Mathematics - Introduction to Euclid's Geometry
Exam Duration: 45 Mins Total Questions : 30
If C is the midpoint of the segment AB, P and Q are midpoints of the segments AC and BC respectively, find BQ.
- (a)
\(1\over2\)AB
- (b)
\(1\over3\)AB
- (c)
\(1\over4\)AB
- (d)
\(1\over5\)AB
If C is the midpoint of the line segment AB, D and E are midpoints of the segments AC and BC respectively, what is the length of AB?
- (a)
2 AD
- (b)
4 BC
- (c)
4 BE
- (d)
2 CD
If AC = PQ and CP= BQ, find the midpoint of the line segment AB
- (a)
P
- (b)
Q
- (c)
C
- (d)
B
Which of the following describe a surface?
- (a)
Length and Breadth
- (b)
Length only
- (c)
Breadth only
- (d)
Length and Height
What are the boundaries of surfaces?
- (a)
Surfaces
- (b)
Angles
- (c)
lines
- (d)
Points
In ancient India, what are the shapes of altars used for house hold rituals?
- (a)
Squares and circles
- (b)
Triangles and rectangles
- (c)
Trapeziums and pyramids
- (d)
Rectangles and squares
Identify the incorrect statement.
- (a)
Only one line can pass through a single point.
- (b)
Only one line can pass through two distinct points
- (c)
A terminated line can be produced indefinitely on both the sides
- (d)
If two circles are equal, their radii are equal.
How many lines can pass through a given point?
- (a)
Two
- (b)
None
- (c)
Only one
- (d)
Infinitely many
What is the number of line segments determined by three collinear points?
- (a)
Two
- (b)
Three
- (c)
Only one
- (d)
Four
To which of the following countries did Euclid belong?
- (a)
Babylonia
- (b)
Egypt
- (c)
Greece
- (d)
India
Which of the following are the three steps from solids to points?
- (a)
Solids - Surfaces - Lines - Points
- (b)
Solids - Lines - Surfaces - Points
- (c)
Lines - Points - Surfaces - Solids
- (d)
Lines - Surfaces - Points - Solids
Which of the following needs a proof?
- (a)
Axiom
- (b)
Theorem
- (c)
Postulate
- (d)
Definition
How many dimensions does a solid has?
- (a)
1
- (b)
2
- (c)
3
- (d)
0
In which of the following forms did Euclid state that all right angles are equal to each other?
- (a)
An axiom
- (b)
A defination
- (c)
A postulate
- (d)
A proof
If a point P lies in between A and B, which of the following is true?
- (a)
AP =\({1\over2}\) AB
- (b)
BP =\({1\over2}\) AB
- (c)
AP + PB = AB
- (d)
AP = BP
Identify the incorrect statement.
- (a)
If a point P lies in between A and B, then AP < AB and BP < AB
- (b)
A line segment has fixed length.
- (c)
One point always determines a unique line.
- (d)
A line segment can be produced indefinitely on either side.
If X, Y, Z are the three points on a line and Y lies between X and Z, which of the following is true?
- (a)
XY+ YZ = XZ.
- (b)
XY + XZ = YZ
- (c)
XZ+YZ= XY
- (d)
\({1\over2}(XY+YZ)=XZ\)
ABCD are the four points on a line.
If AD = BC, which of the following has its length the same as BD?
- (a)
AD
- (b)
BC
- (c)
AC
- (d)
CD
How many common points do two distinct lines in a plane have?
- (a)
Two points
- (b)
Three points
- (c)
One point
- (d)
Four points
Things which are __________of the same things are equal to one another
- (a)
Parallel
- (b)
Not equal
- (c)
Halves
- (d)
Triple
If a point R is the mid-point of a line MN, which axiom states that MR = NR =\(MN\over2\)
- (a)
Axiom 4
- (b)
Axiom 6
- (c)
Axiom 5
- (d)
Axiom 7
If a point A lies in between Band C, which of the following is true?
- (a)
BC =\(1\over2\)AC
- (b)
BC =\(1\over2\)AB
- (c)
AC = BC
- (d)
AB + AC = BC
Which of the following is true about two distinct lines?
- (a)
Always intersect
- (b)
Always either intersect or are parallel
- (c)
Always have two common points.
- (d)
Always parallel
Euclid's Postulate 1 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
Which of the following options has one fixed end point and can be extended in the other direction indefinitely
- (a)
A ray
- (b)
A line
- (c)
A line segment
- (d)
All of these
Which of the following is a false statement?
- (a)
An infinite number of lines through a given point
- (b)
A unique line can be drawn to pass through two given points
- (c)
Ray \(\overline { AB } =Ray\quad \overline { BA } \)
- (d)
A ray has one end point
According to Euclid's axioms, the _______ is greater than the part.
- (a)
half
- (b)
large
- (c)
whole
- (d)
none of these
Which of the following is not a Euclid's axiom?
- (a)
The whole is greater than the part
- (b)
thing which are double of the same things are equal to one another
- (c)
THings which are halves of the same things are equal to one another.
- (d)
If two things are equal, then their sum is equal to \(\frac { 1 }{ 3 } \) of the one thing.
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 __________ two right angles.
- (a)
equal to
- (b)
more than
- (c)
Less than
- (d)
Can't be determined
Find the number of dimension(s) a line has
- (a)
0
- (b)
1
- (c)
2
- (d)
3