## Permutations and Combinations Quiz-13

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. There are n different books and m copies of each in a college library. The number of ways in which a student can make a selection of one or more books is
•  (m+1)n
•  (mn)!/(m!)n
•   mnCn × nC1
•  (m+1)n-1
Solution

Q2. In an steamer there are stalls for 12 animals and there are hours, cows and calves (not less then 12 each) ready to be shipped in how many ways can the ship load be made?
•  312-1
•  312
•  (12)3-1
•  (12)3
Solution

Q3. The expression nCr+4∙nCr-1 + 6∙nCr-2 + 4∙nCr-3 + nCr-4 equals
•   n+4Cr
•  2∙n+4Cr-1
•  4∙nCr
•  11∙ nCr
Solution

Q4. The number of ways of selecting 10 balls from unlimited number of red, black, white and green balls is
•   286
•   84
•   715
•   None of these
Solution

Q5. If 7 points out of 12 are in the same straight line, then the number of triangles formed is
•   19
•   y158
•   y185
•   201
Solution

Q6. The number of words which can be formed the letters of the word MAXIMUM, if two consonants cannot occur together, is
•   4!
•   3! × 4!
•   7!
•   None of these
Solution

Q7. m men and n women are to be seated in a row so that no two women sit together. If m>n, then the number of ways in which they can be seated, is
•  m!(m+1)!/(m-n+1)!
•  m!(m-1)!/(m-n+1)!
•  (m-1)!(m+1)!/(m-n+1)!
•  None of these
• Solution

Q8. If a man and his wife enter in a bus, in which five seats are vacant, then the number of different ways in which they can be seated, is
•  2
•  5
•  20
•  40
Solution

Q9. A man has 7 friends. In how many ways he can invite one or more of them for a tea party?
•  128
•  256
•  127
•  130
Solution

Q10. The number of arrangements of the letters of the word BANANA in which the two N’s do not appear adjacently, is
•  40
•  60
•  80
•  100
Solution

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