# NCERT Class 11-Math՚S: Chapter – 7 Permutations and Combinations Part 4 (For CBSE, ICSE, IAS, NET, NRA 2022)

Get top class preparation for CBSE right from your home: fully solved questions with step-by-step explanation- practice your way to success.

**Question 15**:

All the letters of the word ‘EAMCOT’ are arranged in different possible ways. The number of such arrangements in which no two vowels are adjacent to each other is

(A) 360

(B) 144

(C) 72

(D) 54

**Answer**:

(B) Is the correct choice.

We note that there are 3 consonants and 3 vowels E, A and O. Since no two vowels have to be together, the possible choice for vowels are the places marked as ‘X’ . X M X C X T X, these vowels can be arranged in ways 3 consonants can be arranged in ways. Hence, the required number of ways .

**Question 16**:

Ten different letters of alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have atleast one letter repeated is

(A)

(B)

(C)

(D)

**Answer**:

(A) Is correct choice.

Number of letters words (with the condition that a letter can be repeated) . Again number of words using different letters is . Therefore, required number of letters

Total number of words – Total number of words in which no letter is repeated = 105 .

**Question 17**:

The number of signals that can be sent by 6 flags of different colours taking one or more at a time is

(A)

(B)

(C)

(D)

**Answer**:

The correct answer is B.

Number of signals using one flag

Number of signals using two flags

Number of signals using three flags

Number of signals using four flags

Number of signals using five flags

Number of signals using all six flags

Therefore, the total number of signals using one or more flags at a time is (Using addition principle) .

**Question 18**:

In an examination there are three multiple choice questions and each question has 4 choices. Number of ways in which a student can fail to get all answer correct is

(A)

(B)

(C)

(D)

**Answer**:

The correct choice is (D) .

There are three multiple choice question, each has four possible answers. Therefore, the total number of possible answers will be . Out of these possible answer only one will be correct and hence the number of ways in which a student can fail to get correct answer is .

**Question 19**:

The straight lines and are parallel and lie in the same plane. A total numbers of points are taken on ; *n* points on , *k* points on . The maximum number of triangles formed with vertices at these points are

(A)

(B)

(C)

(D)

**Answer**:

(B) is the correct answer. Here the total number of points are which must give number of triangles but points on taking 3 points at a time gives combinations which produce no triangle. Similarly, and number of triangles can-not be formed. Therefore, the required number of triangles is