MATHS M.C.Q

1. Triangles.

Solution:
The side faces of a pyramid are triangles.

4. Any polygon.

Solution:
A pyramid is a solid figure, whose base is any polygon.

3. 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.

2. 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.

4. Theorem.

Solution:
A statement that requires a proof is called a theorem.

3. 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.

2. 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.

3. Point A, C and B are collinear.

Solution:
If direction ratios of three vectors a, b, c are proportional then they are collinear.

3. Surfaces.

Solution:
Boundaries of solids are surfaces.

4. 1

Solution:
The number of planes passing through three non-collinear points is 1.

4. Universal truths in all branches of mathematics.

Solution:
Axioms are assumed as universal truths in all branches of mathematics because they are taken for granted, without proof.

2. 4 : 2 : 1

Solution:
In Indus Valley Civilization (about 300 BC) the bricks used for construction work were having dimensions in the ratio is 4 : 2 : 1.

1. 13

Solution:
The famous treatise 'The Elements' was divided into 13 chapters by Euclid.

2. Curves.

Solution:
Boundaries of surfaces are curves.

1. Frist axiom.

Solution:
Euclid's first axiom states that 'Things which are equal to the same thing are equal to one another'.
That is,
A's age = B's age and C's age = B' age
⇒ A's age = C's age 

2. 2

Solution:
A surface has 2 dimensions.

2. Greece.

Solution:
Euclid belongs to the country, Greece.

3. 3

Solution:
A solid has 3 dimensions.

2. Thales.

Solution:
Pythagoras was a student of Thales.

1. 0

Solution:
A point is an exact location. A fine dot represents a point. So, a point has 0 dimensions.

3. Greece.

Solution:
Thales belongs to the country, Greece.

3. Nine.

Solution:
The Sriyantra consists of nine interwoven isosceles triangles.

2. Public rituals.

Solution:
In ancient India, altars with combination of shapes like rectangles, triangles and trapeziums were used for public rituals.

2. Second.

Solution:
Euclid's second axiom states that 'If equals are added to equals, the wholes are equal'.
Hence, when x + y = 15, then x + y + z = 15 + z.

1. A definition.

Solution:
Lines are parallel if they do not intersect' is started in the form of a definition.