Mathematics-3.Unit-05-Permutation & Combination Test

1. Total number of 5 digit numbers having all different digits and divisible by 4 that can be formed using the digits {1, 3, 2, 6, 8, 9}, is equal to (A) 192 (B) 32 (C) 1152 (D) 384 2. The number of ways in which 5 colour beads can be used to form a necklace, is (A) 15 (B) 20 (C) 12 (D) 10 3. Total number of ways in which the letters of the word ‘MISSISSIPPI’ be arranged, so that any two S’s are separated, is equal to: (A) 7350 (B) 3675 (C) 6300 (D) None of these 4. Number of six letters words that can be formed using the letters of word ‘ASSIST’ in which S’s alternate with other letter is (A) 12 (B) 24 (C) 18 (D) none of these 5. Total number of words that can be formed using all letters of the word ‘BRIJESH’ that neither begins with ‘I’ nor ends with ‘B’ is equal to: (A) 3720 (B) 4920 (C) 3600 (D) 4800 6. The number of zeros at the end of (127)! is (A) 31 (B) 30 (C) 0 (D) 10 7. Total number of 5 digit number, having all different digits and divisible by 3, that can be formed using the digits {0, 1, 2, 3, 4, 5}, is equal to: (A) 120 (B) 213 (C) 96 (D) 216 8. The number of ways in which N positive signs and n negative signs (N ≥ n) may be placed in a row so that no two negative signs are together is (A) NCn (B) N+1Cn (C) N! (D) N+1Pn 9. Total number of words that can be formed using all letters of the word ‘ANSHUMAN’ is equal to: (A) (B) (C) (D) 10. Everybody in a room shakes hand with everybody else. The total numbers of handshakes is 66. The total number of persons in the room is (A) 11 (B) 12 (C) 13 (D) 14 11. The number of numbers that are less than 1000 that can be formed using the digits 0, 1, 2, 3, 4, 5 such that no digit is being repeated in the formed number, is equal to: (A) 130 (B) 131 (C) 156 (D) 155 12. , then a = (A) 2 (B) 3 (C) 4 (D) none of these 13. men and women are to be seated in a row so that no two women sit together. If , then total number of ways in which they can be seated, is equal to: (A) (B) (C) (D) 14. If 7 points out of 12 are in same straight line, then number of triangles formed is (A) 19 (B) 158 (C) 185 (D) 201 15. Total number of ways in which four boys and four girls can be seated around a round table, so that no two girls sit together, is equal to: (A) 7! (B) (3!)(4!) (C) (4!)(4!) (D) (3!)(3!) 16. The number of ways in which a mixed double game can be arranged amongst nine married couples so that no husband and his wife play in the same game, is equal to: (A) (B) (C) (D) 17. nCr-3 + 3nCr-2 + 3nCr-1 + nCr is equal to (A) n+2Cr-1 (B) n+2Cr (C) n+2Cr+1 (D) n+3Cr 18. Total number of ways, in which 22 different books can be given to 5 students, so that two students get 5 books each and all the remaining students get 4 book each, is equal to: (A) (B) (C) (D) None of these 19. The sides AB, BC, CA of a triangle ABC have 3, 4, 5 interior points respectively on them. Total number of triangles that can be formed using these points as vertices, is equal to: (A) 135 (B) 145 (C) 178 (D) 205 20. In the next word cup of cricket there will be 12 teams, divided equally in two groups. Teams of each group will play a match against each other. From each group 3 top teams will qualify for the next round. In this round each team will play against others once. Four top teams of this round will qualify for the semifinal round, where each team will play against the other three. Two top teams of this round will go to the final round, where they will play the best of three matches. The minimum number of matches in the next world cup will be (A) 54 (B) 53 (C) 38 (D) none of these 21. Total number of permutations of ‘k’ different things, in a row, taken not more than ‘r’ at a time (each thing may be repeated any number of times) is equal to: (A) (B) (C) (D) 22. A teacher takes 3 children from her class to the zoo at a time as often as she can, but she does not take the same three children to the zoo more than once. She finds that she goes to the zoo 84 times more than a particular child goes to the zoo. The number of children in her class is (A) 12 (B) 10 (C) 60 (D) none of these . 23. A variable name in certain computer language must be either a alphabet or alphabet followed by a decimal digit. Total number of different variable names that can exist in that language is equal to: (A) 280 (B) 290 (C) 286 (D) 296 24. Let A = {x l x is a prime number and x < 30} .The number of different rational numbers whose numerator and denominator belong to A is (A) 90 (B) 180 (C) 91 (D) none of these 25. The total number of ways of selecting 10 balls out of an unlimited number of identical white, red and blue balls is equal to: (A) (B) (C) (D) 26. The number of times of the digits 3 will be written when listing the integer from 1 to 1000 is (A) 269 (B) 300 (B) 271 (D) 302 27. A person predicts the outcome of 20 cricket matches of his home team. Each match can result either in a win, loss or tie for the home team. Total number of ways in which he can make the predictions so that exactly 10 predictions are correct, is equal to: (A) (B) (C) (D) 28. The number of ways of selecting 10 balls out of an unlimited number of white, red, blue and green balls is (A) 270 (B) 84 (C) 286 (D) 86 29. A team of four students is to be selected from a total of 12 students. Total number of ways in which team can be selected such that two particular students refuse to be together and other two particular students wish to be together only, is equal to: (A) 220 (B) 182 (C) 226 (D) None of these 30. The number of ways in which a mixed double game can be arranged amongst 9 married couples if no husband and wife play in the same game is (A) 756 (B) 1512 (C) 3024 (D) none of these.