Page 32 - Ganit Kaushal

Chapter Test

I. Multiple Choice Questions (MCQs)

1. Which of the following numbers is a member of a square pattern as well as a triangular pattern?
(a) 16 (b) 25 (c) 36 (d) 4
2. Adding up the centred hexagonal numbers gives a sequence of
(a) squares (b) cubes (c) triangles (d) powers of 2
3. When we multiply a triangular number pattern by 6 and add 1, which of the following sequences do
we get?
(a) Squares (b) Cubes
(c) Triangular numbers (d) Centred hexagonal numbers
4. Adding up the sequence of counting numbers, we get a sequence of
(a) squares (b) cubes (c) triangular numbers (d) hexagonal numbers
5. The sum of two consecutive triangular numbers always gives
(a) squares (b) cubes (c) triangular numbers (d) hexagonal numbers
II. Fill in the blanks.

1. The number of edges in the K graph of the shape sequence of complete graphs is _____.
6
2. The sequence made by counting the small squares in the shape sequence of stacked squares is the
sequence of _____ numbers.

3. The sequence made by counting the small triangles in the shape sequence of stacked triangles is the
sequence of _____ numbers.
4. The 7th term of the sequence of hexagonal numbers is _____.

III. State whether the following statements are True (T) or False (F).
1. Virahānka numbers are a sequence of numbers where each term is the sum of the two preceding ones.
2. Adding up the sequence of odd numbers gives the sequence of triangular numbers.
3. Adding up and down the sequence of counting numbers gives the sequence of square numbers.
4. The Indian mathematician Virahānka conceptualised the sequence of Virahānka numbers in about the
6th century.
5. The sum of the first hundred terms of the sequence of odd numbers gives the cube of 10.
IV. Solve the following questions.

1. Why are 1, 3, 6, 10, 15, …… called a sequence of triangular numbers? Explain it in your own words
with the help of a pictorial representation.
2. Write a sequence of numbers that starts with 1. Now, to get all the next terms, add a continuously
increasing multiple of six to the previous term to get the next term. What sequence do you get? What
will happen if you start adding this sequence up? Explain in your own words.
3. How many small triangles are there in each figure of the shape sequence of stacked triangles? Which
number sequence does this form? Explain in your own words.

4. Determine the sum of the four numbers as given below:
(a) Successor of 32 (b) Predecessor of 40
(c) Predecessor of the predecessor of 56 (d) Successor of the successor of 67

30