**Concept: The question deals with fundamentals of inequality and sign change.**

**Solution:**

6/a(a+1) > 1 and this is not possible for a(a+1)<0

=> a(a+1) >0 and in other words it implies a(a+1) is positive.

=>6 and 1 are positive values too and hence we can now confidently write

6/a(a+1) >1 => 6>a(a+1)

=>a(a+1)<6

=>a^2 + a <6

=>a^2 + a -6 < 0 (Add -6 on both sides)

=>a^2 +3a - 2a -6 < 0

=> a(a+3) - 2(a+3) <6

=> (a+3)(a-2) < 6

Use the wavy line approach now to reach the critical points as -3 and 2,plot them on the number line and consider the negative interval values only

=> +.................(-3

**)................. - ...................**(2)...............+...**NEGATIVE INTERVAL To be considered AS "<" sign in inequality**

=> -3<a<2 and the only option satisfying the range is -2.5

**(option b)**