Tag: maths

Questions Related to maths

Name the technique used in the solution of the problems below :

Question: Show that the following statement is false: If n is an odd integer, then n is prime.

Solution: The given statement is in the form “if p then q” we have to show that this is false, If p then ~q.


If n= 99 is odd integer which is not a prime number. Thus, we conclude that the given statement is false.

validating statements proofs in mathematics mathematical reasoning maths

  1. Counter example

  2. Contrapositive method

  3. Direct method

  4. By Contradiction

Show answer
Correct Option: A

The number of independent measurement required to construct a triangle is -

maths construction circumscribing and inscribing a circle on a regular hexagon constructions related to a circle construction of polygons construction of tangent to a circle construction of tangents construction of line segment and circle of given radius construction related to lines

  1. $3$

  2. $4$

  3. $6$

  4. $2$

Show answer
Correct Option: A
Explanation:

Ans- Three measurements are necessarily required to construct a triangle.

 Whether it can be measurements of all three sides,or all three angles or both

The triangle formed by AB = 3 cm BC = 5 cm AC = 9 cm is__

maths construction circumscribing and inscribing a circle on a regular hexagon constructions related to a circle construction of polygons construction of tangent to a circle construction of tangents construction of line segment and circle of given radius construction related to lines

  1. An equilateral triangle

  2. An isosceles triangle

  3. A scalene triangle

  4. None of these

Show answer
Correct Option: C
Explanation:
Given,  
In $\Delta ABC$  
AB=3cm, BC=5cm and AC=9cm.
Since all sides of triangle ABC are different. So $\Delta$ ABC is a Scalene triangle.

When constructing an inscribed regular hexagon, how will you choose the arc measurement?

maths construction circumscribing and inscribing a circle on a regular hexagon constructions related to a circle construction of polygons construction of tangent to a circle construction of tangents construction of line segment and circle of given radius construction related to lines

  1. radius of the circle

  2. diameter of the circle

  3. chord of the circle

  4. circumference of the circle

Show answer
Correct Option: A
Explanation:

When constructing an inscribed regular hexagon in a circle, we choose radius of the circle as a arc measurement.

The measure of maximum possible exterior angle in a regular polygon is 

maths construction circumscribing and inscribing a circle on a regular hexagon constructions related to a circle construction of polygons construction of tangent to a circle construction of tangents construction of line segment and circle of given radius construction related to lines

  1. $70^o$

  2. $60^o$

  3. $90^o$

  4. $120^o$

Show answer
Correct Option: D
Explanation:
Exterior angle of regular polygon = 180-interior angle
exterior angle is maximum when interior angle is minimum.
And we have minimum interior angle for regular triangle that is 60 degree..
So maximum exterior angle will be 180-60=120
So correct answer is Option D

To construct a quadrilateral minimum of its _________ elements are required.

maths construction circumscribing and inscribing a circle on a regular hexagon constructions related to a circle construction of polygons construction of tangent to a circle construction of tangents construction of line segment and circle of given radius construction related to lines

  1. $3$

  2. $4$

  3. $5$

  4. $2$

Show answer
Correct Option: C
Explanation:

To construct a unique quadrilateral, we will be need a minimum of $5$ dimensions.

If we have five dimensions, we can draw a side first then mark angle on both ends then we can construct a quadrilateral uniquely.
Or if we have three sides and two included angles then also we can construct a unique quadrilateral.
Unless we are constructing any one of the special quadrilaterals.

How many equal parts you will cut the circle to draw inscribing hexagon?

maths construction circumscribing and inscribing a circle on a regular hexagon constructions related to a circle construction of polygons construction of tangent to a circle construction of tangents construction of line segment and circle of given radius construction related to lines

  1. $4$

  2. $5$

  3. $6$

  4. $7$

Show answer
Correct Option: C
Explanation:

Hexagon is a $6$-sided polygon.
So we will cut the circle into $6$ equal parts.

Which tool will you use for cutting a circle into 6 equal parts?

maths construction circumscribing and inscribing a circle on a regular hexagon constructions related to a circle construction of polygons construction of tangent to a circle construction of tangents construction of line segment and circle of given radius construction related to lines

  1. compass

  2. ruler

  3. protector

  4. divider

Show answer
Correct Option: A
Explanation:

We will use compass tool for cutting a circle into $6$ equal parts.

While constructing a circle circumscribing and inscribing a regular hexagon, identify the statement true for the construction?

maths construction circumscribing and inscribing a circle on a regular hexagon constructions related to a circle construction of polygons construction of tangent to a circle construction of tangents construction of line segment and circle of given radius construction related to lines

  1. circle outside and inside hexagon

  2. only hexagon is constructed

  3. only circle is drawn

  4. outside hexagon and inside circle

Show answer
Correct Option: A
Explanation:

While constructing a circle circumscribing and inscribing a regular hexagon, the statement true for the construction is circle outside and inside hexagon.

State true or false:
A quadrilateral is uniquely determined if any four of its elements are known.

maths construction circumscribing and inscribing a circle on a regular hexagon constructions related to a circle construction of polygons construction of tangent to a circle construction of tangents construction of line segment and circle of given radius construction related to lines

  1. True

  2. False

Show answer
Correct Option: B
Explanation:

Above statement is false.

To construct a unique quadrilateral, we will be need a minimum of 5 dimensions.
If we have five dimensions, we can draw a side first then mark angle on both ends then we can construct a quadrilateral uniquely.

Or if we have three sides and two included angles then also we can construct a unique quadrilateral.
Unless we are constructing any one of the special quadrilaterals.