Sequences and S...

$$2.4+4.7+6.10+...(n-1)$$ terms

$$x = (-1)^{a^1} + (-1)^{a^2} + .....(-1)^{a^{1006}}$$
$$ y = (-1)^{a^{1007}} + (-1)^{a^{1008}} + ...+(-1)^{a^{2013}}$$
Then which of the following is true?

Unit digit in the number $$(12357)^{655}$$ is 

The sum of the infinite series, $$\dfrac{1}{1.3}+\dfrac{2}{3.7}+\dfrac{3}{7.13}+\dfrac{4}{13.21}+ ..........$$ is

$${2^{\frac{1}{4}}}.{4^{\frac{1}{8}}}.{8^{\frac{1}{{16}}}}....$$ to $$\infty$$ is equal to

In a class of 80 students it is found that 40 students like Tajmahal and 50 students like Charminar and 18 like both. Then the number of students who do not like neither are.

Out of nine cells of a square, one cell is left blank and in the rest of the cells, numbers are written follow some rule. Get the rule and find out the proper option for the blank cell 

The value of $$\sum_{n=1}^{10}\int_{0}^{n}xdx$$ is

What number corresponds to the fifth missing planet ?

Find the sum of first $$n$$ terms of the series.
$$1^{3}+3\times2^{2}+3^{3}+3\times4^{2}+5^{3}+3\times6^{2}+....$$ If $$n$$ is even.