Permutations and Combinations Quiz-11

Permutations and Combinations Quiz-11

Dear Readers,

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. The number of ways in which 12 balls can be divided between two friends, one receiving 8 an the other 4, is

•  (12!)/(8! 4!)
•  (12! 2!)/(8! 4!)
•  (12!)/(8! 4! 2!)
•  None of these

Solution           

Q2. At an electron, a voter may vote for any number of candidates not greater than the number to be elected. There are 10 candidates and 4 are to be elected. If a voter votes for at least one candidate, then the number of ways in which he can vote, is

•  6210
•  385
•  1110
•  5040

Solution 

Q3. A box contains two white balls, three black balls and four red balls. In how many ways can three balls be drawn from the box, if at least one black ball is to be included in the draw?

•  64
•  45
•  46
•  None of these

Solution  

Q4. The number of ways in which a team of eleven players can be selected from 22 players including 2 of them and excluding 4 of them is

•   ¹⁶C₁₁
•    ¹⁶C₅
•    ¹⁶C₉
•     ²⁰C₉

Solution  

Q5. If ⁸ C_r- ⁷C₃=⁷C₂, then r is equal to

•   3
•   y⁴
•   8
•   6

Solution  

 

Q6. ⁿP_r=3024 and ⁿ C_r=126, then r is

•   5
•   4
•   3
•   2

Solution  

Q7. ⁿC_r + 2ⁿC^(r-1) + ⁿ C_(r-2) is equal to

•  ⁽ⁿ⁺¹⁾C_r
•  ⁽ⁿ⁺¹⁾C_(r+1)
•  ⁽ⁿ⁺²⁾C_r
•  ⁽ⁿ⁺²⁾C_(r+1)

Solution

Q8. If m and n are positive integers more than or equal to 2, m > n, then (mn)! is divisible by

•   (m!)ⁿ,(n!)^m and (m+n)! but not by (m-n)!
•   (m+n)!,(m-n)!,(m!)" but not by (n!)^m
•   (m!)ⁿ,(n!)^m,(m+n)! and (m-n)!
•   (m!)ⁿ and (n!)^m but not by (m+n)! and (m-n)!

Solution

Q9. The number of straight lines can be formed out of 10 points of which 7 are collinear

•  26
•  21
•  25
•  None of these

Solution

Q10. Consider the following statements : 

1. These are 12 points in a plane of which only 5 are collinear, then the number of straight lines obtained by joining these points in pairs is ¹²C₂ - ⁵C₂ 

2. ⁽ⁿ⁺¹⁾C_r - ^(n-1)C_(r-1)=ⁿC_r + ⁿC_(r-2) 

3. Three letters can be posted in five letter boxes in 3^5ways. 

Which of the statements given above is/are correct?

•  Only (1)
•  Only (2)
•  Only(3)
•  None of these

Solution