## Permutations and Combinations Quiz-17

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. How many different non-digit numbers can be formed from the digits of the number 223355888 by rearrangement of the digits so that the odd digits occupy even places?
•  16
•  36
•  60
•  180
Solution

Q2. The total number of ways in which 4 boys and 4 girls can form a line, with boys and girls alternating, is
•  (4!)2
•  8!
•  2(4!)2
•  4!∙5P4
Solution

Q3. If n is even and nC0 < nC1 < nC2 < ⋯ nCnCr+1 nCr+2 > ⋯ > n Cn then, r=
• n/2
•  (n-1)/2
•  (n-2)/2
•  (n+2)/2
Solution

Q4. If  nC(r-1)=36, nCr=84 and nC(r+1)=126, then
•  n=8, r=4
•  n=9, r=3
•  n=7, r=5
•  None of these
Solution

Q5. All possible two factors products are formed from numbers 1, 2, 3, 4,…,200. The number of factors out of the total obtained which are multiples of 5, is
•  5040
•  7180
•  8150
•  None of these
Solution

Q6. If eleven member of a committee sit at a round table so that the President and Secretary always sit together, then the number of arrangements is
•  10!×2
•  9!×2!
•  218
•  None of these
Solution

Q7. A five digit number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4 and 5, without repetition. The total number of ways this can be done, is
•  216
•  240
•  600
•  3125

Solution

Q8. How many different committees of 5 can be formed from 6 men and 4 women on which exact 3 men and 2 women serve?
•  6
•  20
•  60
•  120

Solution

Q9. There were two women participating in a chess tournament. Every participant played two games with the other participants. The number of games that the men played between themselves proved to exceed by 66 the number of games that the men played with the women. The number of participants is
•  6
•  11
•  13
•  None of these
Solution

Q10. The number of ways in which 8 different flowers can be strung to form a garland so that 4 particular flowers are never separated is
•  4! ∙ 4!
•  (8!)/(4!)
•  288
•  None of these
Solution

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Permutations and Combinations Quiz-17