Permutations & Combinations PYQs Set 2 (PDF)

Set 2 of 11 · Questions 31-60 of 315

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Mere Teacher · Previous Year Questions JEE Main Mathematics · Permutations & Combinations · Set 2 (Q31-60)
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31. $If a person has 3 coins of different denominations, the number of different sums can be formed is$ (1) $3$ (2) $7$ (3) $8$ (4) $3!$ 32. $Let Tn denotes the number of triangles which can be formed using the vertices of a regular polygon of n sides. If Tn+1 - Tn = 21, then n equal$ (1) $5$ (2) $7$ (3) $6$ (4) $4$ 33. $The number of ways in which 5 girls and 3 boys can be seated in a row so that no two boys are together is$ (1) $14040$ (2) $14440$ (3) $14000$ (4) $14400$ 34. $The number of 5 -letter words that can be formed by using the letters of the word SARANAM is$ (1) $1120$ (2) $6720$ (3) $480$ (4) $720$ 35. $Among the positive divisors of the number 12600 , if n_{1} is the number of divisors which are multiples of 3 and n_{2} is the number of divisors which are multiples of 14 , then n_{1} + n_{2} =$ (1) $75$ (2) $57$ (3) $51$ (4) $33$ 36. $A question paper has two sections A and B in wrincis section-A had 8 questions and section- B has 6 questions. A student has to answer a total of 10 questions, choosing atleast 4 questions from section-A and atleast 3 questions from section-B. Then the number of ways a student can answer that paper is$ (1) $800$ (2) $820$ (3) $840$ (4) $986$ 37. $In a group of 3 girls and 4 boys, there are two boys B_{1} and B_{2} . The number of ways, in which these girls and boys can stand in a queue such that all the girls stand together, all the boys stand together, but B_{1} and B_{2} are not adjacent to each other, is :$ (1) $96$ (2) $144$ (3) $120$ (4) $72$ 38. $Let x denote the number of ways of arranging m boys and m girls in a row so that no two boys sit together. If y and z give the number of ways of arranging m boys and m girls in a row and around a circular table respectively so that boys and girls sit alternately, then x : y : z =$ (1) $m + 1 : m : m - 1$ (2) $3 : 2 : 1$ (3) $m - 1 : m : 2$ (4) $(m + 1) m : 2 m : 1$ 39. $In how many ways can the letters of the word "MULTIPLE" be arranged keeping the position of the vowels fixed?$ (1) $60$ (2) $360$ (3) $600$ (4) $300$ 40. $How many chords can be drawn through 21 points on a circle?$ (1) $105$ (2) $210$ (3) $420$ (4) $840$ 41. $The number of ways of distributing eight identical rings to three different girls so that every girl gets at least one rings is$ (1) $21$ (2) $120$ (3) $^{8} P_{3}$ (4) $^{8} P_{3} - 6$ 42. $The number of 6 digit numbers that can be formed using the digits 0, 1, 2, 5, 7 and 9 which are divisible by 11 and no digit is repeated, is:$ (1) $72$ (2) $60$ (3) $48$ (4) $36$ 43. $If all permutations of the letters of the word MASK are arranged in the order as in dictionary with or without meaning which one of the following is 19^{th} word?$ (1) $KAMS$ (2) $AKMS$ (3) $SAMK$ (4) $SAKM$ 44. $60 words can be made using all the letters of the word BHBJO, with or without meaning. If these words are written as in a dictionary, then the 50^{th} word is :$ (1) $JBBOH$ (2) $OBBJH$ (3) $OBBHJ$ (4) $HBBJO$ 45. $A scientific committee is to formed from 6 Indians and 8 foreigners, which includes at least 2 Indians anddouble the number of foreigners as Indians. Then the number of ways, the committee can be formed is:$ (1) $560$ (2) $1050$ (3) $1625$ (4) $575$ 46. $A group of students comprises of 5 boys and n girls. If the number of ways, in which a team of 3 students can randomly be selected from this group such that there is at least one boy and at least one girl in each team, is 1750, then n is equal to:$ (1) $28$ (2) $27$ (3) $25$ (4) $24$ 47. $There are 12 points in a plane, no three of which are in the same straight line, except 5 points which are collinear. Then the total number of triangles that can be formed with the vertices at any three of these 12 points is$ (1) $230$ (2) $210$ (3) $200$ (4) $220$ 48. $The number of words, which can be formed using all the letters of the word "DAUGHTER", so that all the vowels never come together, is$ (1) $36000$ (2) $37000$ (3) $34000$ (4) $35000$ 49. $The number of ways in which 6 men and 4 women can be seated around a table so that a particular man and a particular woman never sit adjacent to each other is$ (1) $9 !$ (2) $7 \times 8!$ (3) $8 \times 8!$ (4) $6 \times 7!$ 50. $The sum of all positive divisors of 242 except 1 and itself is$ (1) $156$ (2) $242$ (3) $342$ (4) $399$ 51. $Statement-1 : The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is 9 C_{3} . Statement-2 : The number of ways of choosing any 3 places from 9 different places is 9 C_{3} .$ (1) $Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.$ (2) $Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.$ (3) $Statement-1 is true, Statement-2 is false.$ (4) $Statement-1 is false, Statement-2 is true.$ 52. $The number of ways of arranging the letters of the word LINEAR so that the letters N and R do not come together and E and A come together is$ (1) $80$ (2) $60$ (3) $10$ (4) $144$ 53. $The number of seven digits odd numbers, that can be formed using all the seven digits 1, 2, 2, 2, 3, 3, 5 is _____$ 54. $The number of times the digit 3 will be written when listing the integers from 1 to 1000 is:$ 55. $Mr. Sibbal walk up 16 steps, going up either 1 or 2 steps with each stride there is explosive material on the 8th step so he cannot step there. Then number of ways in which Mr. Sibbal can go up.$ 56. $In an examination of Mathematics paper, there are 20 questions of equal marks and the question paper is divided into three sections: A, B and C. A student is required to attempt total 15 questions taking at least 4 questions from each section. If section A has 8 questions, section B has 6 questions and section C has 6 questions, then the total number of ways a student can select 15 questions is________$ 57. $The number of ways of getting a sum 16 on throwing a dice four times is_____$ 58. $The total number of 3-digit numbers, whose greatest common divisor with 36 is 2, is______.$ 59. $Let m and n, (m < n), be two 2-digit numbers. Then the total numbers of pairs (m, n), such that gcd (m, n) = 6, is ________$ 60. $The integers from 1 to 1000 are written in order around a circle. Starting at 1, every fifteenth number is marked (that is 1, 16, 31, .... etc.). This process in continued untill a number is reached which has already been marked, then find number of unmarked numbers$