Question : Find the probability that a rectangle selected at random from a 10*10 square is a square? a.17/55 b.7/55 c.9/55 d.16/55 Answer : Total number of rectangles = 11C2 * 11C2 = 55*55 Total number of squares = 1^2 + 2^2 ....... 10^2 = 10*11*21/6 = 5*11*7 = 55*7 Required probability = 55*7 / 55*55 = 7/55
Question : There are 4 red & 5 green balls in bag A and 5 red & 6 green balls in bag B. If a bag is selected at random and a ball is selected from that, what is the probability that it is red? Answer :Â Probability of Red Ball =Â Bag A is selected & Red Ball is selected + Bag B is selected & Red Ball is selected ie. (1/2)*(4/9) + (1/2)*(5/11) = Â (1/2)[ (44+45) / 99 ] =Â 89/198
Question : Find the last two digits of (24)^37298Â Answer Last two digits of 24^Odd = 24 Last two digits of 24^Even =Â 76
Question: A fair coin is tossed 43 times. What is the number of cases where number of ‘Head’ > number of ‘Tail’? (A) 2^43 (B) (2^43)-43 (C) 2^42 (D) None of the above. Answer: No. of heads > No. of tails => No. of heads can be 22, 23, 24... 43 Therefore  43C22 + 43C23 + 43C24 .. 43C43 We know that 43C0 + 43C1 + 43C2 ... 43C43 = 2^43 We also know know that our answer has 22 terms which are 43C22 + 43C23 + 43C24 .. 43C43 These 22 terms are equal to = 43C0 + 43C1 + 43C2 .. 43C21 Both of them are equal and add up to 2^43
Question: At what time between 2 and 3 the angle between the hands of clock is 60 degrees? Answer: At 2 o'clock the angle is 60 degree. After t minutes past 2: Minute hand from the vertical = 6t Hour hand from the vertical = 60 + 0.5t Required angle is : 6t - (60 + 0.5t) = 60 ie.  5.5t = 120 Therefore ,  t = 240/11 = 21 9/11 minutes, At 2:21:9/11th min the angle between the hands of a clock would be 60 degrees.