Solution: (d)

Given number series

\(\displaystyle 7\times 2-(2\times 1)=12\)  

\(\displaystyle 12\times 4-(4\times 2)=40\)

\(\displaystyle 40\times 6-(6\times 3)=222\)

\(\displaystyle 222\times 8-(8\times 4)=1742\)

\(\displaystyle 1742\times 10-(10\times 5)=17390\) \(\displaystyle 17390\times 12-(12\times 6)=208608\)

Solution: (c)

The given MCQ on number series is based on the following pattern:

\(\displaystyle 6\times 7+{{7}^{2}}=91\)      

\(\displaystyle 91\times 6+{{6}^{2}}=584\)

\(\displaystyle 584\times 5+{{5}^{2}}=2935\)

\(\displaystyle 2935\times 4+{{4}^{2}}=11756\)

\(\displaystyle 11756\times 3+{{3}^{2}}=35277\)

\(\displaystyle 35277\times 2+{{2}^{2}}=70558\)

Solution: (d)

The given question on number series is based on the following pattern:

\(\displaystyle {{1}^{2}}=1\)

\(\displaystyle {{2}^{2}}=4\)

\(\displaystyle {{3}^{3}}=25\)

\(\displaystyle {{4}^{4}}=256\)

\(\displaystyle {{5}^{5}}=3125\)

\(\displaystyle {{6}^{6}}=46656\)

\(\displaystyle {{7}^{7}}=823543\)

Solution: (b)

The given question on number series is based on the following pattern:

\(\displaystyle 8424\times \frac{1}{2}=4212\)

\(\displaystyle 4212\times \frac{1}{2}=2106\)

\(\displaystyle 2106\times \frac{1}{2}=1051\)

\(\displaystyle 1051\times \frac{1}{2}=526.5\)

\(\displaystyle 526.5\times \frac{1}{2}=263.25\)

\(\displaystyle 263.25\times \frac{1}{2}=131.625\)

Solution: (c)

The given number series question is based on the following pattern:

\(\displaystyle 800\div 2=400\)

\(\displaystyle 400\div 2=200\)

\(\displaystyle 200\div 2=100\)

\(\displaystyle 100\div 2=50\)

\(\displaystyle 50\div 2=25\)