This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Patterns in Squares”.

1. What are triangular numbers?

a) The numbers whose dot pattern can be arranged in triangles

b) The numbers which form a triangle on adding

c) The numbers which have three digits

d) The numbers which do not give perfect squares on adding

View Answer

Explanation: Triangular numbers are the numbers which when arranged in increasing order forms a shape of triangle, the triangle shown below represents the number 6.

2. _____ is a triangular number.

a) 3

b) 2

c) 5

d) 7

View Answer

Explanation: Triangular numbers are the numbers which when arranged in increasing order forms shape of triangle. Here, 3 is the only triangular number. Hence, 3 is the correct answer and others are incorrect.

3. If we combine two consecutive triangular numbers, we get?

a) Rational Number

b) Whole Number

c) Perfect Square

d) Prime Number

View Answer

Explanation: If we combine two consecutive triangular numbers, we get a square number, like

1 + 3 = 4 = 2

^{2}Hence, we get a

**perfect square**when we add two consecutive triangular numbers. Here options other than Perfect Square are incorrect.

4. There are ______ non-squares numbers in between 5^{2} & 6^{2}.

a) 10

b) 11

c) 12

d) 9

View Answer

Explanation: The squares of the numbers 5 & 6 are 25 & 36 respectively. There are 10 numbers between 25 and 36 (i.e. 26, 27, 28, 29, 30, 31, 32, 33, 34, 35). Therefore, the correct answer would be

**10**and the others would be incorrect.

5. ________ is the general formula to find the number of non-square numbers in between two consecutive squares.

a) n^{2}+2n-1

b) n^{2}-1

c) 2n+1

d) n+1

View Answer

Explanation: If we want to find the general formula for the number of non-square numbers in between two consecutive squares, we assume to the natural numbers to be n & n+1

We square and subtract the smaller from the greater number,

(n+1)

^{2}-n

^{2}=(n

^{2}+2n+1)-n

^{2}=2n+1

6. If we add first n odd numbers, we get ______

a) n

b) n-1

c) n^{2}

d) n^{2}-1

View Answer

Explanation: If we add first n odd numbers we get n

^{2}. For example

1+3+5=9=3

^{2}, here we have added first three odd numbers and we get 3

^{2}.

Hence, n

^{2}would be the correct answer and the other options would be incorrect.

7. What would be the square of 1111?

a) 1234321

b) 12321

c) 121

d) 1

View Answer

Explanation: The squares of all the numbers with only 1 as its digit in all its places have a special pattern.

If we need to find the square of number 11, we can write 121. Similarly, square of number 111 is 12321. Therefore, we have the answer without calculating this huge number.

8. If we add first n numbers, we get ______

a) \(\frac{n (n+1)}{2}\)

b) n-1

c) n^{2}

d) n^{2}-1

View Answer

Explanation: If we add first n numbers we get \(\frac{n (n+1)}{2}\). For example, if we add 1 + 2 + 3 + 4 + 5, we get 15.

Here, we added first 5 numbers. Here, \(\frac{n (n+1)}{2} = \frac{5 (5+1)}{2} \)= 15.

Hence, \(\frac{n (n+1)}{2}\) would be the correct answer and the other options would be incorrect.

9. There are ______ non-squares numbers in between 9^{2} & 10^{2}.

a) 15

b) 11

c) 19

d) 9

View Answer

Explanation: The squares of the numbers 9 & 10 are 81 & 100 respectively. There are 19 numbers between 81 and 100. Therefore, the correct answer would be 19 and the others would be incorrect.

10. _____ is not a triangular number.

a) 7

b) 6

c) 10

d) 3

View Answer

Explanation: Triangular numbers are the numbers which when arranged in increasing order forms shape of triangle. Here, 3, 6, 10 are triangular numbers. In the given options, 7 is not a triangular number.

11. Observe the following pattern and supply the missing numbers.

11^{2}= 1 2 1 101^{2}= 1 0 2 0 1 10101^{2}= 102030201 1010101^{2}= ___________

a) 10101

b) 102030101

c) 1020304030202

d) 1020304030201

View Answer

Explanation: We know that 11

^{2}= 121. In 101, we have a 0 between the two 1. There we need to put 0 between 121 making it 10201. In 10101, we have 010 between the two 1. So, we need to put 010 between 121 making it 102030201. Similarly, for 1010101

^{2}we get 1020304030201.

12. Observe the following pattern and supply the missing numbers.

11^{2}= 1 2 1 101^{2}= 1 0 2 0 1 1001^{2}= 1002001 10001^{2}= ___________

a) 10101

b) 1002001

c) 100020001

d) 1002003002001

View Answer

Explanation: We know that 11

^{2}= 121. In 101, we have a 0 between the two 1. There we need to put 0 between 121 making it 10201. In 1001, we have 00 between the two 1. So, we need to put 00 between 121 making it 1002001. Similarly, for 10001

^{2}we get 100020001.

13. What would be the square of 111?

a) 1234321

b) 12321

c) 121

d) 1

View Answer

Explanation: The squares of all the numbers with only 1 as its digit in all its places have a special pattern.

If we need to find the square of number 11, we can write 121. Similarly, square of number 111 is 12321. Therefore, we have the answer without calculating this huge number.

**Sanfoundry Global Education & Learning Series – Mathematics – Class 8**.

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