Permutations and Combinations Quiz-3

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. 2m white counters and 2n red counters are arranged in a straight line with (m + n) counters on each side of a central mark. The number of ways of arranging the counters, so that the arrangements are symmetrical with respect to the central mark, is
  •  m+nCm
  •  2m+2nC2m
  •  1/2 x (m + n)!/m!n!
  •  None of these
Q2.The number of even divisors of the number N = 12600 = 2332527 is
  •  72
  •  54
  •  18
  •  None of these
Number of even divisors is equal to number of ways in which one or more ‘2’, zero more ‘3’, zero or more ‘5’ and zero or more ‘7’ can be selected, and is given by (3)(2 + 1)(2 + 1)(1 + 1) = 54

Q3.  The total number not more than 20 digits that are formed by using the digits 0,1,2,3 and 4 is
  •  520
  •  520 - 1
  •  520 + 1
  •  None of these
Each position can be filled in 5 ways. Hence, the total number of numbers is 520

Q4. There are (n + 1) white and (n + 1) black balls each set numbered 1 to n. The number of ways in which the balls can be arranged in a row so that the adjacent balls are of different color is
  •  (2n + 2)!
  •  (2n + 2)! x 2
  •  (n + 1)! x 2
  •  2{(n + 2)!}2
Since the balls are to be arranged in a row so that the adjacent balls are of different colors, we can therefore begin with a white ball or a black ball. If we begin with a white ball. We find that n + 1 white balls numbered 1 to n + 1 can be arranged in a row in (n + 1)! ways. Now n + 2 places are created among n + 1 white balls which can be filled by n + 1 black balls in (n + 1)! ways So, the total number of arrangements in which adjacent balls are of different colors and first ball is a white ball is (n + 1)! x (n + 1)! = [(n + 1)!]2. But we can begin with a black ball also. Hence, the required number of arrangements is 2[(n + 1)!]2
Q5.If m parallel lines in a plane are intersected by a family of n parallel lines, the number of parallelograms that can be formed is
  •  1/4(mn(m - 1)(n - 1))
  •  1/2(mn(m - 1)(n - 1))
  •  1/4(m2n2)
  •  None of these
The number of selection of two parallel lines from m lines is mC2
The number of selection of two parallel lines from n lines is nC2
Hence, the number of parallelograms lines is mC2 X nC2 = 1/4(mn(m - 1)(n - 1))
Q6. A person predicts the outcome of 20 cricket matches of his home team. Each match can result in a either win, loss or tie for the home team. Total number of ways in which he can make the predictions so that exactly 10 predictions are correct is equal to
  •  20C10 X 210
  •  20C10 X 320
  • 20C10 X 310
  •  20C10 X 220
Matches whose predictions are correct can be selected in 20C10 ways. Now each wrong prediction can be made in 2 ways. Thus, the total number of ways is 20C10 X 210
Q7.The number of ways in which we can distribute mn students equally among m sections is given by
  •  (mn)!/n!
  •  (mn)!/(n!)m
  •  (mn)!/(m!n!)
  •  (mn)m
Q8.The number of possible outcomes in a throw of ordinary dice in which at least one of the dice shows an odd number is
  •  6n - 1
  •  3n - 1
  •  6n - 3n
  •  None of these
The total number of ways is 6 x 6 x ... to n times = 6n. The total number of ways to show only even numbers is 3 x 3 x ... to n times = 3n. Therefore, the required number of ways is 6n - 3n

Q9.The total number of ways of selecting six coins out of 20 one rupee coins, 10 fifty-paise coins and 7 twenty-five paise coins is
  •  28
  •  56
  •  37C6
  •  None of these
Since the total number of selections of r things from n things where each thing can be repeated as many times as one can is n+r-1Cr. Therefore the required number is 3+6-1C6 = 28

Q10. A seven-digit number without repetition and divisible by 9 is to be formed by using seven digits out of 1,2,3,4,5,6,7,8,9. The number of ways in which this can be done is
  •  9!
  •  2(7!)
  •  4(7!)
  • None of these
Sum of 7 digits is a multiple of 9. Sum of numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 is 45; so two left digits should also have sum of 9. The pairs of left numbers are (1,8),(2,7),(3,6),(4,5). With each pair left number of 7-digit number is 7!. So with all 4 pairs, total number is 4 X 7!

author image

Written by: AUTHORNAME


Want to know more

Please fill in the details below:


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


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,Digestion and Absorption Notes PDF,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,Important Biology Notes for NEET Preparation,1,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,
Permutations and Combinations-Quiz-3
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