Question Bank  Modern Math  Hemant Malhotra

Q43) There are 5 red, 7 blue and 1 green balls in an urn. What's the minimum number of balls you need to take out without looking to guarantee that you have got 2 balls of the same colour

Q44) How many arrangemnt can be made in a round table of 8 chairs if 2 of them like to sit opposite to each other

Q45) Two different prime numbers less than 100 are randomly selected and multiplied. What is the probability that product is divisible by 9

Q46) There is a group of nine children, which includes two pairs of identical twins A, B and C, D. In how many ways can the nine children be seated in a row, so that A and B do not sit next to each other and C and D do not sit next to each other?

Q47) How many arrangements are possible with the letters of the word “PROFILE”, if no two consonants are to come together?

Q48) There are 10 different books and 20 copies of each book in a library. In how many ways can one or more than one book be selected?

@Aparajita
say a = correct, b = wrong, c = unattempted questions (a, b and c are non negative)
total = 100
So a + b + c = 100  (1)
now make the equation based on marks
12a  3b  2c = 625  (2)
12 x (1)  (2) gives 15b + 14c = 575
b = (575  14c)/15
b should be an integer. Means 575  14c should be a multiple of 15
575 = 15k + 14c
14c can end only in 0, 2, 4, 6 and 8.
for 15k + 14c = 575 we need c to end in 0 and k should be odd
We also know the max value of c is 41 as 42 * 14 > 575
c = 10, c = 25 and c = 40 satisfies.
So 3 ways

Q49) How many fourdigit even numbers are there which have 0 and 1 as two of the digits and the remaining two are distinct digits among 2, 4 and 6?

Q50) There are 100 people in a community. Each of these people likes one or more of the 3 superstars SK, JA and AK. Ten of them like both SK and JA. 30 of them like both AK and SK. 15 of them like both AK and JA. 35 of them like AK.
How many of them like all the 3 superstars?
a. 5
b. 10
c. 15
d. 20How many of them like exactly one of the 3 superstars?
a. 65
b. 45
c. 35
d. Data insufficient

Q51) A Chartered Accountant applies for a job in two firms X and Y. The probability of his being selected in firm X is 0.7, and being rejected at Y is 0.5 and the probability of being rejected is 0.6. What is the probability that he will be selected in one of the firms?

Q52) In a tournament club X plays each of the 6 other sides once. For each match the probabilities of a win, draw and loss are equal. Find the probability that X finishes with more wins than losses.

Q53) A randomly selects two distinct numbers from the set { 1, 2, 3, 4, 5 }, and B randomly selects a number from the set { 1, 2, ..., 10 } . What is the probability that B's number is larger than the sum of the two numbers chosen by A

Q54) All the possible 5digit numbers are formed using the digits 1, 2, 3, 4, 5  repetition is allowed. If one of those numbers is selected at random what is the probability that it will have exactly one digit repeated and that too occurring twice

Q55) My Facebook profile shows 14 new profile pictures on Mondays, 21 on Tuesdays, 28 on Wednesdays and so on. I use Facebook's 7 reactions  Like, Haha, Sad, Angery, Love, Wow, and Thankful  on specific days from Monday to Sunday, respectively. Starting from Monday and counting up to 28 days, I arrange exactly one picture from each weekday in a spreadsheet. What is the probability that a picture selected at random from the spreadsheet will have a Thankful react?

Q56) What is the Probability of landing a non odd prime on a single throw of two dice?

Q57) IIMB uses a super computer to evaluate the OMR sheets of CAT test takers. The super computer has an accuracy of 99.2% overall, but also interchanges the marks of two different candidates entirely in 0.02% cases. If a candidate whose result was inaccurate is chosen at random, what is the probability that his scores were also interchanged given that 196000 people took the exam?

Q58) Mr A has a terrible sleep schedule. He randomly picks a time between 4 AM and 6 AM to fall asleep, and wakes up at a random time between 11 AM and 1 PM of the same day. What is the probability that A gets between 6 and 7 hours of sleep?

Q59) In a box containing 15 apples, exactly 6 apples are rotten. Each day one apple is taken out from the box. What is the probability that after four days there are exactly 8 apples in the box that are not rotten?
a. 12/91
b. 1/7
c. 2/13
d. None of these

Q60) Probability that Elite's Grid is trending 2/5 and Probability that it is the best available platform for CAT is 1/5. Find the probability that it's neither trending nor the best platform.

Q61) A can hit a target 4 times in 5 shots; B can hit 3 times in 4 shots and C can hit 2 times in 3 shots. They all fire shots, find the probability that atleast 2 shots are hit?