Mathematical Ability Test-5

A and B together can complete a work in 3 days. They start together but after 2 days, B left the work. If the work is completed after two more days, B alone could do the work in:

In a GP consisting of positive terms, each term equals the sum of the next two terms. Then the common ratio of the GP is:

Pipes M and N can alone fill and alone empty the tank in 12 hours and 24 hours respectively. There is a leakage at the bottom of tank which can empty the tank in 72 hours. If both pipes opened together, then in how much time tank will filled?

If y + b = m₁(x + a) and y + b = m₂(x + a) are the equations of the two tangents to the parabola y² = 4ax, then:

Two cards are drawn at random and without replacement from a pack of 52 playing cards. Find the probability that both the cards are black:

A bag contains 4 red and 4 black balls, another bag contains 2 red and 6 black balls. One of the two bags is selected at random and a ball is drawn from the bag which is found to be red. Find the probability that the ball is drawn from the first bag.

The mean of 15 observations is 14. Three more observations are included and the new mean becomes 13. The mean of three new observations is: