## Permutations and Combinations Quiz-15

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. From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and
arranged in a row on the shelf so that the dictionary is always in the middle. Then the number of such arrangement is
•  At least 500 but less than 750
•  At least 750 but less than 1000
•  At least 1000
•  Less than 500
Solution

Q2. How many nine digit numbers can be formed by using the digits 2,2,3,3,5,5,8,8,8 so that the odd digits occupy even positions?
•  7560
•  180
•  16
•  60
Solution

Q3. The figure 4, 5, 6, 7, 8 are written in every possible order. The number of numbers greater than 56000 is
• 72
•  96
•  90
•  98
Solution

Q4. In how many ways 3 letters can be posted in 4 letter-boxes, if all the letters are not posted in the same letter-box?
•  63
•  60
•  77
•  81
Solution

Q5.The lock of a safe consists of five discs each of which features the digits 0, 1, 2, … ,9.
The safe can be opened by dialing a special combination of the digits. The number of days sufficient enough to open the safe. If the work day lasts 13 h and 5 s are needed to dial one combination of digits is
•  9
•  10
•  11
•  12
Solution

Q6. A library has a copies of one book, b copies of each of two books, c copies of each of three books and single copies of d books. The total number of ways in which these book can be distributed, is
•  (a + b + c + d)!/a!b!c!
•  (a + 2b + 3c + d)!/(a!(b!)2(c!)3)
•  (a + 2b + 3c + d)/a!b!c!
•  None of these
Solution

Q7. Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4 and, then men select the chairs from amongst the remaining. The number of possible arrangements is
•  6C3 × 4C2
•   4C2 × 4C3
•  4P2 × 4P3
•  None of these
Solution

Q8.The number of permutations of 4 letters that can be made out of the letters of the word EXAMINATION is
•  2454
•  2452
•  2450
•  1806
Solution

Q9. 20 persons are invited for a party. In how many different ways can they and the host be seated at circular table, if the two particular persons are to be seated on either side of the host?
•  20!
•  218!
•  18!
•  None of these
Solution

Q10. In a circus there are ten cages for accommodating ten animals. Out of these four cages are so small that five out of 10 animals cannot enter into them. In how many ways will it be possible to accommodate ten animals in these ten cages?
•  66400
•  86400
•  96400
•  None of these
Solution

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Permutations and Combinations Quiz-15