Permutations and Combinations-Quiz-8

Permutations and Combinations Quiz-8

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. In a polygon, no three diagonals are concurrent. It the total number of points of intersection of diagonal interior to the polygon is 70, then the number of diagonals of the polygon is

•  20
•  28
•  8
•  None of these

Solution

Q2.The number of words of four letters containing equal number of vowels and consonants, where repetition is allowed, is

•  105²
•  210 X 243
•  105 X 243
•  150 X 21²

Solution

Q3.  If the difference of the number of arrangements of three things from a certain number of dissimilar things and the number of selections of the same number of things from them exceeds 100, then the least number of dissimilar things is

•  8
•  6
•  5
•  7

Solution

Q4. The last digit of (1! + 2! + ... + 2005!)⁵⁰⁰ is

•  9
•  2
•  7
•  1

Solution

Q5.Two player P₁ and P₂ play a series of '2n' games. Each games can result in either a win or a loss for The total number of ways in which P₁ can win the series of these games is equal to

•  1/2(2²ⁿ - ²ⁿC_n)
•  1/2(2²ⁿ - 2 X ²ⁿC_n)
•  1/2(2ⁿ - ²ⁿC_n)
•  1/2(2ⁿ - 2 x ²ⁿC_n)

Solution

Q6. A class contains three girls and four boys, every Saturday, five go on a picnic (a different group of students is sent every week). During the picnic, each girl in the group is given a doll by the accompanying teacher. If all possible groups of five have gone for picnic once, the total number of dolls that the girls have got is

•  21
•  45
•  27
•  24

Solution

Q7.A person always prefers to eat ‘parantha’ and ‘vegetable dish’ in his meal. How many ways can he make his platter in a marriage party if there are three types of paranthas, four types of ‘vegetable dish’ three types of ‘salads’ and two types of ‘sauces’?

•  3360
•  4096
•  3000
•  None of these

Solution

Q8.Let x₁,x₂,...,x_k be the divisors of positive integer ‘n’ (including 1 and n). If x₁ + x₂ +...+ x_k = 75 then ∑_i=11/x_i is equal to

•  75/n²
•  75/n
•  75/k
•  None of these

Solution

Q9.Two teams are to play a series of five matches between them. A match ends in a win, loss or draw for team. A number of people forecast the result of each match and no two people make the same forecast for the series of matches. The smallest group of people in which one person forecasts correctly for all the matches will contain n people, where n is

•  81
•  243
•  486
•  None of these

Solution

Q10.The sum of all four-digit number that can be formed by using the digits 2,4,6,8 (when repetition of digits is not allowed) is

•  133320
•  533280
•  53328
• None of these

Solution

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