Question

If the maximum number of trials required to open
all locks when there are n locks and n keys is 105,
then n =
(1) 13
(2) 14
(3) 35
(4) 20
ANS THIS​

Answer 1

Answer:

Number of Lock & Keys are 14

Step-by-step explanation:

As we have n locks & n Keys

if we start with 1st key then maxiumn in nth attempt lock will be opened

after that n-1 locks & n-1 Keys are reamined

so 2nd key will need max (n-1) attempts

& 3rd key  (n-2) attemts

&(n-1)th key   2 attemts

& nth key    1 attempt

Total number of Max attempts

1 + 2 + 3 +................................(n-2) +(n-1) + n

= n(n+1)/2

maximum number of trials required to open all locks when there are n locks and n keys is 105

=> n(n + 1)/2 = 105

=> n² + n = 210

=> n² + n - 210 = 0

=> n² + 15n - 14n - 210 = 0

=> n(n + 15) -14(n + 15) = 0

=> (n-14)(n+15) = 0

=> n = 14

Number of Lock & Keys are 14

Answer 2

Answer:

14

Step-by-step explanation:

see above for explanation