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Permutations and Combinations

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  1. 151.Let b_1b_2b_3b_4 be a 4-element permutation with b_i1,2,,100 for 1 i4 and b_i b_j for i j,…
  2. 152.The total number of four digit numbers such that each of the first three digits is divisib…
  3. 153.The total number of 4-digit numbers whose greatest common divisor with 18 is 3, is Answer:…
  4. 154.The total number of two digit numbers n, such that 3^n+7^n is a multiple of 10, is Answer:…
  5. 155.The total number of numbers lying between 100 and 1000 that can be formed with the digits …
  6. 156.A natural number has prime factorisation given by n=2^x3^y5^z, where y and z are such that…
  7. 157.The number of seven digit integers with sum of the digits equal to 10 and formed by using …
  8. 158.The total number of positive integral solutions (x,y,z) such that xyz=24 is:
  9. 159.The students S_1,,S_10 are to be divided into 3 groups A, B and C such that each group has…
  10. 160.A scientific committee is to be formed from 6 Indians and 8 foreigners, which includes at …
  11. 161.The sum of all the 4-digit distinct numbers that can be formed with the digits 1, 2, 2 and…
  12. 162.The missing value in the following figure is: Answer: 4
  13. 163.If _r=1^10 r!(r^3+6r^2+2r+5) = (11!), then the value of is equal to: Answer: 160
  14. 164.The number of times the digit 3 will be written when listing the integers from 1 to 1000 i…
  15. 165.Team A consists of 7 boys and n girls, and Team B has 4 boys and 6 girls.
  16. 166.If the sides AB, BC and CA of a triangle ABC have 3, 5 and 6 interior points respectively,…
  17. 167.Consider a rectangle ABCD having 5, 7, 6, 9 points in the interior of the line segments AB…
  18. 168.Words with or without meaning are to be formed using all the letters of the word EXAMINATI…
  19. 169.There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 ar…
  20. 170.If digits are not allowed to repeat in any number formed by using the digits 0, 2, 4, 6, 8…
  21. 171.If ^nP_r = ^nP_r+1 and ^nC_r = ^nC_r-1, then the value of r is equal to:
  22. 172.There are 5 students in class 10, 6 students in class 11 and 8 students in class 12.
  23. 173.Let nN and [x] denote the greatest integer x.
  24. 174.Let n be a non-negative integer.
  25. 175.The sum of all three-digit numbers less than or equal to 500, that are formed without usin…
  26. 176.A number is called a palindrome if it reads the same backward as forward.
  27. 177.Let S=1,2,3,4,5,6,9.
  28. 178.The number of ordered pairs (r,k) for which 6^35C_r = (k^2-3)^36C_r+1, where k is an integ…
  29. 179.An urn contains 5 red marbles, 4 black marbles and 3 white marbles.
  30. 180.If a, b and c are the greatest values of ^19C_p, ^20C_q and ^21C_r respectively, then:
  31. 181.The number of 4 letter words (with or without meaning) that can be formed from the eleven …
  32. 182.Let 25r C_r and C_0+5C_1+9C_2++101C_25=2^25 k, then k is equal to: Answer: 51
  33. 183.If the number of five digit numbers with distinct digits and 2 at the 10th place is 336k, …
  34. 184.Total number of 6-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 app…
  35. 185.Two families with three members each and one family with four members are to be seated in …
  36. 186.The value of (2^1P_0 - 3^2P_1 + 4^3P_2 - up to 51^th term) + (1!-2!+3!-up to 51^th term) i…
  37. 187.If the letters of the word 'MOTHER' be permuted and all the words so formed (with or witho…
  38. 188.The number of words, with or without meaning, that can be formed by taking 4 letters at a …
  39. 189.There are 3 sections in a question paper and each section contains 5 questions.
  40. 190.A test consists of 6 multiple choice questions, each having 4 alternative answers of which…
  41. 191.The total number of 3-digit numbers, whose sum of digits is 10, is: Answer: 54
  42. 192.Let n>2 be an integer.
  43. 193.Consider a class of 5 girls and 7 boys.
  44. 194.The number of natural numbers less than 7,000 which can be formed by using the digits 0,1,…
  45. 195.Let S be the set of all triangles in the xy-plane, each having one vertex at the origin an…
  46. 196.If _i=1^20(^20C_i-1^20C_i+^20C_i-1)^3 = k21, then k equals:
  47. 197.Consider three boxes, each containing 10 balls labelled 1, 2, ..., 10.
  48. 198.There are m men and two women participating in a chess tournament.
  49. 199.The number of four-digit numbers strictly greater than 4321 that can be formed using the d…
  50. 200.A committee of 11 members is to be formed from 8 males and 5 females.