## Permutations and Combinations Quiz-14

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. Three dice are rolled. The number of possible outcomes in which at least one die shows 5 is
•  215
•  36
•  125
•  91
Solution

Q2. If all permutations of the letters of the word AGAIN are arranged as in dictionary, then fifteen word is
•  NAAGI
•  NAGAI
•  NAAIG
•  NAIAG
Solution

Q3.  If P(n, r)=1680 and C(n, r)=70, then 69n + r! is equal to
•  128
•  576
•  256
•  625
Solution

Q4. If  12Pr = 11P6 + 6∙ 11P5  then r is equal to
•  6
•  5
•  7
•  None of them
Solution

Q5. The number of natural numbers less than 1000, in which no two digits are replaced, is
•  738
•  792
•  837
•  720
Solution

Q6. There are 10 true-false questions in an examination. Then, these questions can be answered in
•  240 ways
•  20 ways
•  1024 ways
•  100 ways
Solution

Q7. Let f:{1,2,3,4,5}→{1,2,3,4,4,5} that are onto and f(x)≠i is equal to
•  9
•  44
•  16
•  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. The number of ways in which 21 objects can be grouped into three groups of 8,7 and 6 objects is
•  (20!)/(8! + 7! + 6!)
•  (21!)/(8! 7!)
•  (21!)/(8! 7! 6!)
•  (21!)/(8! + 7! + 6!)
Solution

Q10. The rank of the word MOTHER when the letters of the word are arranged alphabetically as in a dictionary, is
•  261
•  343
•  309
•  273
Solution

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