## Permutations and Combinations Quiz-9

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. In a room, there are 12 bulbs of the same wattage, each having a separate switch. The number of ways to light the room with different amount of illumination is
•  122 - 1
•  212
•  212 - 1
•  122
Solution
Q2.The number of ways of arranging m positive and n(< m + 1) negative signs in a row so that no two negative signs are together is
•  m+1Pn
•  n+1Pm
•  m+1Cn
•  n+1Cm
Solution
Q3.  In an election, the number of candidates is one greater than the persons to be elected. If a voter can vote in 254 ways, the number of candidates is
•  7
•  10
•  8
•  6
Solution

Q4. The number of three-digit numbers of the form xyz such that x < y and z <e; y is
•  276
•  285
•  240
•  244
Solution
Q5.The total number of flags with three horizontal strips in order, which can be formed using 2 identical red, 2 identical green and 2 identical white strips is equal to
•  4!
•  3 X (4!)
•  2 X (4!)
•  None of these
Solution
Q6. The total number of times, the digit ‘3’ will be written, when the integers having less than 4 digits are listed is equal to
•  300
•  310
•  302
•  306
Solution
Q7.The number of distinct natural numbers up to a maximum of four digits and divisible by 5, which can be formed with the digits each digit not occurring more than once in each number is
•  1246
•  952
•  1106
•  None of these
Solution
Q8.Numbers greater than 1000 but not greater than 4000, which can be formed with the digits 0,1,2,3,4 (repetition of digits is allowed), are
•  350
•  375
•  450
•  576
Solution
Q9.The total number of ways of selecting two number from the set {1,2,3,4,...,3n} so that their sum is divisible by 3 is equal to
•  (2n2 - n)/2
•  (3n2 - n)/2
•  2n2 - n
•  3n2 - n
Solution
Q10.In how many ways can a team of six horses be selected out of a stud of 16, so that there shall always be three out of A B C A' B' C' , but never A A' B B' or C C' together
•  840
•  1260
•  960
• 720
Solution

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