Answer: B) 19/42 Explanation: A red ball can be drawn in two mutually exclusive ways  (i) Selecting bag I and then drawing a red ball from it.   (ii) Selecting bag II and then drawing a red ball from it.   Let E1, E2 and A denote the events defined as follows: E1 = selecting bag I, E2 = selecting bag II A = drawing a red ball Since one of the two bags is selected randomly, therefore  P(E1) = 1/2  and  P(E2) = 1/2 Now, PAE1 = Probability of drawing a red ball when the first bag has been selected = 4/7   PAE2  = Probability of drawing a red ball when the second bag has been selected = 2/6  Using the law of total probability, we have   P(red ball) = P(A) = PE1×PAE1+PE2×PAE2                              = 12×47+12×26=1942

1. How to find Speed(s) if distance(d) & time(t) is given:    Speed (S) = Distance (D)Time (T)     Ex: Find speed if a person travels 4 kms in 2 hrs? Speed = D/T = 4/2 = 2 kmph.   2.  Similarly, we can find distance (d)  if speed (s) & time (t) is given by   Distance (D) = Speed (S) x Time (T)   Ex : Find distance if a person with a speed of 2 kmph in 2 hrs? Distance D = S X T = 2 x 2 = 4 kms.    3.  Similarly, we can find time (t) if speed (s) &  distance (d) is given by   Time (T) = Distance (D)Speed (S)   Ex : Find in what time a person travels 4 kms with a speed of 2 kmph? Time T = D/S = 4/2 = 2 hrs.   4. How to convert  km/hr into m/sec :   P km/hr = P x 518 m/sec   Ex : Convert 36 kmph into m/sec? 36 kmph = 36 x 5/18 = 10 m/sec    5. How to convert  m/sec into km/hr :   P m/sec = P x 185 kmph.   Ex : Convert 10 m/sec into km/hr? 10 m/sec = 10 x 18/5 = 36 kmph.   6.  If the ratio of the speeds of A and B is a:b, then the ratio of the times taken by them to cover the same distance is b : a.   7.  Suppose a man covers a certain distance at x km/ hr and an equal distance at y km/hr . Then, the average speed during the whole journey is 2xyx+y km/hr.

Answer: A) 29 Explanation: Let the five consecutive odd numbers be x-4, x-2, x, x+2, x+4 According to the question, Difference between square of the average of first two odd number and the of the average last two odd numbers is 396 i.e, x+3 and x-3 ⇒x + 32 - x - 32 = 396⇒ x2 + 9 + 6x - x2 + 6x - 9 = 396⇒ 12x = 396⇒ x = 33   Hence, the smallest odd number is 33 - 4 = 29.