Select the option that is related to the fifth number in the same way as the second number is related to the first number and the fourth number is related to the third number.

68 : 4 :: 130 : 5 :: 350 : ?

In each set, first number = $$\left(\sec ond\ number\right)^3\ +\sec ond\ number$$

68 : 4

first number = $$\left(\sec ond\ number\right)^3\ +\sec ond\ number$$

= $$\left(4\right)^3\ +4$$

= 64+4

= 68

130 : 5

first number = $$\left(\sec ond\ number\right)^3\ +\sec ond\ number$$

= $$\left(5\right)^3\ +5$$

= 125+5

= 130

350 : ?

first number = $$\left(\sec ond\ number\right)^3\ +\sec ond\ number$$

$$350 = \left(\sec ond\ number\right)^3\ +\sec ond\ number$$

Now we need to check each option one by one to get the correct value in place of the question mark.

Option (a) 6

$$350\ne\ 216+6$$

This equation is not satisfied. So this is not the correct answer. 

Option (b) 8

$$350=\left(8\right)^3\ +8$$
$$350\ne\ 512+8$$

This equation is not satisfied. So this is not the correct answer.
Option (c) 9

$$350=\left(9\right)^3\ +9$$
$$350\ne\ 729+9$$
This equation is not satisfied. So this is not the correct answer.

Option (d) 7

$$350=\left(7\right)^3\ +7$$
$$350=343\ +7$$
350=350

This equation is satisfied. So this is the correct answer.

So '7' will come in place of the question mark.