## Permutations and Combinations Quiz-12

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. A library has ‘a’ copies of one book, ‘b’ copies each of two books, ‘c’ copies each of three books, an single copy of ‘d’ books. The total number of ways in which these books can be arranged in a shelf is equal to
•  (a + 2b + 3c + d)!/(a!(b!)2(c!)3)
•  (a + 2b + 3c + d)!/(a!(2b!)(c!)3)
•  (a + 2b + 3c + d)!/(c!)3
•  (a + 2b + 3c + d)!/(a!(2b!)(3c)!)
Solution
Q2.The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order as in an English dictionary. The number of words that appear before the word COCHIN is
•  360
•  192
•  96
•  48
Solution
Q3.  To fill 12 vacancies there are 25 candidates of which five are from scheduled caste. If three of the vacancies are reserved for scheduled cast candidates while the rest are open to all, the number of ways in which the selection can be made is
•  5C3 X 22C9
•  22C9 - 5C3
•  22C3 + 5C3
•  None of these
Solution

Q4. The number of different ways in which five ‘alike dashes’ and eight ‘alike dots’ can be arranged using only seven of these ‘dashes’ and ‘dots’ is
•  350
•  120
•  1287
•  None of these
Solution
Q5. is a convex quadrilateral and 3, 4, 5 and 6 points are marked on the sides and , respectively. The number of triangles with vertices on different sides is
•  270
•  220
•  282
•  342
Solution
Q6. In a city no two persons have identical set of teeth and there is no person without a tooth. Also no person has more than 32 teeth. If we disregard the shape and size of tooth and consider only the positioning of the teeth, the maximum population of the city is
•  232
•  (32)2 - 1
•  232 - 1
•  232 - 1
Solution
Q7.Two packs of 52 cards are shuffled together. The number of ways in which a man can be dealt 26 cards so that he does not get two cards of the same suit and same denomination is
•  52C26.226
•  104C26
•  2.52C26
•  None of these
Solution
Q8.The total number of ways in which three distinct numbers in A.P. can be selected from the set {1,2,3, ….24} is equal to
•  66
•  132
•  198
•  None of these
Solution
Q9.In an examination of nine papers, a candidate has to pass in more papers than the number of papers in which he fails in order to be successful. The number of ways in which he can be unsuccessful is
•  255
•  256
•  193
•  319
Solution
Q10.The total number of divisors of 480, that are of the form 4n + 2, n >e; 0, is equal to
•  2
•  3
•  4
• None of these
Solution

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