Permutation and Combination Quiz-1

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 4-digit even numbers that can be formed using 0,1,2,3,4,5,6 without repetition is
  •  420
  •  120
  •  300
  •  20

(a) An even number has an even digit at unit place 
 ∴ Required number of even numbers = Number of even numbers having 0 at unit’s place + Number of even numbers having a non-zero digit at unit’s place 
 = 6C3×3 !×1+ 3C1 (6C3×3 !- 5C2×2 !) 
Q2.A father with 8 children takes 3 at a time to the zoological garden, as often as he can without taking the same 3 children together more than once. The number of times he will go to the garden, is
  •  112
  •  56
  •  336
  •  None of these
(b) The number of times he will go to the garden is same as the number of selecting 3 children from 8 children 
 ∴ The required number of times= 8C3=56


  •  2n-1
  •  2n-1
  •  2n+1
  •  2n
(a) nPr= nCr r ! 
 ⇒nPr/r!= nCr 

Q4. If the letters of the word ‘SACHIN’ are arranged in all possible ways and these words are written out as in dictionary, then the word ‘SACHIN’ appears at serial number
  •  601
  •  600
  •  603
  •  602
(a) In the word SACHIN order of alphabets is A, C, H, I, N, S. The number of words starting with A, C, H, I, N are each equal to 5! ∴ Total number of wards5×5!=600 The first word starting with S is SACHIN So, word SACHIN appears at serial number 601

Q5.Three straight lines L1,L2,L3 are parallel and lie in the same plane. A total of m points are taken on L1,n points on L2,k points on L3. The maximum number of triangles formed with vertices at these points are
  •  m+n+kC3
  •  m+n+kC3-mC3-nC3
  •  m+n+kC3+mC3+nC3
  •  None of these
 (d) Total number of points on a three lines are m+n+k 
 ∴ maximum number of triangles = m+n+kC3-mC3-nC3-kC3 (subtract those triangles in which point on the same line)

Q6.Eight chair 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 chair marked 1 to 4; and then the men select the chairs from amongst the remaining. The number of possible arrangement is
  •  6C3x4C2
  •  4C2+4P3
  • 4P2x6P3
  •  None of these
(c) Since, first the 2 women select the chairs amongst 1 to 4 in 4P2 ways. 
 Now, from the remaining 6 chairs three men could be arranged in 6P3 ways. 
 ∴ Total number of arrangements= 4P2x6P3

Q7.A polygon has 44 diagonals, then the number of its sides are
  •  8
  •  7
  •  11
  •  None of these
(c) Let number of sides of polygon=n
 ⇒ nC2-n=44 [given] 
 ⇒ n!/2!(n-2)!-n=44 
 ⇒ n(n-1)-2n=88 
 ⇒ n2-3n-88=0
 ⇒ (n-11)(n+8)=0 
 ⇒ n=11,-8 Since, sides cannot be negative 
 ∴ n=11

Q8.The total number of flags with three horizontal strips, in order that can be formed using 2 identical red, 2 identical green and 2 identical white strips, is equal to
  •  2(4!)
  •  4!
  •  3(4!)
  •  None of these
(b) All strips are of different colours, then the number of flags =3!=6 
 When two strips are of same colour, then the number of flags = 3C13!2=18 
 ∴ Total number of flags=6+18=24=4!

Q9.The value of 47C4+ 5r=152-rC3 is equal to
  •  52C4
  •  47C6
  •  52C5
  •  None of these
(a) 47C4+∑5r=1 52-rC3
= 47C4+51C3+50C3+49C3+48C3+47C3 
 = 51C3+50C3+49C3+48C3+(47C3+47C4) = 52C4

Q10. If there are n number of seats and m number of people have to be seated, then how many ways are possible to do this(m < n)?
  •  nCm
  •  nCn×(m-1)!
  •  n-1Pm-1
  • nPm
(d) ∵ Total number of seats=n and number of people=m Ist person can be seated in n ways IInd person can be seated in (n-1) ways ⋯⋯⋯⋯⋯ ⋯⋯⋯⋯⋯ ⋯⋯⋯⋯ mth person can be seated in (n-m+1)ways 
 ∴ Total number of ways =n(n-1)(n-2)…(n-m+1)=nPm 
 Alternate In out of n seats m people can be seated in nPm ways

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,
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