List of top Mathematics Questions on Some More Interesting Patterns

The following numbers are obviously not perfect squares. Give reason. 

1. 1057 
2. 23453 
3. 7928 
4. 222222 
5. 64000 
6. 89722 
7. 222000 
8. 505050

Without adding find the sum 

1. \(1 + 3 + 5 + 7 + 9\) 
2. \(1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 \)
3. \(1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23\)

How many numbers lie between squares of the following numbers? 

1. \(12\) and \(13\) 
2.  \(25\) and \(26\) 
3.  \(99\) and \(100\)

Using the given pattern, find the missing numbers. 
\(1^ 2 + 2^2 + 2^2 = 3^2\)
\(2^ 2 + 3^2 + 6^2 = 7^2 \)
\(3^ 2 + 4^2 + 12^2 = 13^2 \)
\(4 ^2 + 5^2 + ....^2 = 21^2 \)
\(5^ 2 +....^2 + 30^2 = 31^2\) 
\(6^ 2 + 7^2 + ....^2 = ....^2\)

Observe the following pattern and supply the missing number. 
\(11^2 = 121\) 
\(101^2 = 10201\) 
\(10101^2 = 102030201\) 
\(1010101^2 = …\) 
\(...^2= 10203040504030201\)

Observe the following pattern and find the missing digits. 
\(11^2\) = \(121\) 
\(101^2\) = \(10201\) 
\(1001^2 = 1002001\) 
\(100001^2 = 1…2…1 \)
\(10000001^2 = …\)

The squares of which of the following would be odd numbers? 

1. 431 
2. 2826 
3. 7779 
4. 82004

What will be the unit digit of the squares of the following numbers? 

1. 81 
2. 272 
3.  799 
4.  3853 
5.  1234 
6.  26387 
7.  52698 
8.  99880 
9.  12796
10.  55555