Sequences and S...

Let $$S_1=\displaystyle \sum_{K=1}^{n}K,S_2=\sum_{K=1}^{n}K^2$$ and $$S_3=\displaystyle \sum_{K=1}^{n}K^3$$, then $$\dfrac{S_{1}^{4}S_{2}^{2}-S_{2}^{2}S_{3}^{2}}{S_{1}^{2}+S_{3}^{2}}$$ is equal to

The first three terms of a sequence are 3,3,6 and each term after the second is the sum of two terms preceding it, the 8th term of the sequence is

Choose the most appropriate option which follows the pattern

What is the next term to this series, 2, 3, 7, 16, 32, and 57...?

The value of the expression

If D=4 and COVER = 63, then BASIC is equal to

If $$5\times 9=144; 7\times 8=151:4\times 6=102,$$ then $$2\times 5=?$$

Observe the given pattern
$$4\times 0+1=01$$
$$4\times1+2=06$$ 
$$4\times 2+3=11$$
$$4\times 3+4=16$$
Then the value of $$4\times8+9 $$ is -----