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Permutations and Combinations Quiz-18

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. In an examination there are three multiple choice questions and each question has 4 choices. Number of ways in which a student can fail to get all answers correct, is
•  11
•  12
•  27
•  63
Solution

Q2. The number of diagonals that can be drawn by joining the vertices of an octagon is
•  28
•  48
•  20
•  None of these
Solution

Q3. A code word consists of three letters of the English alphabet followed by two digits of the decimal system. If neither letter nor digit is repeated in any code word, then the total number of code words is
• 1404000
•  16848000
•  2808000
•  None of these
Solution

Q4. There are n straight lines in a plane, no two of which are parallel and no three pass through the same point. Their points of intersection are joined. Then, the number of fresh lines thus obtained is
•  (n(n-1)(n-2))/8
•  (n(n-1)(n-2)(n-3))/6
•  (n(n-1)(n-2)(n-3))/8
•  None of the above
Solution

Q5. The number of ways in which four persons be seated at a round table, so that all shall not have the same neighbours in any two arrangements is
•  24
•  6
•  3
•  4
Solution

Q6. The number of diagonals that can be drawn in a polygon of 15 sides, is
•  16
•  60
•  90
•  80
Solution

Q7. The number of 5 digits numbers of the from abcba in which a b, is
•  320
•  340
•  360
•  380

Solution

Q8. A shopkeeper sells three varieties of perfumes and he has a large number of bottles of the same size of each variety in his stock. There are 5 places in a row in his showcase. The number of different ways of displaying the three varieties of perfumes in the show case is
•  6
•  50
•  150
•  None of these

Solution

Q9. The total numbers of greater than 100 and divisible by 5, that can be formed from the digits 3,4,5,6 if no digit is repeated is
•  24
•  48
•  30
•  12
Solution

Q10. A man invites a party to (m+n) friends to dinner and places m at one round table and n at another. The number of ways of arranging the guests is
•  (m+n)!/(m! n!)
•  (m+n)!/((m-1)!(n-1)!
•  (m-1)!(n-1)!
•  None of these
Solution

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Permutations and Combinations Quiz-18