Permutation And Combination - Study Mode

[#151] In the next World cup of cricket there will be 12 teams, divided equally in two groups. Teams of each group will play a match against each other. From each group 3 top teams will qualify for the next round. In this round each team will play against each others once. Four top teams of this round will qualify for the semifinal round, where they play the best of three matches. The Minimum number of matches in the next World cup will be:
Correct Answer

(B) 53

Explanation

Solution: The number of matches in first round, = 6 C 2 + 6 C 2 Number of matches in next round, = 6 C 2 Number of matches in semifinals, = 4 C 2 Total number of matches, = 6 C 2 + 6 C 2 + 6 C 2 + 4 C 2 + 2 = 53

[#152] There are 10 person among whom two are brother. The total number of ways in which these persons can be seated around a round table so that exactly one person sit between the brothers , is equal to:
Correct Answer

(A) 7! × 2!

Explanation

Solution: Total number of ways = 7! × 2!

[#153] If letters of the work KUBER are written in all possible orders and arranged as in a dictionary, then the rank of the word KUBER will be:
Correct Answer

(A) 67

Explanation

Solution: Step 1: Arrange the letters in alphabetical order The word KUBER consists of the letters: B, E, K, R, U (sorted order) Step 2: Count words before "KUBER" Words starting with 'B' = 4! = 24 Words starting with 'E' = 4! = 24 Words starting with 'K' and second letter 'B' = 3! = 6 Words starting with 'K' and second letter 'E' = 3! = 6 Words starting with 'K' and second letter 'R' = 3! = 6 Step 3: Find the position of "KUBER" After 24 (B) + 24 (E) + 6 (KB) + 6 (KE) + 6 (KR) = 66 words, the next word is KUBER Rank of "KUBER" = 67 Final Answer: Option A (67)

[#154] A letter lock consists of 4 rings, each ring contains 9 non-zero digits. This lock can be opened by setting four digit code with the proper combination of each of the 4 rings. Maximum how many codes can be formed to open the lock ?
Correct Answer

(B) 9 4

Explanation

Solution: There are 9 non-zero digits to arrange themselves at 4 different position. Each letter can be arrange at different position in 9 different ways.
So, required number of ways,
= 9 × 9 × 9 × 9
= 9 4

[#155] 10 students are to be seated in two rows equally for the Mock test in a room. There are two sets of papers, Code A and Code B. each of two rows can have only one set of paper but different that from other row. In how many ways these students can be arranged ?
Correct Answer

(C) 7257600

Explanation

Solution: 5 students can be seated out of 10 students in 10 C 5 ways
Remaining 5 will be seated in, = 5 C 5 ways
Students of each row can be arranged as,
= 5! × 5! ways
Two sets of paper can be arranged themselves in,
= 2! ways
Thus, Total arrangement,
= 10 C 5 × 5! × 5! × 2
= 7257600