XAT 2011 — QA & DI Question 19
Simple EquationsEasy
Passage / Data
Answer the following question based on the information given below.
A man standing on a boat south of a light house observes his shadow to be 24 meters long, as measured at the sea level. On sailing 300 meters eastwards, he finds his shadow as 30 meters long, measured in a similar manner. The height of the man is 6 meters above sea level.
The domain of the function
f(x) = log7{ log3(log5(20x – x2 – 91 ))} is:
Answer & solution
- A
(7, 13)
(8, 12)
- C
(7, 12)
- D
(12, 13)
- E
None of the above
Solution
f(x) = log7{ log3(log5(20x – x2 – 91 ))}
As log of negative numbers is not defined,
log3 (log5 (20x - x2 - 91)) > 0
∴ log5 (20x - x2 - 91)) > 30
∴ log5 (20x - x2 - 91) > 1
∴ 20x - x2 - 91 > 5
∴ 20x - x2 - 96 > 0
∴ x2 - 20x + 96 < 0
∴ (x - 12) (x - 8) < 0
∴ 8 < x < 12
Hence, option (b).