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.

डेनिश ईस्ट इंडिया कंपनी का गठन वर्ष 1616 में हुआ था। कंपनी ने 17वीं और 18वीं शताब्दी के दौरान भारत सहित एशिया में व्यापार और औपनिवेशिक गतिविधियों में भूमिका निभाई थी। इसने भारत के विभिन्न हिस्सों में व्यापारिक चौकियाँ और किले स्थापित किए, विशेषकर दक्षिण-पूर्वी तट पर ट्रांक्यूबार (अब थारंगमबाड़ी) में।

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.