Time at which they meet at starting point
= LCM of 2, 4 and 5.5

Correct Option: B

Time at which they meet at starting point
= LCM of 2, 4 and 5.5
= 44 h

In any 4 consecutive natural numbers:

Two numbers will be divisible by 2, one of which will be divisible by 4, at least one number will be divisible by 3.

Correct Option: C

In any 4 consecutive natural numbers:

Two numbers will be divisible by 2, one of which will be divisible by 4, at least one number will be divisible by 3.

These facts give us a lower bound of 2 x 4 x 3 = 24 for the solution.

But 24 is also the product of the first 4 consecutive natural numbers, so it is also an upper bound.

Since 2, 3, 5, 17 are prime numbers and
The given expression = (2³)²⁰ x (3 x 5)²⁴ x (17)¹⁵
= 2⁶⁰ x 3²⁴ x 5²⁴ x 17¹⁵

Correct Option: C

Since 2, 3, 5, 17 are prime numbers and
The given expression = (2³)²⁰ x (3 x 5)²⁴ x (17)¹⁵
= 2⁶⁰ x 3²⁴ x 5²⁴ x 17¹⁵

So the total number of prime factors in the given expression is (60 + 24 + 24 + 15 ) = 123.

Interval of changes = (L . C . M of 48, 72, 108) sec. = 432 sec.
So, the lights will simultaneously changes after every 432 seconds i,e 7 min. 12 sec.

Correct Option: A

Interval of changes = (L . C . M of 48, 72, 108) sec. = 432 sec.
So, the lights will simultaneously changes after every 432 seconds i,e 7 min. 12 sec.
So, the next simultaneously changes will take place at 8 : 27 : 12 hrs.

Given, length of four metal roads are 78, 104, 117 and 169 cm.
Now,
78 = 13 x 2 x 3,
104 = 13 x 2 x 2 x 2,
117 = 13 x 3 x 3,
169 = 13 x 13

Correct Option: B

Given, length of four metal roads are 78, 104, 117 and 169 cm.
Now,
78 = 13 x 2 x 3,
104 = 13 x 2 x 2 x 2,
117 = 13 x 3 x 3,
169 = 13 x 13

Length of each piece of rod as long as possible, HCF = 13 CM
∴ Number of piece = 6 + 8 + 9 + 13 = 36