What will come in place of question mark (?) in the following number series?
31, 32, 36, ?, 61, 86

The correct option is 45.

To find the missing number in the given series, let us analyze the pattern of differences between consecutive terms:

Given series: 31, 32, 36, ?, 61, 86

Let us calculate the difference between adjacent terms:

$32-31=1$

$36-32=4$

Notice that the differences are perfect squares of consecutive integers:

$1=1^2$

$4=2^2$

Following this pattern, the next difference between 36 and the missing number (?) should be $3^2=9$.

Therefore, the missing number is:

$36+9=45$

We can verify the rest of the series with the subsequent perfect squares:

Next difference ($4^2=16$):

$45+16=61$

Following difference ($5^2=25$):

$61+25=86$

Since all terms match perfectly, the missing number replacing the question mark (?) is 45.