Permutations and Combinations-Quiz-11

Permutations and Combinations Quiz-11

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. 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

•  ²ⁿC_n
•  ^2n-1C_n+1
•  ^2n-1C_n+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 2^n-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 i^th box contains at least i number of balls is

•  ⁿ²C_n-1
•  ^n2-1C_n-1
•  ^(n2+n-2)/2C_n-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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