Solution: (b)

The pattern of the number series is :

353 + 1 = 354

354 – 3 = 351

351 + 5 = 356

356 – 7 = 349

349 + 9 =  358

Solution: (c)

The pattern of the number series is :

\(\displaystyle 1+{{2}^{2}}=1+4=5\)

\(\displaystyle 5+{{2}^{3}}=5+8=13\)

\(\displaystyle 13+{{2}^{4}}=13+16=29\)

\(\displaystyle 29+{{2}^{5}}=29+32=61\)

\(\displaystyle 61+{{2}^{6}}=61+64=125\)

Solution: (e)

The pattern of the number series is :

\(\displaystyle 17+{{1}^{3}}=17+1=18\)

\(\displaystyle 18+{{2}^{3}}=18+8=26\)

\(\displaystyle 26+{{3}^{3}}=26+27=53\)

\(\displaystyle 53+{{4}^{3}}=53+64=117\)

\(\displaystyle 117+{{5}^{3}}=117+125=242\)

Solution: (a)

\(\displaystyle \frac{1}{4}+\frac{1}{4}=\frac{1}{2}\)

\(\displaystyle \frac{1}{2}+\frac{1}{4}=\frac{3}{4}\)

\(\displaystyle \frac{3}{4}+\frac{1}{4}=1\)

\(\displaystyle 1+\frac{1}{4}=1\frac{1}{4}\)

\(\displaystyle ?=1\frac{3}{4}+\frac{1}{4}=2\)

Solution: (a)

The pattern of the number series is :

\(\displaystyle \frac{1}{2}+\frac{1}{2}=1,1+\frac{1}{2}=1\frac{1}{2}\)

\(\displaystyle 1\frac{1}{2}+\frac{1}{2}=2\)

\(\displaystyle ?=3+\frac{1}{2}=3\frac{1}{2}\)

Solution: (b)

The pattern of the number series is :

\(\displaystyle 219-3=216={{6}^{3}}\)

\(\displaystyle 344-219=125={{5}^{3}}\)

\(\displaystyle 408-344=64={{4}^{3}}\)

\(\displaystyle ?=408+{{3}^{3}}=408+27=435\)

Solution: (c)

The pattern of the number series is as given below:

\(\displaystyle 2\times 7=14\)

\(\displaystyle 14\times 6=84\)

\(\displaystyle 84\times 5=420\)

\(\displaystyle 420\times 4=1680\)

\(\displaystyle 1680\times 3=5040\)

\(\displaystyle 5040\times 2=10080\)

Solution: (d)

The pattern of the number series is as given below:

\(\displaystyle {{3}^{3}}=27;{{5}^{3}}=125\)

\(\displaystyle {{7}^{3}}=343;{{9}^{3}}=729\)

\(\displaystyle {{11}^{3}}=1331;{{13}^{3}}=21973\)

\(\displaystyle {{15}^{3}}=3375\)

Solution: (a)

The pattern of the number series is as given below:

358 – 2 = 356

356 – 4 = 352

352 – 8 = 344

344 – 16 = 328

328 – 32 = 296

296 – 64 = 232

Solution: (b)

The pattern of the number series is as given below:

\(\displaystyle 50000\div 5=10000\)

\(\displaystyle 10000\div 4=2500\)

\(\displaystyle 2500\div 5=500\)

\(\displaystyle 500\div 4=125\)

\(\displaystyle 125\div 5=25\)

\(\displaystyle 25\div 4=6.25\)

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