Choose the correct alternative to complete the series: $a...abbb...cccd....ddccc....bb...ba$

Choose the correct alternative to fill in the blanks in the series: $aab....ab...cabcca....bcab....c$

Fill in the blank space for the given series with the correct alternative.
$2, 6, 12, 20, 30, 42, 56, (\ldots)$

In the arrangement $P, 2, 6, M, 9, K, S, 4, V, 7$,the positions of the $1^{st}$ and the $6^{th}$ elements are interchanged,those of the $2^{nd}$ and the $7^{th}$ are interchanged,and so on. Then,which of the following will be the $4^{th}$ element from the left end in the new arrangement?

Fill in the blank space for the given series with the correct alternative.
$2, 5, 9, (\ldots), 20, 27$

How many such $4$s are there in the following number series,each of which is immediately followed by $5$ but not immediately preceded by $3$?
$5, 4, 4, 3, 3, 4, 5, 4, 5, 5, 3, 4, 4, 3, 4, 5, 4, 3, 3, 5, 4, 5, 4, 3, 5, 4, 4, 3, 5, 4$