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INFOMATHS WORK-SHEET-2 (OLD QUESTIONS) PERMUTATION & COMBINATION / PROBABILITY 19. PERMUTATIONS & COMBINATIONS 1. How many words can be formed out of the letters of the word ‘PECULIAR’ beginning with P and ending with R ? PU CHD-2012 (A) 100 (B) 120 (C) 720 (D) 150 2. If M = {1, 2, 3, 4, 5, 7, 8, 10, 11, 14, 17, 18}. Then how many subsets of M contains only odd integers. Pune-2012 (a) 26 (b) 212 (c) 211 (d) None of these 3. No. of seven digit integers with sum of digits equal to 10, formed by digits 1, 2, 3 only are Pune-2012 (a) 55 (b) 66 (c) 77 (d) 88 4. How many nos. between 1 and 10,000 which are either even, ends up with 0 or have the sum of their digits divisible by 9. Pune-2012 (a) 5356 (b) 5456 (c) 5556 (d) 5656 5. The number of words that can be formed by using the letters of the word Mathematics that start as well as end with T is NIMCET-2012 (a) 80720 (b) 90720 (c) 20860 (d) 37528 6. The number of different license plates that can be formed in the format 3 English letters (A …. Z) followed by 4 digits (0, 1 ….. 9) with repetitions allowed in letters and digits is equal to NIMCET-2012 (a) 263 × 104 (b) 263 + 104 (c) 36 (d) 263 7. In which of the following regular polygons, the number of diagonals is equal to number of sides? NIMCET-2012 (a) Pentagon (b) Square (c) Octagon (d) Hexagon 8. 100 ! = 1 2 3 ….. 100 ends exactly in how many zeroes? HCU-2011 (a) 24 (b) 10 (c) 11 (d) 21 9. Let a and b be two positive integers. The number of factors of 5 a7b are HCU-2011 (a) 2(a+b) (b) a + b + 2 (c) ab + 1 (d) (a + 1) (b + 1) 10. A polygon has 44 diagonals, the number of its sides is NIMCET-2011, PU CHD-2011 (a) 9 (b) 10 (c) 11 (d) 12 11. The number of ways of forming different nine digit numbers from the number 223355888 by rearranging its digit so that the odd digits occupy even positions is NIMCET-2011 (a) 16 (b) 36 (c) 60 (d) 180 12. There are n numbered seats around a round table. Total number of ways in which n1(n1 < n) persons can sit around the round table, is equal to BHU-2011 (a) 13. 14. 15. 16. 17. 18. n Cn1 (b) n Pn1 (c) n 20. 21. 22. 23. 24. 25. 26. 27. How many different words can be formed by jumbling the word MISSISSIPPI in which no two S are adjacent? KIITEE-2010 (a) 8.6C4.7C4 (b) 6.78C4 (c) 6.8.7C4 (d) 7.6C4.8C4 The number of ways in which 6 men and 5 women can dine at a roundtable, if no two women are to sit together is given by KIITEE-2010 (a) 6! 5! (b) 30 (c) 5! 4! (d) 7! 5! Total number of divisors of 200 are PGCET-2010 (a) 10 (b) 6 (c) 12 (d) 5 How many different paths in the xy-plane are there from (1, 3) to (5, 6) if a path proceeds one step at a time by going either one step to the right (R) or one step upward (U)? (NIMCET – 2009) (a) 35 (b) 40 (c) 45 (d) None of these There are 10 points in a plane. Out of these 6 are collinear. The number of triangles formed by joining these points is (NIMCET – 2009) (a) 100 (b) 120 (c) 150 (d) None of these A man has 7 friends. The number of ways in which he can invite one or more of his friends to a party is (KIITEE – 2009) (a) 132 (b) 116 (c) 127 (d) 130 The number of ways in which the letter of word ARTICLE can be rearranged so that the odd places are always occupied by consonants is (KIITEE – 2009) (a) 576 (b) 4C3 4! (c) 2(4!) (d) None of these Nine hundred distinct n – digit positive numbers are to be formed using only the digits 2, 5, 7. The smallest value of n for which this is possible is (KIITEE – 2009) (a) 6 (b) 8 (c) 7 (d) 9 Total number of 6 – digit numbers in which all the odd digits and only odd digits appear is (KIITEE – 2009) (a) 28. 29. 30. 31. 32. Cn1 1 (d) n Pn1 1 The number of subsets of a set containing n distinct object is BHU-2011 (a) nC1 + nC2 + nC3 + nC4 + …… + nCn (b) 2n – 1 (c) 2n + 1 (d) nC0 + nC1 + nC2 + ….. + nCn A five digit number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4 and 5 without repetitions. The total number of ways this can be done is : PU CHD-2011 (A) 216 (B) 600 (C) 240 (D) 3125 Total number of ways in which five + and seven – signs can be arranged in a line such that no two + signs occur together is : PU CHD-2010 (A) 56 (B) 42 (C) 28 (D) 21 All letters of the word AGAIN are permuted in all possible ways and the words so formed (with or without meaning) are written in dictionary order then the 50th word is : PU CHD-2010 (A) NAAGI (B) NAAIG (C) IAANG (D) INAGA How many ways are there to arranged the letters in the word GARDEN with the vowels in alphabetical order? PU CHD-2009 (a) 120 (b) 480 (c) 360 (d) 240 A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is : KIITEE-2010 (a) 346 (b) 140 (c) 196 (d) 280 33. 34. 35. 36. 37. 38. 39. 1 5 (6!) 2 (b) 1 (6!) 2 (c) 6! (d) N.O.T Find the total number of ways a child can be given at least one rupee from four 25 paise coins, three 50 paise coins and two onerupee coins HYDERABAD CENTRAL UNIVERSITY - 2009 (a) 53 (b) 51 (c) 54 (d) 55 How many 5-digit prime numbers can be formed using the digits 3, 5, 7, 2 and 1 once each? HYDERABAD CENTRAL UNIVERSITY - 2009 (a) 1 (b) 5! – 4! (c) 0 (d) 5! If there are 20 possible lines connecting non-adjacent points of a polygon, how many sides does it have? HYDERABAD CENTRAL UNIVERSITY - 2009 (a) 12 (b) 10 (c) 8 (d) 9 From 5 different green balls, four different blue balls and three different red balls, how many combinations of balls can be chosen taking at least one green and one blue ball? HYDERABAD CENTRAL UNIVERSITY - 2009 (a) 60 (b) 3720 (c) 4096 (d) None of these The number of even proper factors of 1008 is HYDERABAD CENTRAL UNIVERSITY - 2009 (a) 24 (b) 22 (c) 23 (d) 25 An eight digit number divisible by 9 is to be formed by using 8 digits out of the digits 0, 1, … 9 without replacement. The number of ways in which this can be done is NIMCET - 2008 (a) 9! (b) 2(7!) (c) 4(7!) (d) 36(7!) The number of ordered pairs (m, n), m, n {1, 2, … 100} such that 7m + 7n is divisible by 5 is NIMCET - 2008 (a) 1250 (b) 2000 (c) 2500 (d) 5000 Twenty apples are to be given among three boys so that each gets atleast four apples. How many ways it can be distributed? KIITEE - 2008 (a) 22C20 (b) 90 (c) 18C8 (d) None The number of arrangements of the letters of the word SWAGAT taking three at a time is KIITEE - 2008 (a) 72 (b) 120 (c) 14 (d) None The number of points (x, y, z) in space, whose each co-ordinate is a negative integer such that x + y + z + 12 = 0 is KIITEE - 2008 (a) 110 (b) 385 (c) 55 (d) None There are three piles of identical yellow, black and green balls and each pile contains at least 20 balls. The number of ways of selecting 20 balls if the number of black balls to be selected is twice the number of yellow balls is. KIITEE - 2008 (a) 6 (b) 7 (c) 8 (d) 9 x1, x2, x3 N. The number of solutions of the equations x1. x2. x3 = 24300 is IP Paper – 2006 INFOMATHS/MCA/MATHS/OLD QUESTIONS INFOMATHS 40. 41. 42. 43. (a) 480 (b) 512 (c) 560 (d) 756 In how many different ways can the letters of the word DISTANCE can be arranged so that all the vowels come together Karnataka PG-CET paper – 2006 (a) 720 (b) 4320 (c) 4200 (d) 3400 In a chess tournament each of the six players will play every other player exactly once. How many matches will be played during the tournament? Karnataka PG-CET paper – 2006 (a) 12 (b) 15 (c) 30 (d) 36 In an objective type examination, 120 objective type questions are there : each with 4 options P, Q, R and S. A candidate can choose either one of these options or can leave the question unanswered. How many different ways exist for answering this question paper? NIMCET – 2008 (a) 5120 (b) 4120 (c) 1205 (d) 1204 A four digit number a3a2a1a0 is formed from digits 1 … 9 such that 3. 4. a i 1 2 if ai + 1 is even otherwise i = 0, 1, 2 5. ai a a i 1 or i 1 2 2 a is the smallest integer larger than a and a is the largest 44. 45. 46. integer smaller than a. The smallest value that a3 can have is (Hyderabad Central University - 2009) (a) 5 (b) 7 (c) 9 (d) 1 Four students have to be chosen – 2 girls as captain and vice – captain and 2 boys as captain and vice – captain. There are 15 eligible girls and 12 eligible boys. In how many ways can they be chosen if Sunitha is sure to be captain? HYDERABAD CENTRAL UNIVERSITY - 2009 (a) 114 (b) 1020 (c) 360 (d) 1848 From city A to B, there are 3 different roads. From B to C there are 5 and from C to D there are 2 different roads. Laxman has to go from A to D attending to some work in B and C on the way and has to come back in the reversed order. In how many ways can he complete his journey if he does not take the exact same path while coming back? HYDERABAD CENTRAL UNIVERSITY - 2009 (a) 250 (b) 870 (c) 90 (d) 100 The number of ways in which 12 blue balls, 12 green balls and one black ball can be arranged in a row with the black ball in the middle and arrangements of the colours of balls being symmetrical about the black ball, is IP Paper – 2006 (a) (c) 47. 24! 2 2 !12 ! (b) 2 24 ! 6. (c) x k mn k m n (d) kx k mn 7. 8. 9. A4 B4 the lines A1 B1 , A2 B2 , 16 81 1 1 (b) , 2 4 1 (c) ,1 2 10. x k 137 81 1 1 1 , , respectively. If they all 2 3 4 1 2 (b) 1 2n (c) 1 2n1 (d) None of these One hundred identical coins each with probability P of showing up heads re tossed. If 0 < P < 1 and the probability of heads showing on 50 coins is equal to that of heads on 51 coins; then the value of P is NIMCET-2012 (a) 12. 1 (d) 1, 2 try to solve the problem, what is the probability that the problem will be solved? NIMCET-2012, MP-2008 (a) 1/2 (b) 1/4 (c) 1/3 (d) 3/4 If a fair coin is tossed n times, then the probability that the head comes odd number of times is NIMCET-2012 (a) 11. A3 B3 (D) A determinant is chosen at random from the set of all determinants of matrices of order 2 with elements 0 and 1 only. The probability that the determinant chosen is non-zero is NIMCET-2012 (a) 3/16 (b) 3/8 (c) 1/4 (d) None of these Coefficients of quadratic equation ax2 + bx + c = 0 are chosen by tossing three fair coins where ‘head’ means one and ‘tail’ means two. Then the probability that roots of the equation are imaginary is NIMCET-2012 (a) 7/8 (b) 5/8 (c) 3/8 (d) 1/8 A problem in Mathematics is given to three students A, B and C whose chances of solving it are 1 2 (b) 49 101 (c) 50 101 (d) 51 101 Let P be a probability function on S = (l1, l2, l3, l4) such that 1 1 1 P l2 , P l3 , P l4 . Then P(l1) is 3 6 9 PROBABILITY 1. All the coefficients of the equation ax2 + bx + c = 0 are determined by throwing a six-sided un-biased dice. The probability that the equation has real roots is HCU-2012 (a) 57/216 (b) 27/216 (c) 53/216 (d) 43/216 2. Suppose 4 vertical lines are drawn on a rectangular sheet of paper. name (C) NIMCET-2012 A student took five papers in an examination, where the full marks were the same for each paper. The marks obtained by the student in these papers were in the proportion 6:7:8:9:10. The student obtained 3/5 of the total full marks. The number of papers in which the student obtained less than 45 per cent marks is IP Paper – 2006 (a) 2 (b) 3 (c) 4 (d) None of these We 137 729 1 , the values of P(A|B) and P (B|A) respectively are 2 1 1 (a) , 4 2 12! 6 ! 6 ! (b) (B) Let P(E) denote the probability of event E. Given P(A) = 1, P(B) A contractor hires k people for a job and they complete the job in x days. A month later he gets a contract for an identical job. At this time he has with him k + m + n people for the job, the number of days it will require for them to complete it, is IP Paper – 2006 (a) x + m + n 48. (A) 12! (d) 2 6 ! 6 ! 12 !12 What is the probability that the figure thus formed has disconnected loops? HCU-2012 (a) 1/3 (b) 2/3 (c) 3/6 (d) 1/6 In a village having 5000 people, 100 people suffer from the disease Hepatitis B. It is known that the accuracy of the medical test for Hepatitis B is 90%. Suppose the medical test result comes out to be positive for Anil who belongs to the village, then what is the probability that Anil is actually having the disease. HCU-2012 (a) 0.02 (b) 0.16 (c) 0.18 (d) 0.3 Let A, B and C be the three events such that P(A) = 0.3, P(B) = 0.4, P(C) = 0.8, P(A B) = 0.08, P(A C) = 0.28, P(A B C) = 0.09. If P(A B C) 0.75, then P(B C) satisfies : PU CHD-2012 (A) P(B C) ≤0.23 (B) P(B C) ≤0.48 (C) 0.23 ≤P(B C) ≤0.48 (D) P(B C) ≤0.15 A number is chosen from each of the two sets {1, 2, 3, 4, 5, 6, 7, 8, 9} and {1, 2, 3, 4, 5, 6, 7, 8, 9}. If P denotes the probability that the sum of the two numbers be 10 and Q the probability that their sum be 8, then (P + Q) is PU CHD-2012 BHU-2012 (a) 7/18 13. and respectively. Suppose two players A and B join two 14. disjoint pairs of end points within A1 to A4 and B1 to B4 respectively without seeing how the other is marking. 2 (b) 1/3 (c) 1/6 (d) 1/5 The probability that A, B, C can solve problem is 1 1 1 , , 3 3 3 respectively they attempt independently, then the probability that the problem will solved is : BHU-2012 (a) 1/9 (b) 2/9 (c) 4/9 (d) 2/3 In a single throw with two dice, the chances of throwing eight is : BHU-2012 INFOMATHS/MCA/MATHS/OLD QUESTIONS INFOMATHS 15. 16. 17. 18. 19. 20. 21. (a) 7/36 (b) 1/18 (c) 1/9 (d) 5/36 A single letter is selected at random from the word “probability”. The probability that it is a vowel, is : BHU-2012 (a) 3/11 (b) 4/11 (c) 2/11 (d) 0 An unprepared student takes a five question true-false exam and guesses every answer. What is the probability that the student will pass the exam if at least four correct answers is the passing grade? HCU-2011 (a) 3/16 (b) 5/32 (c) 1/32 (d) 1/8 Answer questions 17 and 18 using the following text: In a country club, 60% of the members play tennis, 40% play shuttle and 20% play both tennis and shuttle. When a member is chosen at random, What is the probability that she plays neither tennis nor shuttle? HCU-2011 (a) 0.8 (b) 0.2 (c) 0.5 (d) 0.4 If she plays tennis, what is the probability ability that she also plays shuttle? HCU-2011 (a) 2/3 (b) 2/5 (c) 1/3 (d) 1/2 If E is the event that an applicant for a home loan in employed C is the event that she possesses a car and A is the event that the loan application is approved, what does P(A|E C) represent in words? HCU-2011 (a) Probability that the loan is approved, if she is employed and possesses a car (b) Probability that the loan is approved, if she is either employed or possesses a car (c) Probability that the loan is approved, if she is neither employed nor possesses a car. (d) Probability that the loan is approved and she is employed, given that she possesses a car An anti-aircraft gun can take a maximum of four slots at an enemy plane moving away from it. The probability of hitting the plane at the first, second, third and fourth slots are 0.4, 0.3, 0.2 and 0.1 respectively. The probability that the gun hits the plane then is NIMCET-2011 (a) 0. 5 (b) 0.7235 (c) 0.6976 (d) 1.0 A random variable X has the following probability distribution x 0 1 2 3 4 5 6 7 8 P(X = x) a 3a 5a Then the value of ‘a’ is 22. 23. 26. 27. 28. 29. 11a 13a 15a 1 8 (B) 2 7 (C) 1 625 (D) 1 2 (b) 49 50 (c) 101 101 (d) 51 101 30. A dice is tossed 5 times. Getting an odd number is considered a success. Then the variance of distribution of success is KIITEE-2010 (a) 8/3 (b) 3/8 (c) 4/5 (d) 5/4 31. If A and B are events such 3 P A B , 4 that 2 1 P A B , P A , then P A B is 3 4 32. 33. 34. KIITEE-2010 (a) 5/12 (b) 3/8 (c) 5/8 (d) 1/4 If A and B are any two mutually exclusive events, then P(A|AB) is equal to (PGCET– 2009) (a) P(AB) (b) P(A)/(P(A) + P(B)) (c) P(B)/P(AB) (d) None of these A man has 5 coins, two of which are double – headed, one is double – tailed and two are normal. He shuts his eyes, picks a coin at random, and tosses it. The probability that the lower face of the coin is a head is (NIMCET – 2009) (a) 1/5 (b) 2/5 (c) 3/5 (d) 4/5 A and B are independent witnesses in a case. The probability that A speaks the truth is ‘x’ and that B speaks the truth is ‘y’. If A and B agree on a certain statement, the probability that the statement is true is (NIMCET – 2009) (a) (c) 35. xy xy (1 x)(1 y ) (b) 1 x 1 y xy 1 x 1 y (d) 17a 36. 37. 3N 1 N 1 5N 3 4N 3 (B) (C) (D) N 9N 3 3N 9N 3 38. Probability of happening of an event A is 0.4 Probability that in 3 independent trials, event A happens atleast once is:PU CHD-2009 (a) 0.064 (b) 0.144 (c) 0.784 (d) 0.4 A die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then P(A B) is : PU CHD-2009 (a) 3/5 (b) 0 (c) 1 (d) 1/6 India plays two matches each with West Indies and Australia. In any match the probabilities of India getting points 0, 1 and 2 are 0.45, 0.05 and 0.50 respectively. Assuming that the outcomes are independent, the probability f India getting at least 7 points is NIMCET-2010 (a) 0.8750 (b) 0.0875 (c) 0.0625 (d) 0.0250 A coin is tossed three times The probabilities of getting head and tail alternatively is NIMCET-2010 (a) 1/11 (b) 2/3 (c) 3/4 (d) 1/4 One hundred identical coins, each with probability P of showing up a head, are tossed. If 0 < p < 1 and if the probability of heads on 39. 40. 41. 42. 3 1 x 1 y xy and P ( A ) 1 . 4 Then events A and B are (NIMCET – 2009) (a) independent but not equally likely (b) mutually exclusive and independent (c) equally likely and mutually exclusive (d) equally likely but not independent. The probability that a man who is 85 yrs. old will die before attaining the age of 90 is 1/3. A1, A2, A3 and A4 are four persons who are 85 yrs. old. The probability that A1 will die before attaining the age of 90 and will be the first to die is (NIMCET – 2009) (a) 16 625 xy 1 x 1 y Let A and B be two events such that 1 1 P ( A B ) , P ( A B) 6 4 The numbers X and Y are selected at random (without replacement) from the set (1, 2, .....3N). The probability that x2 – y2 is divisible by 3 is : PU CHD-2010 (A) 25. 9a (a) NIMCET-2011 (a) 1/81 (b) 2/82 (c) 5/81 (d) 7/81 Three coins are thrown together. The probability of getting two or more heads is BHU-2011 (a) 1/4 (b) 1/2 (c) 2/3 (d) 3/8 If four positive integers are taken at random and are multiplied together, then the probability that the last digit is 1, 3, 7 or 9 is : PU CHD-2010 (A) 24. 7a exactly 50 coins is equal to that of heads on exactly 51 coins then the value of p, is NIMCET-2010 65 81 (b) 13 81 (c) 65 324 (d) 13 108 An anti aircraft gun can take a maximum of four shots at an enemy plane moving away from it. The probabilities of hitting the plane at first, second, third and fourth shot are 0.4, 0.3, 0.2 and 0.1 respectively. The probability that the gun hits the plane then is (MCA : NIMCET – 2009) (a) 0.6972 (b) 0.6978 (c) 0.6976 (d) 0.6974 Let A = [2, 3, 4, …., 20, 21] number is chosen at random from the set A and it is found to be a prime number. The probability that it is more than 10 is (MCA : KIITEE – 2009) (a) 9/10 (b) 1/5 (c) 1/10 (d) None of these Find the probability that a leap year will contain either 53 Tuesday or 53 Wednesdays. HYDERABAD CENTRAL UNIVERSITY - 2009 (a) 1/5 (b) 2/5 (c) 2/3 (d) 3/7 Probability that atleast one of A and B occurs is 0.6. If A and B occur simultaneously with probability 0.3, then P(A') + P(B') is HYDERABAD CENTRAL UNIVERSITY - 2009 (a) 0.9 (b) 1.15 (c) 1.1 (d) 2 The sum of two positive real numbers is 2a. The probability that product of these two numbers is not less than 3/4 times the greatest possible product is HYDERABAD CENTRAL UNIVERSITY - 2009 (a) 1/2 (b) 1/3 (c) 1/4 (d) 9/16 If two events A and B such that P(A') = 0.3, P(B) = 0.5 and P(A B) = 0.3, then P(B/AB') is : NIMCET - 2008 (a) 1/4 (b) 3/8 (c) 1/8 (d) None INFOMATHS/MCA/MATHS/OLD QUESTIONS INFOMATHS 43. 44. A pair of unbiased dice is rolled together till a sum of either 5 or 7 is obtained. The probability that 5 comes before 7 is. NIMCET - 2008 (a) 3/5 (b) 2/5 (c) 4/5 (d) None A letter is taken at random from the letters of the word ‘STATISTICS’ and another letter is taken at random from the letters of the word ‘ASSISTANT’. The probability that they are the same letter is. NIMCET - 2008 (a) 45. 46. 47. (c) 49. 13 90 (c) 19 90 45 3 2 4 90 2 (b) 1 132 (b) 1 44 (c) 5 132 (a) 54. 56. 57. 58. 63. 64. 2 (d) 7 132 66. 1 1 , 3 4 and 1 . The probability that exactly one 5 5 12 (b) 7 30 (c) 13 30 (d) 3 5 67. 1 6 (b) 2 3 (c) 625 1296 (d) 69. 671 1296 70. 3 10 (b) 7 10 (c) 24 91 (d) 71. 72. 73. 67 91 Probability of four digit numbers, which are divisible by three, formed out of digits 1, 2, 3, 4, 5 is : MP COMBINED – 2008 (a) 1/5 (b) 1/4 (c) 1/3 (d) 1/2 Let A and B be two events with P(A) = 1/2, P(B) = 1/3 and P(A B) = 1/4 , What is P(A B)? KARNATAKA - 2007 (a) 3/7 (b) 4/7 (c) 7/12 (d) 9/122 If three unbiased coins are tossed simultaneously then the probability of getting exactly two heads is ICET - 2007 (a) 1/8 (b) 2/8 (c) 3/8 (d) 4/8 A person gets as many rupees as the number he gets when an unbiassed 6 – faced die is thrown. If two such dice are thrown the probability of getting Rs. 10 is. ICET - 2007 (a) 1/12 (b) 5/12 (c) 13/10 (d) 19/10 76. 4 31 256 (d) 37 256 7 12 (b) 11 12 (c) 1 2 (d) 5 6 1 12 (b) 1 15 (c) 2 27 (d) 1 10 (e) 1 20 3 14 (b) 1 2 (c) 3 13 (d) 1 3 16 256 (b) 1 286 (c) 37 256 (d) 28 256 1 13 2 (b) 3 9 16 (c) 10 (d) N.O.T. If P(A' B') is equal to 19/60 then P(AB) is equal to UPMCAT Paper – 2002 (a) 75. (c) Prob. of getting an odd number or a no. less than 4 in throwing a dice is : MP– 2004 (a) 1/3 (b) 2/3 (c) 1/2 (d) 3/5 Given A and B are mutually exclusive events. IFP (B) = 0. 15, P(A B) = 0.85, P(A) is equal to UPMCAT Paper – 2002 (a) 0.65 (b) 0.3 (c) 0.70 (d) N.O.T. In a pack of 52 cards, the probability of drawing at random such that it is diamond or card king is : UPMCAT Paper – 2002 (a) 1/26 (b) 4/13 (c) 3/13 (d) 1/4 Given A and B are mutually exclusive events. if: P (A B) = 0.8, P(B) = 0.2 then P(A) is equal to UPMCAT–2002 (a) 0.5 (b) 0.6 (c) 0.4 (d) N.O.T. Two dice are thrown once the probability of getting a sum 9 is given by : UPMCAT Paper – 2002 (a) 1/12 (b) 1/18 (c) 1/6 (d) N.O.T. In a pack of 52 cards. Two cards are drawn at random. The probability that it being club card is : UPMCAT Paper – 2002 (a) 74. 29 256 The probability of getting atleast 6 head in 8 trials is: MP– 2004 (a) 68. (b) The probabilities that a husband and wife will be alive 20 years from now are given by 0.8 and 0.9 respectively. What is the probability that in 20 years at least one, will be alive? Karnataka PG-CET : Paper – 2006 (a) 0.98 (b) 0.02 (c) 0.72 (d) 0.28 A bag contains 4 white and 3 black balls and a second bag contains 3 white and 3 black balls. If a ball is drawn from each of the bags, then the probability that both are of same colour is : MP Paper – 2004 (a) MP COMBINED – 2008 39 256 A and B play a game of dice. A throws the die first. The person who first gets a 6 is the winner. What is the probability that A wins? PUNE Paper – 2007 (a) 6/11 (b) 1/2 (c) 5/6 (d) 1/6 A player is going to play a match either in the morning or in the afternoon or in the evening all possibilities being equally likely. The probability that he wins the match is 0.6, 0.1 and 0.8 according as if the match is played in the morning, afternoon or in the evening respectively. Given that he has won the match, the probability that the match was played in the afternoon is IP Univ. Paper – 2006 (a) 65. and the probability that neither of them occurs is 1/6. If two dice are tossed the probability of getting the sum at least 5 is PUNE Paper – 2007 (a) An untrue coin is such that when it is tossed the chances of appearing head is twice the chances of appearance of tail. The chance of getting head in one toss of the coin is : MP COMBINED – 2008 (a) 1/3 (b) 1/2 (c) 2/3 (d) 1 The probability of randomly chosing 3 defectless bulbs from 15 electric bulbs of which 5 bulbs are defective, is : MP COMBINED – 2008 (a) 55. 1 90 4 62. 1 3 Then the probability of occurrence of A is. ICET – 2005 (a) 5/6 (b) 1/2 (c) 1/12 (d) 1/18 8 coins are tossed simultaneously. The probability of getting atleast six heads is ICET – 2005 (a) Different words are written with the letters of PEACE. The probability that both E’s come together is : MP COMBINED – 2008 (a) 1/3 (b) 2/5 (c) 3/5 (d) 4/5 The probability of throwing 6 at least one in four throws of a die is: MP COMBINED – 2008 (a) 53. 61. Probabilities of three students A, B and C to pass an examination student will pass is: 52. 5 8 (d) None 210 are respectively 51. (d) Let E be the set of all integers with 1 in their units place. The probability that a number n chosen from [2, 3, 4, … 50] is an element of E is ICET - 2007 (a) 5/49 (b) 4/49 (c) 3/49 (d) 2/49 A and B independent events. The probability that both A and B occur is Two balls are drawn at random from a bag containing 6 white, 4 red and 5 black balls. The probability that both these balls are black, is : MP COMBINED – 2008 (a) 1/21 (b) 2/15 (c) 2/21 (d) 2/35 6 boys and 6 girls sit in a row randomly. The probability that all the girls sit together is : MP COMBINED – 2008 (a) 50. (b) 60. A six faced die is a biased one. It is thrice more likely to show an odd number than to show an even number. It is thrown twice. The probability that the sum of the numbers in the two throws is even, is. NIMCET - 2008 (a) 4/8 (b) 5/8 (c) 6/8 (d) 7/8 A letter is known to have come from either TATANAGAR or CALCUTTA. On the envelope, just two consecutive letters, TA, are visible. The probability that the letter has come from CALCUTTA is NIMCET - 2008 (a) 4/11 (b) 1/3 (c) 5/12 (d) None A card is drawn from a pack. The card is replaced and the pack is reshuffled. If this is done six times, the probability that 2 hearts, 2 diamonds and 2 club cards are drawn is. KIITEE – 2008 (a) 48. 1 45 59. 41 60 (b) 37 60 (c) 31 60 (d) N.O.T. If the events A and B are mutually exclusive then P (A B) is given by : UPMCAT Paper – 2002 (a) P(A) + P(B) (b) P(A)P(B) (c) P(A) P(B/A) (d) N.O.T. If A and B are two events, the prob. that exactly one of them, occurs in given by: UPMCAT Paper – 2002 INFOMATHS/MCA/MATHS/OLD QUESTIONS (c) P A B P A B (a) 77. 78. P A B P A B (b) P A B P A B INFOMATHS 1 11 D 21 A 31 A 41 A 51 B 61 D 71 C (d) None of these A bag contains 6 red and 4 green balls. A fair dice is rolled and a number of balls equal to that appearing on the dice is chosen from the urn at random. The probability that all the balls selected are red is. NIMCET – 2008 (a) 1/3 (b) 3/10 (c) 1/8 (d) none A number x is chosen at random from (1, 2, …. 10). The probability that x satisfies the equation (x – 3) (x – 6) (x – 10) = 0 is ICET - 2007 (a) 2/5 (b) 3/5 (c) 3/10 (d) 7/10 2 12 A 22 B 32 B 42 D 52 D 62 D 72 D 3 13 4 B 14 A D 23 D 33 C 43 D 53 C 63 A 73 D 24 C 34 A 44 C 54 C 64 B 74 A PROBABILITY 5 6 C D 15 16 + B 25 26 C 35 36 A C 45 46 B A 55 56 A C 65 66 A B 75 76 A D 7 B 17 27 B 37 C 47 B 57 C 67 D 77 D 8 A 18 28 D 38 D 48 C 58 A 68 B 78 C 9 D 19 29 D 39 D 49 A 59 B 69 B 10 A 20 C 30 D 40 C 50 C 60 B 70 B ANSWERS WORKSHEET-2 (OLD QUESTIONS) 1 C 11 C 21 C 31 B 41 B 2 A 12 B 22 A 32 C 42 A PERMUTATIONS & COMBINATIONS 3 4 5 6 7 8 9 C C B A A A D 13 14 15 16 17 18 19 D A A B C C D 23 24 25 26 27 28 29 A C D C A C C 33 34 35 36 37 38 39 D C C A C B D 43 44 45 46 47 48 D D B B D D 10 C 20 A 30 C 40 B 5 INFOMATHS/MCA/MATHS/OLD QUESTIONS