Consider the following matrix:

3	8	10	2	?	1
6	56	90	2	20	0

What is the missing number at ‘?’ in the matrix ?

The correct option is 5.

To find the missing number, we can analyze the relationship between the numbers in the first row and the corresponding numbers in the second row for each column.

Let the number in the first row be represented by $x$ and the number in the second row directly below it be represented by $y$.
By examining each column, we can see a clear mathematical pattern where the number in the second row is obtained by multiplying the number in the first row by the number that is one less than itself. That is:

$y=x\times (x-1)$

Let us verify this relationship for the known columns in the matrix:

First Column:
Here, $x=3$ and $y=6$.
Applying the pattern:
$3\times (3-1)=3\times 2=6$
This matches the value in the second row.

Second Column:
Here, $x=8$ and $y=56$.
Applying the pattern:
$8\times (8-1)=8\times 7=56$
This matches the value in the second row.

Third Column:
Here, $x=10$ and $y=90$.
Applying the pattern:
$10\times (10-1)=10\times 9=90$
This matches the value in the second row.

Fourth Column:
Here, $x=2$ and $y=2$.
Applying the pattern:
$2\times (2-1)=2\times 1=2$
This matches the value in the second row.

Sixth Column:
Here, $x=1$ and $y=0$.
Applying the pattern:
$1\times (1-1)=1\times 0=0$
This matches the value in the second row.

Fifth Column (with the missing number):
Let the missing number in the first row be $x$. The corresponding number in the second row is $20$.
Following the same relationship:
$x\times (x-1)=20$
We need to find a number which, when multiplied by its predecessor, equals $20$. Since $5\times 4=20$, we have:
$x=5$
Therefore, the missing number at '?' is indeed 5.