## Permutations and Combinations Quiz-12

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. Consider the fourteen lines in the plane given by y = x + r, y = x + r, where r ∈ {0,1,2,3,4,5,6}. The number of squares formed by these lines whose diagonals are of length 2 is
•  9
•  16
•  25
•  36
Solution

Q2. The total number of natural numbers of six digits that can be made with digits 1,2,3,4, if all digits are to appear in the same number at least once, is
•  1560
•  840
•  1080
•  480
Solution

Q3.

•  28
•  27
•  26
•  None of these
Solution

Q4. The number of ways of painting the faces of a cube with six different colours is
•   1
•   6
•   6!
•   None of these
Solution

Q5. If N is the number of positive integral solution of x1x2x3x= 770, then the value of N is
•   250
•   y252
•   y254
•   256
Solution

Q6. Consider the following statements : 1. The product of r consecutive natural numbers is always divisible by r.

2. The total number of proper positive divisors of 115500 is 94
3. A pack of 52 cards can be divided equally among four players order in 52!/(13!)4 ways.
Which of the statement given above is/are correct?
•   Only (1)
•   Only (2)
•   Only (3)
•   All of (1), (2) and (3)
Solution

Q7. How many numbers lying between 999 and 10000 can be formed with the help of the digits 0, 2, 3, 6, 7, 8 when the digits are not be repeated?
•  100
•  200
•  300
•  400
• Solution

Q8. The total number of selections of fruit which can be made from 3 bananas, 4 apples and 2 oranges, is
•  39
•  315
•  512
•  None of these
Solution

Q9. The number of ways in which five identical balls can be distributed among ten identical boxes such that no box contains more than one ball, is
•  10!
•  10!/5!
•  10!/(5!)2
•  None of these
Solution

Q10. In how many ways can 5 books be selected out of 10 books, if two specific books are never selected?
•  56
•  65
•  58
•  None of these
Solution

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Permutations and Combinations Quiz-12