Permutations & Combinations PYQs Set 5 (PDF)

Set 5 of 11 · Questions 121-150 of 315

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Mere Teacher · Previous Year Questions JEE Main Mathematics · Permutations & Combinations · Set 5 (Q121-150)
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121. $The number of 4 digit numbers without repetition that can be formed using the digits 1, 2, 3, 4, 5, 6, 7 in which each number has two odd digits and two even digits is$ (1) $432$ (2) $450$ (3) $436$ (4) $454$ 122. $If " C_{r} denotes the number of combinations of ' n' things taken ' r' at a time, then the expression^{n} C_{r + 1} +^{n} C_{r - 1} + 2^{n} C_{r} equals$ (1) $^{n + 2} C_{r}$ (2) $^{n + 2} C_{r + 1}$ (3) $^{n + 1} C_{r}$ (4) $^{n + 1} C_{r + 1}$ 123. $The number of integers x, y, z, w satisfying x + y + z + w = 25 and x, y, z \geq - 1, w \geq 1, is$ (1) $^{28} C_{3} \dots + 1$ (2) $^{30} C_{3}$ (3) $^{29} C_{3}$ (4) $^{31} C_{3}$ 124. $If all the words with or without meaning made using all the letters of the word "NAGPUR" are arranged as in a dictionary, then the word at 315^{th} position in this arrangement is :$ (1) $NRAGUP$ (2) $NRAPUG$ (3) $NRAPGU$ (4) $NRAGPU$ 125. $If the letters of the word "SACHIN" are arranged in all possible ways and these words are written out as in dictionary, then the word "SACHIN" appears at serial number -$ (1) $602$ (2) $603$ (3) $600$ (4) $601$ 126. $A team of 5 students is to be selected from 12 students. If two particular students are to be included in that team, then the number of ways that such team can be selected is$ (1) $792$ (2) $180$ (3) $120$ (4) $90$ 127. $There are 20 straight lines in a plane such that no two of them are parallel and no three of them are concurrent. If their points of intersection are joined, then the number of new line segments formed are$ (1) $3420$ (2) $14535$ (3) $2907$ (4) $17955$ 128. $The number of 3 - digit numbers, that are divisible by either 3 or 4 but not divisible by 48, is$ (1) $472$ (2) $432$ (3) $507$ (4) $400$ 129. $The English alphabets have 5 vowels and 21 consonants. How many words with two different vowels and two different consonants can be formed from the alphabet?$ (1) $2100 \times 2!$ (2) $210 \times 2!$ (3) $210 \times 4!$ (4) $2100 \times 4!$ 130. $There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a total of 5 questions, choosing at least one question from each section. Then the number of ways, in which the candidate can choose the questions, is:$ (1) $2250$ (2) $3000$ (3) $1500$ (4) $2255$ 131. $The number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2 apples, is$ (1) $406$ (2) $130$ (3) $142$ (4) $136$ 132. $Let S = 1, 2, 3, 4, 5, 6, 7, 8, 9 . Let x be the number of 9 -digit numbers formed using the digits of the set S such that only one digit is repeated and it is repeated exactly twice. Let y be the number of 9-digit numbers formed using the digits of the set S such that only two digits are repeated and each of these is repeated exactly twice. Then,$ (1) $56 x = 9 y$ (2) $29 x = 5 y$ (3) $45 x = 7 y$ (4) $21 x = 4 y$ 133. $The number of ways in which four letters can be put in four addressed envelopes so that no letter goes into envelope meant for it is$ (1) $8$ (2) $12$ (3) $16$ (4) $9$ 134. $A natural number n such that n! ends in exactly 1000 zeros is$ (1) $4010$ (2) $4000$ (3) $4009$ (4) $4004$ 135. $Group A consists of 7 boys and 3 girls, while group B consists of 6 boys and 5 girls. The number of ways, 4 boys and 4 girls can be invited for a picnic if 5 of them must be from group A and the remaining 3 from group B, is equal to:$ (1) $8750$ (2) $9100$ (3) $8925$ (4) $8575$ 136. $a, b, c are three particular speakers among the 10 speakers of a meeting. The number of ways of arranging all the 10 speakers on the dias in a row so that all the three speakers a, b, c do not sit together is$ (1) $714 (7!)$ (2) $89 (8!)$ (3) $719 (7!)$ (4) $84 (8!)$ 137. $All the letters of the word 'MOTHER' are written in all possible ways and the strings of letters (with or without meaning) so formed are written as in a dictionary order. Then the position of the word 'THROEM' is$ (1) $642$ (2) $648$ (3) $647$ (4) $646$ 138. $The number of ways of distributing 500 dissimilar boxes equally among '50' persons is$ (1) $500! / (10!)^{50} \cdot 50!$ (2) $500! / (50!)^{10} .10 !$ (3) $500! / (50!)^{10}$ (4) $500! / (10!)^{50}$ 139. $The number of odd positive divisors of 67500 is$ (1) $16$ (2) $18$ (3) $20$ (4) $22$ 140. $The total number of 4 -digit numbers whose grealest common divisor with 18 is 3, is$ 141. $There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 are wicketkeepers. The number of ways, a team of 11 players be selected from them so as to include at least 4 bowlers, 5 batsmen and 1 wicketkeeper, is ___$ 142. $Let n be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that all the girls stand consecutively in the queue. Let m be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that exactly four girls stand consecutively in the queue. Then the value of \frac{m}{n} is$ 143. $There are 5 students in class 10,6 students in class 11 and 8 students in class 12. If the number of ways, in which 10 students can be selected from them so as to include at least 2 students from each class and at most 5 students from the total 11 students of class 10 and 11 is 100k, then k is equal to$ 144. $A class contains b boys and g girls. If the number of ways of selecting 3 boys and 2 girls from the class is 168, then b + 3 g is equal to$ 145. $Let S = (m, n) : m, n \in 1, 2, 3, \dots \dots, 50 . If the number of elements (m, n) in S such that 6^{m} + 9^{n} is a multiple of 5 is p and the number of elements (m, n) in S such that m + n is a square of a prime number is q , then p + q is equal to____.$ 146. $The number of 6-letter words, with or without meaning, that can be formed using the letters of the word MATHS such that any letter that appears in the word must appear at least twice, is$ 147. $Let f(n) denote the number of different ways in which the positive integer 'n' can be expressed as sum of 1s and 2s. for example f(d) = 5 {2 + 2, 2 + 1 + 1, 1 + 2 + 1, 1 + 1 + 2, 1 + 1 + 1 + 1}. Now that order of 1s and 2s is important. Then determine f(f(6))$ 148. $The total number of 3-digit numbers, whose sum of digits is 10, is$ 149. $The lines L_{1}, L_{2}, \dots, I_{20} are distinct. For n = 1, 2, 3, \dots, 10 all the lines L_{2 n - 1} are parallel to each other and all the lines L_{2 n} pass through a given point P . The maximum number of points of intersection of pairs of lines from the set (L_{1}, L_{2}, \dots, L_{20}) is equal to :$ 150. $The number of 4-digit numbers which are neither multiple of 7 nor multiple of 3 is .$