A fair coin is tossed 11 times. What is the probability that only the first two tosses will yield heads ?

2508 ÷ 15.02 ÷ ? x 11 = 200
? 2508/15 + ? x 11 = 200
? ? = (200 - 167.2) x 1/11 = 2.98 ? 3

Upstream speed of boat = Boat's speed in still water - Rate of stream = 4 - 2 = 2 km/h

Let the requirement odd integers be N, N +2 and N + 4
Then, N + (N + 2) + (N + 4) = 57
? 3N = 51
? N = 17
? The integers are 17, 19, 21.

Because of stoppages, train covers 50 km less per hour.
? Time taken taken to cover 50 km = 50/150 h = (50/150) x 60 = 20 min

Let age of Raman's daughter = N yr
Then, age of Raman's = 3N yr
and age of Raman's mother = (13/9) x 3N = 13N/3 yr
According to the question, N + 3N + 13N/3 = 125
? 3N + 9N + 13N = 125 x 3
? N = (125 x 3)/25 = 15
Hence, required difference = 13N/3 - N = 10N/3
= (10 x 15)/3 = 50 yr

Let boat's rate upstream be U and boat's rate downstream = V

According to the question.
Distance covered in 528 min = Distance covered in 240 min
? Distance covered in 8 h 48 min = Distance covered in 4 h
? U x 8⁴/₅ = V x 4
? (44 x U)/5 = 4V
? V = (11 x U)/5
? Required ratio = (V + U)/2 : (V - U)/2
? = (11U/5 + U)/2 : (11U/5 - U)/ 2
? = 16U/5 : 6U/5 = 8 : 3

Let A's age 10 years ago = x years
Then, B's age 10 years ago = 2x years
? (x + 10) / (2x + 10) = 3 / 4
? 4(x + 10) = 3(2x + 10)
? x(6 - 4) = 40 - 30
? x = 5

&ther4; Total of their present ages = (x + 10) + (2x + 10)
= (3x + 20)
= 35 years

Let B's present age be x years then A's present age be (x + 9) years
As per the given condition
(x + 9 + 10) = 2(x - 10)
? x = 39

? The present age of B = 39 years

75/100 = 0.75