9394949438

[LATEST]$type=sticky$show=home$rm=0$va=0$count=4$va=0




Permutations and Combinations Quiz-1

Dear Readers,

Permutations and Combinations is one of the most important chapters of Algebra in the JEE syllabus and other engineering exams. For JEE Mains, it has 4% weightage and for JEE Advanced, it has 5% weightage..

Q1. The number of ways in which we can get a score of 11 by throwing three dice is
  •  18
  •  27
  •  45
  •  56
Solution
Dice is marked with numbers 1, 2, 3, 4, 5, 6. If the sum of dice in three throws is 11, then observations must be 1, 4, 6;…1, 5, 5;…2, 3, 6;…2, 4, 5;… 3, 3, 5; …3, 4, 4
We can get this observation in 3! + 3!/2! + 3! + 3! + 3!/2! + 3!/2! = 27 ways


Q2.There are two bags each containing balls. If a man has to select equals number of balls from both the bags the number of ways in which he can do so if he must chose at least one ball from each bag is
  •  m2
  •  2mCm
  •  2mCm - 1
  •  None of these
Solution
The number of ways of selecting r(0 ≤ r ≤ m) balls out of m is mCr.
Therefore, the number of ways if selecting balls from each of the bag is (mCr)2, Further the number of ways of selecting equal number of balls from each of the two bags, choosing at least one from each bag, is
(mC1)2 + (mC2)2 + ... + (mCm)2 = 2mCm - 1
[∵ (mC0)2 + (mC1)2 + ... + (mCm)2 = 2mCm]


Q3.  Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First, the women choose the chairs from amongst the chairs marked 1 to 4, and then the men select the chairs from amongst the remaining. The number of possible arrangements is
  •  6C3 x 4C2
  •  4P2 x 4P3
  •  4C2 + 4P3
  •  None of these
Solution
Two women can choose two chairs out of 1, 2, 3, 4 in 4C2 ways, and can arrange among themselves in 2! ways. Three men can choose 3 chairs out of 6 remaining chairs in 6C3 ways and can arrange themselves in 3! ways.
Therefore, total number of possible arrangements is 4C2 X 2! X 6C3 X 3! = 4P2 X 6P3

Q4.  n is selected from the set {1,2,3,...,10} and the number 2n + 3n + 5n is formed. Total number of ways of selecting so that the formed number is divisible by 4 is equal to
  •  50
  •  49
  •  48
  •  None of these
Solution
Q5.Let A = {x1, x2, x3, ..., x7}, B = {y1, y2, y3}. The total number of functions f:A → B that are on to and there are exactly three element in such that f(x) = y2 is equal to
  •  490
  •  510
  •  630
  •  None of these
Solution
 Three elements from set ‘A’ can be selected in 7C3 ways. Their image has to be Remaining 2 images can be y2assigned to remaining 4 pre-images in 24 ways. But the function is onto, hence the number of ways is 24 - 2. Then the total number of functions is 7C3 X 14 = 490

Q6. Number of ways in which 25 identical things be distributed among five persons if each gets odd number of things is
  •  25C4
  •  12C8
  • 14C10
  •  13C13
Solution
Q7.The number of integral solutions of x + y + z = 0 with x ≥-5, y≥-5,z≥-5, is
  •  134
  •  136
  •  138
  •  140
Solution
Let x = p, y = q - 5 and z = r - 5, where p,q,r ≥ 0
Then the given equation reduces to p + q + r = 15 -- (1)
Now, we have to find non-negative integral solution of Eq. (1). The total number of such solutions is 15+3-1C3-1 = 17C2 = 136


Q8.The total number of five-digit numbers of different digits in which the digit in the middle is the largest is
  •  
  •  T33(3!)
  •  30(3!)
  •  None of these
Solution
Q9.The total number of ways in which persons can be divided into couples is
  •  2n!/(n!n!)
  •  2n!/(2!)n
  •  2n!/(n!(2!)n)
  •  None of the above
Solution
Here, we are dividing 2n people in group of 2 each, and we are concerned with mere grouping. Hence, the required number of ways is 2n!/(n!(2!)n)

Q10. In how many different ways can the first 12 natural numbers be divided into three different groups such that numbers in each group are in A.P.?
  •  1
  •  5
  •  6
  • 4
Solution
No group of four members from the first 12 natural number can have the common difference 4.
If one group including 1 is selected with the common difference 1, then the other two group can have the common difference 1 or 2.
If one group including 1 is selected with the common difference 2, then one of the other two groups can have the common difference 2 and the remaining group will have common difference 1.
If one group including 1 is selected with common difference 3, then the other two group can have the common difference 3 Therefore, the required number of ways is 2 + 1 + 1 = 4

author image

Written by: AUTHORNAME

AUTHORDESCRIPTION

Want to know more

Please fill in the details below:

INNER POST ADS

Latest IITJEE Articles$type=three$c=3$author=hide$comment=hide$rm=hide$date=hide$snippet=hide

Latest NEET Articles$type=three$c=3$author=hide$comment=hide$rm=hide$date=hide$snippet=hide

Name

Admissions,1,Alternating Current,60,AP EAMCET 2020,1,Basic Maths,2,BCECE 2020,1,best books for iit jee,2,best coaching institute for iit,1,best coaching institute for iit jee preparation,1,best iit jee coaching delhi,1,best iit jee coaching in delhi,2,best study material for iit jee,4,BITSAT Registration 2020,1,Blog,62,books for jee preparation,1,books recommended by iit toppers,3,Capacitance,3,CBSE,1,CBSE accounts exam,1,CBSE boards,1,CBSE NEET,9,cbse neet 2019,3,CBSE NEET 2020,1,cbse neet nic,1,Centre of Mass,2,Chemistry,58,Class 12 Physics,15,coaching for jee advanced,1,coaching institute for iit jee,2,Collision,2,COMEDK UGET 2020 Application Form,1,COMEDK UGET 2020 Exam Form,1,COMEDK UGET news,1,CUCET 2020,2,Current Electricity,4,CVR college,1,Electromagnetic Induction,3,Electronics,1,Electrostatics,3,Energy,1,Engineering & Medical,1,Fluid Mechanics,4,Gravitation,2,GUJCET 2020 Application Form,1,Heat,4,iit admission,1,iit advanced,1,iit coaching centre,3,iit coaching centre in delhi,2,iit coaching classes,2,iit coaching in delhi,1,iit coaching institute in delhi,1,iit entrance exam,1,iit entrance exam syllabus,2,iit exam pattern,2,iit jee,5,iit jee 2019,3,iit jee advanced,2,iit jee books,3,iit jee coaching,2,iit jee exam,3,iit jee exam 2019,1,iit jee exam pattern,3,iit jee institute,1,iit jee main 2019,2,iit jee mains,3,iit jee mains syllabus,2,iit jee material,1,iit jee online test,3,iit jee practice test,3,iit jee preparation,6,iit jee preparation in delhi,2,iit jee preparation time,1,iit jee preparation tips by toppers,2,iit jee question paper,1,iit jee study material,3,iit jee study materials,2,iit jee syllabus,2,iit jee syllabus 2019,2,iit jee test,3,iit preparation,2,iit preparation books,5,iit preparation time table,2,iit preparation tips,2,iit syllabus,2,iit test series,3,IITJEE,100,IPU CET,1,JEE Advanced,83,jee advanced exam,2,jee advanced exam pattern,1,jee advanced paper,1,JEE Books,1,JEE Coaching Delhi,3,jee exam,3,jee exam 2019,6,JEE Exam Pattern,2,jee exam pattern 2019,1,jee exam preparation,1,JEE Main,85,jee main 2019,4,JEE Main 2020,1,JEE Main 2020 Application Form,2,JEE Main 2020 news,2,JEE Main 2020 Official Answer Key,1,JEE Main 2020 Registration,1,JEE Main 2020 Score,1,JEE Main application form,1,jee main coaching,1,JEE Main eligibility criteria,3,jee main exam,1,jee main exam 2019,3,jee main online question paper,1,jee main online test,3,JEE Main Paper-2 Result,1,jee main registration,2,jee main syllabus,2,JEE mains 2020,1,jee mains question bank,1,jee mains test papers,3,JEE Mock Test,2,jee notes,1,jee past papers,1,JEE Preparation,2,jee preparation in delhi,1,jee preparation material,4,JEE Study Material,1,jee syllabus,6,JEE Syllabus Chemistry,1,JEE Syllabus Maths,1,JEE Syllabus Physics,1,jee test series,3,KCET - 2020,1,Kinematics,1,Latest article,5,Latest Articles,61,Latest News,34,latest news about neet exam,1,Laws of Motion,2,Magnetic Effect of Current,3,Magnetism,3,MHT CET 2020,2,MHT CET 2020 exam schedule,1,Modern Physics,1,NCERT Solutions,15,neet,3,neet 2019,1,neet 2019 eligibility criteria,1,neet 2019 exam date,2,neet 2019 test series,2,NEET 2020,2,NEET 2020 Application Form,1,NEET 2020 Eligibility Criteria,1,NEET 2020 Registration,1,neet application form,1,neet application form 2019 last date,1,Neet Biology Syllabus,1,Neet Books,3,neet eligibility criteria,3,neet exam 2019,7,neet exam application,1,neet exam date,1,neet exam details,1,neet exam pattern,6,neet exam pattern 2019,2,neet examination,1,neet mock test 2019,1,Neet Notes,3,Neet Online Application Form,3,neet online test,2,neet past papers,1,neet physics syllabus,1,neet practice test,2,NEET preparation books,1,neet qualification marks,1,NEET question paper 2019,1,neet question papers,1,neet registration,1,Neet Study Material,3,neet syllabus,6,neet syllabus 2019,5,NEET Syllabus 2020,1,neet syllabus chemistry,1,neet syllabus for biology,1,neet syllabus for physics,1,neet test series,1,neet ug 2019,2,news,5,online study material for iit jee,1,Optical Instruments,1,Physics,110,physics books for iit jee,1,Power,1,Practical Physics,1,Quiz,5,Ray Optics,1,Rotational Motion,3,SHM,3,Simple Harmonic Motion,3,study materials for iit jee,1,Study Notes,110,study notes for iit jee,1,Thermodynamics,4,TS EAMCET Notification,2,Units and Dimensions,1,UPSEE 2020,1,UPSEE 2020 Application Form,2,UPSEE EXAM,1,Vectors,2,VITEE Application form,1,Wave Motion,3,Wave Optics,1,WBJEE 2020 Admit Card,1,WBJEE 2020 Answer Key,1,Work,1,
ltr
item
BEST NEET COACHING CENTER | BEST IIT JEE COACHING INSTITUTE | BEST NEET, IIT JEE COACHING INSTITUTE: Permutations and Combinations-Quiz-1
Permutations and Combinations-Quiz-1
https://1.bp.blogspot.com/-ZHSzfpa1RGE/YNyypljpenI/AAAAAAAAAwI/Cz-oOZEAa8QPIfkj_NdFmjQf2-jIsXlHQCLcBGAsYHQ/s400/PC.jpg
https://1.bp.blogspot.com/-ZHSzfpa1RGE/YNyypljpenI/AAAAAAAAAwI/Cz-oOZEAa8QPIfkj_NdFmjQf2-jIsXlHQCLcBGAsYHQ/s72-c/PC.jpg
BEST NEET COACHING CENTER | BEST IIT JEE COACHING INSTITUTE | BEST NEET, IIT JEE COACHING INSTITUTE
https://www.cleariitmedical.com/2021/07/permutations-and-combinations-quiz-1.html
https://www.cleariitmedical.com/
https://www.cleariitmedical.com/
https://www.cleariitmedical.com/2021/07/permutations-and-combinations-quiz-1.html
true
7783647550433378923
UTF-8
Loaded All Posts Not found any posts VIEW ALL Readmore Reply Cancel reply Delete By Home PAGES POSTS View All RECOMMENDED FOR YOU LABEL ARCHIVE SEARCH ALL POSTS Not found any post match with your request Back Home Sunday Monday Tuesday Wednesday Thursday Friday Saturday Sun Mon Tue Wed Thu Fri Sat January February March April May June July August September October November December Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec just now 1 minute ago $$1$$ minutes ago 1 hour ago $$1$$ hours ago Yesterday $$1$$ days ago $$1$$ weeks ago more than 5 weeks ago Followers Follow THIS CONTENT IS PREMIUM Please share to unlock Copy All Code Select All Code All codes were copied to your clipboard Can not copy the codes / texts, please press [CTRL]+[C] (or CMD+C with Mac) to copy