Permutations & Combinations PYQs Set 4 (PDF)

Set 4 of 11 · Questions 91-120 of 315

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Mere Teacher · Previous Year Questions JEE Main Mathematics · Permutations & Combinations · Set 4 (Q91-120)
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91. $The number of ways of arranging all the letters of the word "SUNITHA" so that the vowels always occupy the first, middle and last places is$ (1) $5040$ (2) $24$ (3) $3$ (4) $144$ 92. $A committee of 11 members is to be formed from 8 malesand 5 females. If m is the number of ways the committee is formed with at least 6 males and n is the number of waysthe committee is formed with at least 3 females, then:$ (1) $m + n = 68$ (2) $m = n = 78$ (3) $n = m - 8$ (4) $m = n = 68$ 93. $There are 7 identical white balls and 3 identical black balls. The number of distinguishable arrangements in a row of all the balls, so that no two black balls are adjacent is$ (1) $120$ (2) $89 \cdot (8!)$ (3) $56$ (4) $42 \times 5^{4}$ 94. $If n is the number of ways five different employees can sit into four indistinguishable offices where any office may have any number of persons including zero, then n is equal to:$ (1) $47$ (2) $53$ (3) $51$ (4) $43$ 95. $The number of 5 card combinations out of a deck of 52 cards if there is exactly one are in each combination is$ (1) $823764$ (2) $363428$ (3) $778320$ (4) $542380$ 96. $All the words that can be formed using alphabets A, H, L, U, R are written as in dictionary (no alphabet is repeated). Then the rank of the word RAHUL is \dots\dots..$ (1) $70$ (2) $71$ (3) $73$ (4) $74$ 97. $The number of different 5 - digit numbers greater than 50000 that can be formed using the digits 0 , 1, 2, 3, 4, 5, 6, 7, such that the sum of their first and last digits should not be more than 8, is$ (1) $4608$ (2) $5720$ (3) $5719$ (4) $4607$ 98. $The letters of the word OUGHT are written in all possible ways and these words are arranged as in a dictionary, in a series. Then the serial number of the word TOUGH is$ (1) $89$ (2) $84$ (3) $86 `$ (4) $79$ 99. $The number of seven - digit integers with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only is$ (1) $77$ (2) $42$ (3) $35$ (4) $82$ 100. $The number of divisors of 7! is$ (1) $24$ (2) $72$ (3) $64$ (4) $60$ 101. $If \frac{^{n + 1} C _{r + 1}}{^{n + 1} C _{r}} = \frac{n - r + 1}{m}, then m =$ (1) $r$ (2) $r - 1$ (3) $r + 1$ (4) $1 - r$ 102. $The number of sequences of ten terms, whose terms are either 0 or 1 or 2 , that contain exactly five 1 s and exactly three 2 s , is equal to :$ (1) $360$ (2) $2520$ (3) $1820$ (4) $45$ 103. $A question paper consists of two sections having 3 and 4 questions respectively. The following note is given on the paper. "It is not necessary to attempt all the questions. One question from each section is compulsory". In how many ways can a candidate select the questions?$ (1) $105$ (2) $210$ (3) $27$ (4) $25$ 104. $Let S = {1, 2, 3....., 100}. The number of non-empty subsets A of S such that the product of element in A is even is :$ (1) $2^{50} + 1$ (2) $2^{50} (2^{50} -1)$ (3) $2^{100} - 1$ (4) $2^{50} -1$ 105. $Everybody in a room shakes hands with everybody else. The total number of handshakes is 45 . The total number of persons in the room is$ (1) $9$ (2) $10$ (3) $5$ (4) $15$ 106. $There are 4 oranges, 5 apples, 7 mangoes in a fruit basket. The number of ways of selecting at least one fruit from among the fruits in the basket is$ (1) $210$ (2) $240$ (3) $209$ (4) $239$ 107. $A polygon has 54 diagonals. The number of sides of this polygon is\dots\dots\dots..$ (1) $12$ (2) $15$ (3) $16$ (4) $9$ 108. $If^{10} P_{r} = 604800 and^{10} C_{r} = 120 then r =$ (1) $14$ (2) $7$ (3) $8$ (4) $16$ 109. $A and B are non-singleton sets and n (A \times B) = 35 . If B \subset A then^{n (A)} C_{n (B)} =$ (1) $28$ (2) $35$ (3) $42$ (4) $21$ 110. $Let 0 \leq r \leq n . If^{n + 1} C_{r + 1} :^{n} C_{r} :^{n - 1} C_{r - 1} = 55 : 35 : 21, then 2 n + 5 r is equal to:$ (1) $50$ (2) $62$ (3) $55$ (4) $60$ 111. $Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys A and B, who refuse to be the members of the same team, is:$ (1) $500$ (2) $200$ (3) $300$ (4) $350$ 112. $A person writes letters to 6 friends and addresses the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that at least two of them are in the wrong envelopes? Notation: D_{n} = n! (\sum_{i = 0}^{n} \frac{( - 1 ) ^{i}}{i !})$ (1) $^{6} C_{4} \cdot D_{2}$ (2) $\sum_{r = 3}^{6}^{6} C_{6 - r} \cdot D_{r}$ (3) $\sum_{r = 2}^{6}^{6} C_{6 - r} \cdot D_{r}$ (4) $^{6} C_{1} D_{5} +^{6} C_{0} \cdot D_{6}$ 113. $If 3 sisters and 8 other girls are together playing a game, then the number of ways in which all the girls are seated around a circle such that the three sisters are not seated together, is$ (1) $11! \times 8$ (2) $8! \times 504$ (3) $7! \times 210$ (4) $8! \times 84$ 114. $The number of 4 letter words (with or without meaning) that can be formed from the eleven letters of the word EXAMINATION is$ 115. $The number of 5-digit natural numbers, such that the product of their digits is 36, is$ 116. $The number of 9 digit numbers, that can be formed using all the digits of the number 123412341 so that the even digits occupy only even places, is ________$ 117. $The number of 3-digit numbers, formed using the digits 2, 3, 4, 5 and 7 , when the repetition of digits is not allowed, and which are not divisible by 3 , is equal to_____$ 118. $If the letters of the word MOTHER be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the word MOTHER is:$ 119. $In a row, there are 81 rooms, whose door no. are 1,2,.......,81, initially all the door are closed. A person takes 81 round of the row, numbers as 1^{s t} round, 2^{n d} round ........ 8 1^{t h} round. In each round, he interchange the position of those door number, whose number is multiple of the round number. Find out after 8 1^{s t} round, How many doors will be open.$ 120. $The number of seven digit positive integers formed using the digits 1, 2,3 and 4 only and sum of the digits equal to 12 is________.$