Permutations and Combinations-Quiz-10

Permutations and Combinations Quiz-10

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. The sum of the digits in the unit’s place of all numbers formed with the help of 3,4,5,6 taken all at a time is

•  18
•  432
•  108
•  144

Solution

Q2.There are three coplanar parallel lines. If any p points are taken on each of the lines, the maximum number of triangles with vertices on these points is

•  3p²(p - 1) + 1
•  3p²(p - 1)
•  p²(4p - 3)
•  None of these

Solution

Q3.  The total number of ways in which 15 identical blankets can be distributed among four persons so that each of them gets at least two blankets is equal to

•  ¹⁰C₃
•  ⁹C₃
•  ¹¹C₃
•  None of these

Solution

Q4. How many different nine-digit numbers can be formed from the number 223355888 by rearranging its digits so that the odd digits occupy even positions?

•  16
•  36
•  60
•  180

Solution

Q5.The total number of three-letter words that can be formed from the letter of the word ‘SAHARANPUR’ is equal to

•  210
•  237
•  247
•  227

Solution

Q6. A is a set containing 'n' different elements. A subset P of A is chosen. The set A is reconstructed by replacing the elements of .A subset Q of A is again chosen. The number of ways of choosing and so that P∩Q contains exactly two element is

•  ⁿC₃ X 2ⁿ
•  ⁿC₂ X 3^n-2
•  3^n-2
•  None of these

Solution

Q7.A train timetable must be compiled for various days of the week so that two trains twice a day depart for three days, one train daily for two days and three trains once a day for two days. How many different timetables can be compiled?

•  140
•  210
•  133
•  72

Solution

Q8.Three boys of class X, four boys of class XI and five boys of class XII sit in a row. The total number of ways in which these boys can sit so that all the boys of same class sit together is equal to

•  (3!)²(4!)(5!)
•  (3!)(4!)²(5!)
•  (3!)(4!)(5!)
•  (3!)(4!)(5!)²

Solution

Q9.In a group of boys, two boys are brothers and six more boys are present in the group. In how many ways can they sit if the brothers are not to sit long with each other?

•  2 X 6!
•  ⁷P₂ X 6!
•  ⁷C₂ X 6!
•  None of these

Solution

Q10.If n objects are arranged in a row, then the number of ways of selecting three of these objects so that no two of them are next to each other is

•  ^n-2C₃
•  ^n-3C₂
•  ^n-3C₃
• None of these

Solution

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