InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Find x in each of the following:(i) 1/4! + 1/5! = x/6!(ii) x/10! = 1/8! + 1/9!(iii) 1/6! + 1/7! = x/8! |
|
Answer» (i) 1/4! + 1/5! = x/6! As we know that 5! = 5 × 4 × 3 × 2 × 1 6! = 6 × 5 × 4 × 3 × 2 × 1 Therefore by using these values, 1/4! + 1/5! = x/6! 1/4! + 1/(5×4!) = x/6! (5 + 1) / (5×4!) = x/6! 6/5! = x/(6×5!) x = (6 × 6 × 5!)/5! = 36 Thus, the value of x is 36. (ii) x/10! = 1/8! + 1/9! As we know that 10! = 10 × 9! 9! = 9 × 8! Therefore by using these values, x/10! = 1/8! + 1/9! x/10! = 1/8! + 1/(9 × 8!) x/10! = (9 + 1)/(9 × 8!) x/10! = 10/9! x/(10 × 9!) = 10/9! x = (10 × 10 × 9!)/9! = 10 × 10 = 100 ∴ The value of x is 100. (iii) 1/6! + 1/7! = x/8! As we know that 8! = 8 × 7 × 6! 7! = 7 × 6! Therefore by using these values, 1/6! + 1/7! = x/8! 1/6! + 1/(7 × 6!) = x/8! (1 + 7)/(7 × 6!) = x/8! 8/7! = x/8! 8/7! = x/(8 × 7!) x = (8 × 8 × 7!)/7! = 8 × 8 = 64 Hence, the value of x is 64. |
|