Random Puzzles 

Workings

Hint
The 8-letter word begins with the letter G.

Answer
Generous.
lend + ge = le + ge + nd = legend

liar + ne = li + ne + ar = linear

pale + ro = pa + ro + le = parole

coin + us = co + us + in = cousin

Workings

Hint
Another example, PEN is a complete word because:
   -en = ten
   p-n = pin
   pe- = pea

Answer
Three of the words are not complete: flew, rook, lamp.

Reasoning
The remaining 7 words can be changed as follows:
team:  -eam = beam
 t-am = tram
 te-m = term
 tea- = tear

cost:  -ost = host
 c-st = cast
 co-t = coat
 cos- = cosy

flew:  -lew = blew
 f-ew = ---- X
 fl-w = flow
 fle- = flex

ward:  -ard = card
 w-rd = word
 wa-d = wand
 war- = warm

fail:  -ail = nail
 f-il = foil
 fa-l = fall
 fai- = fair

rook:  -ook = book
 r-ok = ---- X
 ro-k = rock
 roo- = roof

soft:  -oft = loft
 s-ft = sift
 so-t = sort
 sof- = sofa

most:  -ost = cost
 m-st = mast
 mo-t = moat
 mos- = moss

lamp:  -amp = damp
 l-mp = lump
 la-p = ---- X
 lam- = lamb
Note that LARP is an uppercase acronym, and not in any of my word lists.

load:  -oad = road
 l-ad = lead
 lo-d = loud
 loa- = loaf

Workings

Hint
One of the words is Antelope.

Answer
ln      =  lion
ntlp    =  antelope
gzll    =  gazelle
strch   =  ostrich
wl      =  owl
rbn     =  robin
rdvrk   =  aardvark
dr      =  deer
clt     =  ocelot or colt
bs      =  ibis

Workings

Hint
This is a tricky question related to number bases.

Answer
200.

Each number in the sequence is a representation of the number 32 in different bases, starting with base 10.
Base 10: 32  = 3 x 10^1 + 2 x 10^0          = 3 x 10 + 2         = 32
Base 9 : 35  = 3 x 9^1  + 5 x 9^0           = 3 x 9 + 5          = 32
Base 8 : 40  = 4 x 8^1  + 0 x 8^0           = 4 x 8 + 0          = 32
Base 7 : 44  = 4 x 7^1  + 4 x 7^0           = 4 x 7 + 4          = 32
Base 6 : 52  = 5 x 6^1  + 2 x 6^0           = 5 x 6 + 2          = 32
Base 5 : 112 = 1 x 5^2  + 1 x 5^1 + 2 x 5^0 = 1 x 25 + 1 x 5 + 2 = 32
Base 4 : 200 = 2 x 4^2  + 0 x 4^1 + 0 x 4^0 = 2 x 16 + 0 + 0     = 32