Let’s examine the relationship between each pair of adjacent terms:

The first term, 6, is divided by 2 to give the second term, 3.
The second term, 3, is multiplied by 4 (2^2) to give the third term, 12.
The third term, 12, is divided by 2 to give the fourth term, 6.
The fourth term, 6, is multiplied by 4 (2^2) to give the fifth term, 24.

From this pattern, we can see that each alternate term is obtained by multiplying the previous term by 4 and then dividing by 2. Applying this pattern to the fifth term, which is 24, we would divide it by 2 to get the missing number:
24 ÷ 2 = 12

Therefore, the missing number in the sequence is 12. The correct answer is (b) 12.

The correct answer is 1.2

To find the reciprocal of the sum of reciprocals of 2 and 3, we need to calculate the sum of their reciprocals first. The reciprocal of a number x is 1/x.
So, the reciprocal of 2 is 1/2, and the reciprocal of 3 is 1/3.
The sum of the reciprocals of 2 and 3 is:
1/2 + 1/3 = 3/6 + 2/6 = 5/6

Now, to find the reciprocal of 5/6, we take the reciprocal of 5/6, which is simply flipping the numerator and denominator:
Reciprocal of 5/6 = 6/5

Therefore, the reciprocal of the sum of the reciprocals of 2 and 3 is 6/5 = 1.2
Answer = 1.2

The Correct answer is 8 elements.

The power set of a set is the set of all possible subsets of that set, including the empty set and the set itself.
For the set {1, 2, 3}, the elements are {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, and {1, 2, 3}. Additionally, the empty set {} is also an element of the power set.

Therefore, the power set of {1, 2, 3} has a total of 8 elements: {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}, {}.

The total time the man spent walking and riding the automobile is:

1/3 hour (walking) + 1/2 hour (automobile ride) = 2/6 hour + 3/6 hour = 5/6 hour

So the man spent 1/2 hour on the automobile ride, which is a fraction of:

(1/2) ÷ (5/6) = (1/2) × (6/5) = 3/5

Therefore, the man rode on the automobile for 3/5 of the total time he consumed.

The answer is equal to 0.6, which is equivalent to 60%.

To obtain the percentage, we can multiply the fraction by 100:

3/5 * 100 = 60%

Therefore, the man rode on the automobile for 60% of the total time he consumed.