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

1. What kind of figure does the number 15 show in triangular representation?

a) Triangular form with base 5

b) Triangular form with base 4

c) Triangular form with base 3

d) Triangular form with peak 1

View Answer

Explanation: Triangular numbers are the numbers which form a triangle when arranged in increasing form. When the number 15 is arranged in increasing form the base of the triangle has 5 dots, which goes on decreasing and reaches the peak upto 1.

2. When we add fourth and fifth triangular number we get ______

a) 5^{2}

b) 6^{2}

c) 25^{2}

d) 25^{3}

View Answer

Explanation: The fourth and fifth triangular numbers are 10 & 15.

10 + 15 = 25 = 5

^{2}. Therefore 5

^{2}is the correct answer and the other options are incorrect. The options should be read carefully as the options are very close.

3. There are _____ non-square numbers between 65^{2} & 66^{2}.

a) 130

b) 65

c) 131

d) 129

View Answer

Explanation: In these types of questions we can use the shortcut in order to reach the answer quickly. We can use the formula (2n+1). When we use this formula we consider one of the numbers as n and the hence the second number is(n+1). Here n=65.

Therefore when we substitute n=65 in the formula we get,

[2×(65)+1]=131.

4. In some cases, there can be less than two non-square numbers between two square numbers.

a) True

b) False

View Answer

Explanation: There are two cases where there are less than two non-square numbers between two square numbers, the cases are as follows.

Case 1:- 0

^{2}& 1

^{2}Here there is not a single number between squares.

Case 2:- 1

^{2}& 2

^{2}Here there are two numbers between the squares.

Hence the given statement is true and cannot be false.

5. We get the square of _____ number if we add first 11 odd numbers.

a) 11

b) 12

c) 5

d) 13

View Answer

Explanation: There is an interesting pattern in squares, when we add first n odd numbers we get n

^{2}. So here when we add the first eleven odd numbers, we get 11

^{2}. Hence the correct answer would be 11

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

6. On subtracting first 25 odd numbers from first 30 odd numbers we get _____

a) 5^{2}

b) 375

c) 5

d) 275

View Answer

Explanation: If we add the first 25 odd numbers, we get 625 (i.e.25

^{2}) and when we add first 30 odd numbers, we get 900 (i.e.30

^{2}). When we calculate the difference between the two, we get 275. Hence 275 is the correct answer and the others are incorrect.

7. A square is formed by sum of two _____________

a) Natural numbers

b) Consecutive Natural numbers

c) Alternate Natural numbers

d) Consecutive Whole numbers

View Answer

Explanation: When we add two consecutive natural numbers, we get a square (This happens in a few cases and not all cases). For example: 3

^{2}=4+5=9.

8. Which is the lower consecutive natural number forming the square 13?

a) 85

b) 84

c) 83

d) 82

View Answer

Explanation: The square of number 13 is formed by two consecutive natural numbers and they are 84 & 85. If we need to find the lower number (i.e.84 in this case) we can calculate like this, \(\frac{13^2-1}{2}=\frac{169-1}{2}=\frac{168}{2}\)=84.

9. (a-1)×(a+1)=_______

a) a^{2}-1

b) a^{2}+1

c) a^{2}

d) a^{2}+2

View Answer

Explanation: We have (a-1)×(a+1). Opening the brackets, we get,

(a-1)×(a+1)=(a

^{2}+a-a-1)=(a

^{2}-1). Hence, we conclude this (a-1)×(a+1) to be the correct answer.

10. What would be the square of 11111?

a) 123454321

b) 1234321

c) 12321

d) 121

View Answer

Explanation: The numbers which have 1 in all the digits show a beautiful pattern.

For example: 11

^{2}=121….111

^{2}=12321 and this goes on. This can be very helpful in finding squares.

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

To practice all areas of Mathematics, __ here is complete set of 1000+ Multiple Choice Questions and Answers__.

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