Random Interesting Patterns Followed by Square Numbers

Q. Which of the following numbers can never be a perfect square?

1. 6 _ _ 9
2. _ 258
3. 144 _ 0
4. 30 _ 5

Q. $\begin{array}{cc}(Number{)}^2& Value\\ {11}^2& 121\\ {101}^2& 10201\\ {1001}^2& 1002001\\ {100001}^2& 10000200001\\ {10000001}^2& ?\end{array}$
By analyzing the pattern, find the missing number in the table.

1. 100002000001
2. 10000020000001
3. 100000020000001
4. 10000002000001

Q. The area of a square plot is $101\frac{1}{400}{m}^2$. Find the length of one side of the plot.

1. $12\frac{5}{6}m$
2. $12\frac{1}{6}m$
3. $13\frac{2}{5}m$
4. $10\frac{1}{20}m$

Q.

The square whose area is $100m^2$ is divided into 5 rectangles of equal area. If the length of the rectangle is 10 m, then find the breadth.

1. $2m$

2. $\frac{1}{2}m$

3. $4m$

4. $\frac{2}{5}m$

Q.

Prove that there are infinitely many positive integer as such that 2a is a square, 3a is a cube and 5a is a fifth power.

Q.

What is the value of 5.8 + 7.3?

1. 14.1

2. 13.2

3. 13.1

4. 12.1

Q.

$\text{Find the value of}(66666{)}^2.$

1. 445544554455

2. 4444355556

3. 4444655556

4. 222237776

Q.

$\text{Find the value of}(66666{)}^2.$

1. 445544554455

2. 222237776

3. 4444355556

4. 4444655556