Given that ;

$1^2+2^2=\frac{2\times 3\times 5}{6}, 1^2+2^2+3^2=\frac{3\times 4\times 7}{6}, 1^2+2^2+3^2+4^2=\frac{4\times 5\times 9}{6} \mathrm{etc}$

Using the above pattern, determine ${\left(10\right)}^2+{\left(11\right)}^2+{\left(12\right)}^2+{\left(13\right)}^2+.........+{\left(50\right)}^2$

In the question given below, the numbers in the figures are related. Identify their relationships and find the missing numbers in the given figures.

Which number will replace the question mark?

In the question given below, the numbers in the figures are related. Identify their relationships and find the missing numbers in the given figures.

In the question given below, the numbers in the figures are related. Identify their relationships and find the missing numbers in the given figures.

Select the combination of letters that when sequentially placed in the blanks of the given series will complete the series.

$\mathrm{l} \mathrm{\_} \mathrm{chtlgc} \mathrm{\_} \mathrm{tlg} \mathrm{\_} \mathrm{ht} \mathrm{\_} \mathrm{gc} \mathrm{\_} \mathrm{tlgch} \mathrm{\_}$

If, in a two-digit number, the digit at unit place is $x$ and the digit at tens place is $4$, then the two-digit number is _____.

Which number will replace the question mark?

Consider a three-digit number with the following properties:

I. If its digits in units place and tens place are interchanged, the number increases by $36$
II. If its digits in units place and hundreds place are interchanged, the number decreases by $198$ .

Now, suppose that the digits in tens place and hundreds place are interchanged. Then, the number

Express the square number as the sum of odd numbers :

$36=$

Express the square number as the sum of odd numbers :

$49=$

Express the square number as the sum of odd numbers :

$100=$

Evaluate $(38{)}^2–(37{)}^2$.