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Permutations and Combinations Quiz-20

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. Four dice are rolled. The number of possible outcomes in which at least one dice shows 2 is
•  625
•  671
•  1023
•  1296
Solution

Q2. The number of four-digit even numbers that can be formed using 0,1,2,3,4,5,6 without repetition is
•  120
•  300
•  420
•  20
Solution

Q3. The sum of the digits in the unit place of all numbers formed with the help of 3, 4, 5, 6 taken all, at a time, is
• 18
•  108
•  432
•  144
Solution

Q4. If k+5Pk+1=(11(k-1))/2∙ k+3Pk, then the values of k are
•  7 and 11
•  6 and 7
•  2 and 11
•  2 and 6
Solution

Q5. The number of ways in which 9 persons can be divided into three equal groups is
•  1680
•  840
•  560
•  280
Solution

Q6. There are 15 persons in a party and each person shakes hand with another. The total number of hand shakes is
•  15 P2
•  15C2
•  15!
•  2×15!
Solution

Q7. Six points in a plane be joined in all possible ways by indefinite straight lines and if no two of them be coincident or parallel, and no three pass through the same point (with the exception of the original 6 points). The number of distinct points or intersection is equal to
•  105
•  45
•  51
•  None of these

Solution

Q8. The number of ways in which mn students can be distributed equal among n sections, is
•  (mn)n
•  (mn)!/(m!)n
•  (mn)!/m!
•  (mn)!/m!n!

Solution

Q9. A rectangle with sides 2m-1 and 2n-1 divided into square of unit length. The number of rectangle which can be formed with sides of odd length is
•  m2 n2
•  mn(m+1)(n+1)
•  4m+n-1
•  None of these
Solution

Q10. If  nPr=30240 and nCr=252, then the ordered pair (n, r) is equal to
•  (12, 6)
•  (10, 5)
•  (9, 4)
•  (16, 7)
Solution

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