10$ then $x + y + z = 10 + z$. The Euclid’s axiom that illustrates this statement is:
  • A
    First Axiom.
  • ✓
    Second Axiom.
  • C
    Third Axiom.
  • D
    Fourth Axiom.
Answer
Correct option: B.
Second Axiom.
The Euclid’s axiom that illustrates the given statement is second axiom, according to which. If equals are added to equals, the wholes are equal.
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MCQ 61 Mark
How many points can be common in two distinct straight lines?
  • ✓
    One
  • B
    Two
  • C
    Three
  • D
    None
Answer
Correct option: A.
One
One
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MCQ 71 Mark
Which of the following is a solid?
  • A
    Rectangle.
  • B
    Circle.
  • ✓
    Cylinder.
  • D
    Square.
Answer
Correct option: C.
Cylinder.
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 81 Mark
Write the correct answer in the following: The number of dimensions, a surface has:
  • A
    $1$
  • ✓
    $2$
  • C
    $3$
  • D
    $0$
Answer
Correct option: B.
$2$
Boundaries of a solid are called surfaces. A surface (plane) has only length and breadth. So, it has two dimensions.
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MCQ 91 Mark
The side faces of a pyramid are:
  • ✓
    Triangles.
  • B
    Squares.
  • C
    Trapeziums.
  • D
    Polygons.
Answer
Correct option: A.
Triangles.
The side faces of a pyramid are triangles.
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MCQ 101 Mark
If two line segments are equal then they are called:
  • A
    Line segment
  • B
    Ray
  • ✓
    Congruent
  • D
    None of these
Answer
Correct option: C.
Congruent
If two line segments are equal then they are called congruent segments.
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MCQ 111 Mark
Which of the following statements are true?
  • A
    Only one line can pass through a single point.
  • B
    There is an infinite number of lines that pass through two distinct points.
  • ✓
    A terminated line can be produced indefinitely on both sides.
  • D
    If two circles are equal, then their radii are unequal.
Answer
Correct option: C.
A terminated line can be produced indefinitely on both sides.
A terminated line can be produced indefinitely on both sides.
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MCQ 121 Mark
The number of line segments determined by three non-collinear points is:
  • A
    $0$
  • ✓
    $3$
  • C
    $1$
  • D
    $2$
Answer
Correct option: B.
$3$
You need two points to draw a line segment. If the points $A, B$ and are non-collinear, we can draw the lines: $A B, A C$, $B A, B C, C A, C B$. Now, line $A B$ is the same as line $B A$, same for lines $A C$ and $C A$ and $B C$ and $C B$. So, the lines are $A B, B C$, and $AC 3$ lines only.
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MCQ 131 Mark
In this figure, if $AC = BD$, then:
  • A
    $AB \neq CD$
  • B
    $BC = CD$
  • C
    $AB = BC$
  • ✓
    $AB = CD$
Answer
Correct option: D.
$AB = CD$
We have, $AC = BD$
$\Rightarrow AB + BC = BC + CD$
$\Rightarrow AB = CD.$
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MCQ 141 Mark
A $.......$ is an exact location in space.
  • A
    Line.
  • B
    Solid.
  • C
    Surface.
  • ✓
    Point.
Answer
Correct option: D.
Point.
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 151 Mark
Which of the following is not a solid?
  • A
    Cube.
  • B
    Cone.
  • C
    Cylinder.
  • ✓
    Circle.
Answer
Correct option: D.
Circle.
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 pyramid is a solid figure, whose base is:
  • A
    Only a triangle.
  • B
    Only a square.
  • C
    Only a rectangle.
  • ✓
    Any polygon.
Answer
Correct option: D.
Any polygon.
A pyramid is a solid figure, whose base is any polygon.
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MCQ 171 Mark
Which of the following is not a rectilinear figure?
  • ✓
    Circle.
  • B
    Square.
  • C
    Rectangle.
  • D
    Rhombus.
Answer
Correct option: A.
Circle.
A rectilinear figure is a figure all of whose edges meet at right angles.
A circle has no edge.
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MCQ 181 Mark
Three or more lines are called concurrent lines if they pass through $.........$ point.
  • A
    Two
  • B
    Three
  • ✓
    Same
  • D
    None of these
Answer
Correct option: C.
Same
Same
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MCQ 191 Mark
Euclid’s Postulate $1$ is:
  • ✓
    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
Correct option: A.
A straight line may be drawn from any point to any other point.
A straight line may be drawn from any point to any other point.
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MCQ 201 Mark
Two intersecting lines cannot be parallel to the same line is stated in the form of:
  • A
    A theorem.
  • ✓
    A postulate.
  • C
    A definition.
  • D
    None of these.
Answer
Correct option: B.
A postulate.
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 221 Mark
The number of lines passing through one point.
  • ✓
    Infinite
  • B
    $1$
  • C
    $2$
  • D
    $3$
Answer
Correct option: A.
Infinite
Infinite number of lines can pass through a single point.
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MCQ 231 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.
  • ✓
    If two circles are equal, then their radii are equal.
  • D
    A line has a definite length.
Answer
Correct option: C.
If two circles are equal, then their radii are equal.
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 241 Mark
A surface of shape has:
  • A
    Length, breadth and thickness
  • ✓
    Length and breadth only
  • C
    Length and thickness only
  • D
    Breadth and thickness only
Answer
Correct option: B.
Length and breadth only
Length and breadth only
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MCQ 251 Mark
Write the correct answer in the following: Greek’s emphasised on:
  • A
    Inductive reasoning.
  • ✓
    Deductive reasoning.
  • C
    Both $A$ and $B.$
  • D
    Practical use of geometry.
Answer
Correct option: B.
Deductive reasoning.
The Greeks were interested in establishing the truth of the statements they discovered using deductive reasoning. A Greek mathematician, Thales is credited with giving the first known proof.
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MCQ 261 Mark
“Lines are parallel if they do not intersect” is stated in the form of:
  • A
    A proof.
  • B
    A postulate.
  • ✓
    A definition.
  • D
    An axiom.
Answer
Correct option: C.
A definition.
Euclid gave the definition of parallel lines in Book I, Definition $23$ just before the five postulates.
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MCQ 271 Mark
The Sri yantra consists of $.........$ interwoven isosceles triangles.
  • A
    Three.
  • B
    One.
  • C
    Six.
  • ✓
    Nine.
Answer
Correct option: D.
Nine.
The Sri Yantra $('$great object$')$ belongs to a class of devices used in meditation, mainly by those belonging to the Hindu tantric tradition.
The diagram consists of nine interwoven isosceles triangles four points upwards, representing Sakti, the primordial female essence of dynamic energy, and five$-$point downwards, representing Siva, the primordial male essence of static wisdom The triangles are arranged in such a way that they produce $43$ subsidiary triangles, at the center of the smallest of which there is a big dot known as the Bindu.
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MCQ 281 Mark
Which of the following needs a proof?
  • ✓
    Theorem.
  • B
    Definition.
  • C
    Postulate.
  • D
    Axiom.
Answer
Correct option: A.
Theorem.
Theorem $-$ a mathematical statement that is proved using rigorous mathematical reasoning.
 In a mathematical paper, the term theorem is often reserved for the most important results.
Axiom/ Postulate $-$ a statement that is assumed to be true without proof.
These are the basic building blocks from which all theorems are proved $($Euclid’s five postulates, Zermelo$-$Fraenkel axioms, Peano axioms$)$.
Definition $-$ a precise and unambiguous description of the meaning of a mathematical term.
It characterizes the meaning of a word by giving all the properties and only those properties that must be true.
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MCQ 291 Mark
Write the correct answer in the following: ‘Lines are parallel if they do not intersect’ is stated in the form of:
  • A
    An axiom.
  • ✓
    A definition.
  • C
    A postulate.
  • D
    A proof.
Answer
Correct option: B.
A definition.
$'$Lines are parallel, if they do not intersect$’$ is the definition of parallel lines.
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MCQ 301 Mark
Write the correct answer in the following: The total number of propositions in the Elements are:
  • ✓
    $465$
  • B
    $460$
  • C
    $13$
  • D
    $55$
Answer
Correct option: A.
$465$
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 311 Mark
Two lines are said to be ________ if they intersect at right angles.
  • A
    Concurrent.
  • B
    Parallel.
  • ✓
    Perpendicular.
  • D
    None of these.
Answer
Correct option: C.
Perpendicular.
A line is perpendicular to another if it meets or crosses it at right angles $(90^\circ ).$
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MCQ 321 Mark
It is known that if $a + b = 4$ then $a + b - c = 4 - c$. The Euclid’s axiom that illustrates this statement is:
  • ✓
    $III$ axiom.
  • B
    $II$ axiom.
  • C
    $I$ axiom.
  • D
    $IV$ axiom.
Answer
Correct option: A.
$III$ axiom.
If equals be subtracted from equals, the remainder are equal.
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MCQ 331 Mark
The things which are double of same things are:
  • A
    Halves of same thing
  • B
    Double of the same thing
  • ✓
    Equal
  • D
    Unequal
Answer
Correct option: C.
Equal
Equal
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MCQ 341 Mark
The number of lines passing through two distinct points.
  • A
    $4$
  • ✓
    $1$ 
  • C
    $3$
  • D
    $2$
Answer
Correct option: B.
$1$ 
Only one line can pass through two given distinct points.
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MCQ 351 Mark
Write the correct answer in the following: The three steps from solids to points are:
  • ✓
    Solids $-$ surfaces $-$ lines $-$ points.
  • B
    Solids $-$ lines $-$ surfaces $-$ points.
  • C
    Lines $-$ points $-$ surfaces $-$ solids.
  • D
    Lines $-$ surfaces $-$ points $-$ solids.
Answer
Correct option: A.
Solids $-$ surfaces $-$ lines $-$ points.
The three steps from solids to points are solids$-$surface$-$lines$-$points.
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MCQ 361 Mark
Two lines are said to be parallel if:
  • A
    They intersect each other at any point.
  • ✓
    They do not intersect each other at any point.
  • C
    The angle between these lines is 90 degree.
  • D
    None of these
Answer
Correct option: B.
They do not intersect each other at any point.
Two lines are said to be parallel if they do not intersect each other at any point.The angle between these lines is $180$ degree.
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MCQ 371 Mark
In ancient India, the shapes of altars used for household rituals were:
  • A
    Squares and rectangles.
  • ✓
    Squares and circles.
  • C
    Triangles and rectangles.
  • D
    Trapeziums and pyramids.
Answer
Correct option: B.
Squares and circles.
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 381 Mark
The total number of propositions in the Euclid’s Elements is:
  • ✓
    $465$
  • B
    $13$
  • C
    $460$
  • D
    $32$
Answer
Correct option: A.
$465$
Euclid's Elements is a mathematical and geometric treatise consisting of $13$ books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt circa $300 \ BC$. It is a collection of definitions, postulates (axioms), propositions (theorems and constructions), and mathematical proofs of the propositions. There are $131$ definitions, $465 $propositions, $5$ Postulates and $5$ common notions in Euclid's Elements.
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MCQ 391 Mark
It is known that if $x + y = 10$ then $x + y + z = 10 + z$. Euclid’s axiom that illustrates this statement is:
  • A
    First Axiom
  • ✓
    Second Axiom
  • C
    Third axiom
  • D
    Fourth Axiom
Answer
Correct option: B.
Second Axiom
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 401 Mark
Write the correct answer in the following: Boundaries of surfaces are:
  • A
    Surfaces.
  • ✓
    Curves.
  • C
    Lines.
  • D
    Points.
Answer
Correct option: B.
Curves.
The boundaries of surfaces are curves.
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MCQ 411 Mark
Write the correct answer in the following: The number of interwoven isosceles triangles in Sriyantra $($in the Atharvaveda$)$ is:
  • A
    Seven.
  • B
    Eight.
  • ✓
    Nine.
  • D
    Eleven.
Answer
Correct option: C.
Nine.
The number of interwoven isosceles triangle in Sriyantra $($in the Atharva Veda$)$ is nine.
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MCQ 421 Mark
Three or more lines intersecting at the same point are said to be:
  • A
    Intersecting.
  • ✓
    Concurrent.
  • C
    Collinear.
  • D
    None of these.
Answer
Correct option: B.
Concurrent.
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 431 Mark
Euclid’s fifth postulate implies the existence of:
  • A
    Perpendicular lines.
  • ✓
    Parallel lines.
  • C
    Intersecting lines.
  • D
    None of these.
Answer
Correct option: B.
Parallel lines.
According to Euclid's fifth postulate, if a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles, then the two straight lines, if produced indefinitely, meet on that side on which the sum of angles is less than two right angles.
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MCQ 441 Mark
Write the correct answer in the following:
Thales belongs to the country:
  • A
    Babylonia.
  • B
    Egypt.
  • ✓
    Greece.
  • D
    Rome.
Answer
Correct option: C.
Greece.
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 451 Mark
If $p, q$ and $t$ are three straight lines such that $p \| q$ and $p \| t$, then.
  • ✓
    $q \| t$
  • B
    $q = t$
  • C
    $q \perp t$
  • D
    None of these
Answer
Correct option: A.
$q \| t$
When two lines are parallel to the same line, they are parallel to each other.
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MCQ 461 Mark
The first known proof that ‘the circle is bisected by its diameter’ was given by:
  • A
    Pythagoras
  • ✓
    Thales
  • C
    Euclid
  • D
    Hypatia
Answer
Correct option: B.
Thales
Thales
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MCQ 471 Mark
Euclid stated that if equals are subtracted from equals, the remainders are equal in the form of:
  • A
    A definition.
  • B
    A theorem.
  • ✓
    An axiom.
  • D
    None of these.
Answer
Correct option: C.
An axiom.
This is Euclid's third axiom stating subtraction of equals. An algebraic version of Euclid’s second axiom would read “if $x = y$, and if $a = b,$ then $x - a = y - b.”$
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MCQ 481 Mark
Which of the following needs a proof?
  • A
    Axiom.
  • B
    Postulate.
  • C
    Definition.
  • ✓
    Theorem.
Answer
Correct option: D.
Theorem.
A statement that requires a proof is called a theorem.
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MCQ 491 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.
  • ✓
    The floor and the ceiling of a room are parallel planes.
  • D
    Two adjacent walls of a room are parallel planes.
Answer
Correct option: C.
The floor and the ceiling of a room are parallel planes.
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 501 Mark
The number of dimension, a point has:
  • A
    $2$
  • B
    $3$
  • C
    $1$
  • ✓
    $0$
Answer
Correct option: D.
$0$
Because point has no part.
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