Solution: (d)

The pattern of the series is as follows:

\(\displaystyle 2\times 4+2=10\)

\(\displaystyle 10\times 4+2=42\)

\(\displaystyle 42\times 4+2=170\)

\(\displaystyle 170\times 4+2=682\)

Solution: (b)

The pattern of the series is as follows:

\(\displaystyle 600-{{9}^{2}}=600-81=519\)

\(\displaystyle 519-{{8}^{2}}=519-64=455\)

\(\displaystyle 455-{{7}^{2}}=455-49=406\)

\(\displaystyle 406-{{6}^{2}}=406-36=370\)

Solution: (c)

\(\displaystyle 2\times 8=16\)

\(\displaystyle 16\times 7=112\)

\(\displaystyle 112\times 6=672\)

\(\displaystyle 672\times 5=3360\)

\(\displaystyle 3360\times 4=13440\)

\(\displaystyle 13440\times 3=40320\)

? = 40320                 

Solution: (c)

\(\displaystyle 4000\div 2=2000\)

\(\displaystyle 2000\div 2=1000\)

\(\displaystyle 1000\div 2=500\)

\(\displaystyle 500\div 2=250\)

\(\displaystyle 250\div 2=125\)

\(\displaystyle 125\div 2=62.5\)

? = 62.5

Solution: (e)

\(\displaystyle 45+1\times 12=45+12=57\)

\(\displaystyle 57+2\times 12=57+24=81\)

\(\displaystyle 81+3\times 12=81+36=117\)

\(\displaystyle 117+4\times 12=117+48=165\)

\(\displaystyle 165+5\times 12=165+60=225\)