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Permutations and Combinations Quiz-19

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 how many ways can 4 prizes be distributed among 3 students, if each students can get all the 4 prizes?
•  4!
•  34
•  34-1
•  33
Solution

Q2. The number of diagonals that can be drawn by joining the vertices of an octagon is
•  24 ways
•  48 ways
•  26 ways
•  36 ways
Solution

Q3. Total number of four digit odd numbers that can be formed by using 0,1,2,3,5,7 is
• 216
•  375
•  400
•  720
Solution

Q4. The total number of ways in which 12 persons can be divided into three group of 4 persons each is
•  (12!)/((3!)3 4!)
•  (12!)/(4!)3
•  (12!)/((4!)33!)
•  (12!)/(3!)4
Solution

Q5. The sides AB,BC,CA of a triangle ABC have 3,4 and 5 interior points respectively on them. The total number of triangles that can be constructed by using these points as vertices is
•  220
•  204
•  205
•  195
Solution

Q6. A set contains (2n+1) elements. The number of subsets of this set containing more than n elements is equal to
•  2(n-1)
•  2n
•  2(n+1)
•  22n
Solution

Q7. A student is allowed to select at most n books from a collection of (2n+1) books. If the total number of ways in which he can select one book is 63, then the value of n is equal to
•  2
•  3
•  4
•  1

Solution

Q8. The number of all possible words that can be formed using the letters of the word “MATHEMATICS” is
•  (11!)/(2! 2! 2!)
•  11!
•   11C1
•  None of these

Solution

Q9. There are 5 historical moments, 6 gardens and 7 shopping malls in the city. In how many ways a tourist can visit the city, if he visits at least one shopping mall?
•  25.26.(27-1)
•  24.26.(27-1)
•  25.25.(26-1)
•  None of these
Solution

Q10. The total number of ways of dividing mn things into n equal groups, is
•  (m+n)!/(m! n!)
•  (m+n)!/((m-1)!(n-1)!
•  (m-1)!(n-1)!
•  None of these
Solution

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