## Permutations and Combinations Quiz-16

As per analysis for previous years, it has been observed that students preparing for JEE MAINS find Mathematics out of all the sections to be complex to handle and the majority of them are not able to comprehend the reason behind it. This problem arises especially because these aspirants appearing for the examination are more inclined to have a keen interest in Mathematics due to their ENGINEERING background.  Furthermore, sections such as Mathematics are dominantly based on theories, laws, numerical in comparison to a section of Engineering which is more of fact-based, Physics, and includes substantial explanations. By using the table given below, you easily and directly access to the topics and respective links of MCQs. Moreover, to make learning smooth and efficient, all the questions come with their supportive solutions to make utilization of time even more productive. Students will be covered for all their studies as the topics are available from basics to even the most advanced..

Q1. If 2n+1P(n-1): 2n-1Pn = 3∶5, then n is equal to
•  4
•  6
•  3
•  8
Solution

Q2. These are 12 volleyball players in a college, out of which a team of 9 players is to be formed. If the captain always remains the same, then in how many ways can the team be formed?
•  36
•  108
•  99
•  165
Solution

Q3. How many numbers consisting of 5 digits can be formed in which the digits 3, 4 and 7 are used only once and the digit 5 is used twice?
• 30
•  60
•  45
•  90
Solution

Q4. How many numbers between 5000 and 10,000 can be formed using the digits 1,2,3,4,5,6,7,8,9, each digit appearing not more than once in each number?
•  8P3
•  8C8
•  5!×8C3
•  5!×8C3
Solution

Q5. The number of ordered triplets of positives integers which are solutions of the equations z + y + z=100, is
•  6005
•  4851
•  5081
•  None of these
Solution

Q6. In an election there are 8 candidates, out of which 5 are to be chosen. If a voter may vote for any number of candidates but not greater than the number to be choosen, Then in how many ways can a voter vote?
•  216
•  114
•  218
•  None of these
Solution

Q7. Sixteen men compete with one another in running swimming and riding. How many prize lists could be made if there were altogether 6 prizes of different values, one for running, 2 for swimming and 3 for riding?
•  16×15×14
•  163×152×14
•  163×15×142
•  162×15×14

Solution

Q8.The total number of all proper factors of 75600 is
•  120
•  119
•  118
•  None of these

Solution

Q9. Ten persons, amongst whom are A,B and C to speak at a function. The number of ways in which it can be done, if A wants to speak before B and B wants to speak before C is
•  10!/6
•  3! 7!
•  10P3.7!
•  None of these
Solution

Q10. Number if divisors of the form (4n+2),n ≥ 0 of the integer 240 is
•  4
•  8
•  10
•  3
Solution

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