Permutations & Combinations PYQs Set 8 (PDF)

Set 8 of 11 · Questions 211-240 of 315

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Mere Teacher · Previous Year Questions JEE Main Mathematics · Permutations & Combinations · Set 8 (Q211-240)
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211. $The number of different permutations of letters that can be formed by taking 4 letters at a time from the letters of the word 'REPETITION' is$ (1) $210$ (2) $720$ (3) $1398$ (4) $5040$ 212. $Team 'A' consists of 7 boys and n girls and Team 'B' has 4 boys and 6 girls. If a total of 52 single matches can be arranged between these two teams when a boy plays against a boy and a girl plays against a girl, then n is equal to :$ (1) $5$ (2) $2$ (3) $4$ (4) $6$ 213. $The number of values of n \in N for which^{n + 2} C_{2} :^{n + 3} C_{1} = 4 : 2 is$ (1) $0$ (2) $1$ (3) $2$ (4) $3$ 214. $In how many ways can 5 balls be placed in 4 tins if any number of balls can be placed in any tin?$ (1) $^{5} P_{4}$ (2) $^{5} C_{4}$ (3) $4^{5}$ (4) $5^{4}$ 215. $The greatest positive integer which divides (n + 16) (n + 17) (n + 18) (n + 19), for all positive integers n, is$ (1) $6$ (2) $24$ (3) $28$ (4) $20$ 216. $All the letters of the word PUBLIC are written in all possible orders and these words are written as in a dictionary with serial numbers. Then the serial number of the word PUBLIC is$ (1) $576$ (2) $578$ (3) $580$ (4) $582$ 217. $The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one ball is$ (1) $75$ (2) $150$ (3) $210$ (4) $243$ 218. $The number of four-digit numbers formed by using the digits 0, 2, 4, 5 and which are not divisible by 5, is$ (1) $10$ (2) $8$ (3) $6$ (4) $4$ 219. $If^{22} P_{r + 1} :^{20} P_{r + 2} = 11 : 52, then r is equal to$ (1) $3$ (2) $5$ (3) $7$ (4) $9$ 220. $The number of ways is which 3 identical balls can be distributed into 7 distinct bins is$ (1) $49$ (2) $84$ (3) $35$ (4) $42$ 221. $The number of ways in which 3 boys and 2 girls can sit on a bench so that no two boys are adjacent is$ (1) $6$ (2) $10$ (3) $12$ (4) $32$ 222. $The number of seven digit integers, with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only, is$ (1) $55$ (2) $66$ (3) $77$ (4) $88$ 223. $The number of ways, in which 16 oranges can be distributed to four children such that each child gets at least one orange, is$ (1) $455$ (2) $429$ (3) $403$ (4) $384$ 224. $The largest n \in N, for which 7^{n} divides 101 !, is :$ (1) $16$ (2) $15$ (3) $18$ (4) $19$ 225. $The total number of permutations of n different things taken not more than r at a time, when each thing may be repeated any number of times is$ (1) $\frac{n ( n ^{r + 1} - 1 )}{n - 1}$ (2) $\frac{n ^{r + 1} - 1}{n - 1}$ (3) $\frac{n ( n ^{r} - 1 )}{n - 1}$ (4) $\frac{n ^{r} - 1}{n - 1}$ 226. $The number of ways of choosing 10 objects out of 31 objects of which 10 are identical and the remaining 21 are distinct is:$ (1) $2^{20} - 1$ (2) $2^{21}$ (3) $2^{20}$ (4) $2^{20} + 1$ 227. $The number of positive divisors of 252 is$ (1) $9$ (2) $5$ (3) $18$ (4) $10$ 228. $Let S = 1, 2, 3, \dots, 100 The number of non-empty subsets A of S such that the product of elements in A is even is :$ (1) $2^{100} - 1$ (2) $2^{50} (2^{50} - 1)$ (3) $2^{50} - 1$ (4) $2^{50} + 1$ 229. $The sum of all the 4 -digit distinct numbers that can be formed with the digits 1,2,2 and 3 is:$ (1) $26664$ (2) $122664$ (3) $122234$ (4) $22264$ 230. $Find the number of positive unequal integral solution of the equation x + y + z = 20.$ 231. $Let A = {1, a1, a2......al8, 77} be a set of integers with 1 < a1 < a2 < ..... < al8 < 77. Let the set A + A = {x + y :x,y A} contain exactly 39 elements. Then, the value of a1 + a2 +.....+ al8 is equal to_________.$ 232. $Let 5 digit numbers be constructed using the digits 0, 2, 3, 4, 7, 9 with repetition allowed, and are arranged in ascending order with serial numbers. then the serial number of the number 42923 is$ 233. $The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word SYLLABUS such that two letters are distinct and two letters are alike, is$ 234. $The number of 5 digit numbers which are divisible by 4, with digits from the set {1, 2, 3, 4, 5} and the repetition of digits is allowed, is _______.$ 235. $The total number of six digit numbers, formed using the digits 4, 5, 9 only and divisible by 6, is ________$ 236. $All the letters of the word "GTWENTY" are written in all possible ways with or without meaning and these words are written as in a dictionary. The serial number of the word "GTWENTY" IS$ 237. $The number of words (with or without meaning) that can be formed from all the letters of the word “LETTER” in which vowels never come together is :$ 238. $In an examination, there are 5 multiple choice questions with 3 choices, out of which exactly one is correct. There are 3 marks for each correct answer, -2 marks for each wrong answer and 0 mark if the question is not attempted. Then, the number of ways a student appearing in the examination gets 5 marks is .$ 239. $Let S denote the set of 4-digit numbers abcd such that a > b > c > d and P denote the set of 5 -digit numbers having product of its digits equal to 20. Then n (S) + n (P) is equal to____.$ 240. $Let S = {4, 6, 9} and T = {9, 10, 11, ..., 1000}. If A= {a, + + ...+ : k N, ,, , ...,aS}, then the sum of all the elements in the set T - A is equal to______.$