Permutations and Combinations Quiz-11

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. Total number of six-digit numbers in which all and only odd digits appear is
•  5/2(6!)
•  6!
•  1/2(6!)
•  None of these
Solution
Q2.In a three-storey building, there are four rooms on the ground floor, two on the first and two on the second floor. If the rooms are to be allotted to six persons, one person occupying one room only, the number of ways in which this can be done so that no floor remains empty is
•  8P6 - 2(6!)
•  8P6
•  8P5(6!)
•  None of these
Solution
Q3.  If nC3 + nC4 > n+1C3, then
•  n > 6
•  n > 7
•  n < 6
•  None of these
Solution

Q4. If r,s,t are prime numbers and p,q are the positive integers such that LCM of p,q is r2s4t2, then the number of ordered pairs (p,q) is
•  252
•  254
•  225
•  224
Solution
Q5.Let f(n,k) denote the number of ways in which k identical balls can be coloured with n colours so that there is at least one ball of each color. Then f(2n,n) must be equal to
•  2nCn
•  2n-1Cn+1
•  2n-1Cn+1
•  None of these
Solution
Q6. The total number of positive integral solution of 15 < x1 + x2 + x3 <e; 20 is equal to
•  685
•  785
•  1125
•  None of these
Solution
Q7.In a certain test, there are n questions. In the test 2n-i students gave wrong answers to at least i questions, where i = 1,2,...,n. If the total number of wrong answers given is 2047, then n is equal to
•  10
•  11
•  12
•  13
Solution
Q8.The total number of ways in which n2 number of identical balls can be put in numbered boxes (1,2,3, …. ) such that ith box contains at least i number of balls is
•  n2Cn-1
•  n2-1Cn-1
•  (n2+n-2)/2Cn-1
•  None of these
Solution
Q9.Fifteen identical balls have to be put in five different boxes. Each box can contain any number of balls. The total number of ways of putting the balls into the boxes so that each box contains at least two balls is equal to
•  9C5
•  10C5
•  6C5
•  10C6
Solution
Q10.Rajdhani express going from Bombay to Delhi stops at five intermediate stations, 10 passengers enter the train during the journey with 10 different ticket of two classes. The number of different sets of tickets they may have is
•  15C10
•  20C10
•  30C10
• None of these
Solution

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