Maths MCQ Class 11 Ch-7 | Permutations & Combinations

  Mathematics

MCQ | Class 11 | Chapter 07
Permutations & Combinations

Multiple Choice Questions (MCQ)

• MCQ Based on the  arrangements or Permutations.

• MCQ  Based on the Selections or Combinations.

• MCQ Based on the Factorial notations.

Features

• In this post given below you find the important MCQ which are strictly according to the CBSE syllabus and are very useful for the CBSE Examinations. 
• Solution Hints are also given to some difficult problems. 
• Each MCQ contains four options from which one option is correct. 

Action Plan

• First of all students should Learn and write all basic points and Formulas related to the Permutations & Combinations
• Start solving  the NCERT Problems with examples.
• Solve the important assignments on the Permutations & Combinations Chapter 7 Class XI.
• Then start solving the following MCQ.

MCQ | CHAPTER 7 | CLASS 11
PERMUTATIONS & COMBINATIONS

Question : 1 A child has 2 pencil and 3 erasers. In how many ways he can take a pencil and an eraser?

a) 5
b) 6
c) 8
d) 9

Answer b

Question : 2 The number of combination of n distinct objects taken r at a time is given by

(a) ^n/2C_r                    

(b) ^n/2C_r/2                      

(c) ⁿC_r/2                        

(d) ⁿC_r

Answer d

Question : 3 If an event can occur in ‘m’ different ways, following which another event can occur in ‘n’ different ways, then the total numbers of occurrence of the events in the given order is

a) m + n                       

b) m – n                      

c) m x n                         

d) m/n

Answer c

Question : 4 If there are 4 paths to travel from Delhi to Kanpur, then in how many ways a person can travel from Delhi to Kanpur and came back to Delhi?

a) 4
b) 8
c) 12
d) 16

Answer d

 

Question : 5 There are 10 true-false questions in an examination. These questions can be answered in:

a) 20 ways

b) 100 ways

c) 512 ways

d) 1024 ways

Answer: d

Explanation:

Given that there are 10 questions.

Each question can be answered in two ways. (i.e. either true or false).

Hence, the number of ways these questions can be answered is 2¹⁰, which is equal to 1024.

Question : 6 Find the number of 5 letter words which can be formed from word PULSE without repetition.

a) 20
b) 60
c) 120
d) 240

Answer c

Question : 7 Find the number of 5 letter words which can be formed from word PULSE if repetition is allowed.

a) 25
b) 120
c) 125
d) 3125

Answer d

Question : 8 How many 5-digit numbers are possible without repetition of digits?

a) 27216
b) 50400
c) 100000
d) 90000

Answer a

Question : 9 How many 5-digit numbers are possible if repetition of digits is allowed?

a) 27216
b) 50400
c) 100000
d) 90000

Answer d

Question : 10  If ⁿP₅ = 60ⁿ⁻¹P₃, the value of n is

a) 6

b) 10

c) 12

d) 16

Answer: b

Question : 11 How many 4 digits even numbers are possible from digits 1 to 9 if repetition is allowed?

a) 6561
b) 2016
c) 1344
d) 2916

Answer d

Question : 12 A circle have 25 points on it. What is the possible number of chords are there ?

a) 250                     

b) 300                      

c) 325                              

d) 400

Answer b

Question : 13 How many 4 digits even numbers are possible from digits 1 to 9 if repetition is allowed?

a) 6561
b) 2016
c) 1344
d) 2916

Answer d

Question : 14 How many 4 digits even numbers are possible from digits 1 to 9 if repetition is not allowed?

a) 6561
b) 2016
c) 1344
d) 2916

Answer c

Question : 15 How many 5-digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67 and no digit appears more than once?

a) 336                

b) 448              

c) 588                     

d) 235

Answer a

Question : 16 How many numbers lying between 100 and 1000 can be formed with the digits 0, 1, 2, 3, 4, 5, if the repetition of the digits is not allowed?

a) 300            

b) 250                     

c) 100           

d) 200

Answer c

Question : 17 Find the number of permutations of word DEPENDENT.

a) 13240
b) 15120
c) 16320
d) 17400

Answer b

Question : 18 How many 3-digit numbers are possible using permutations without repetition of digits if digits are 1-9?

a) 504
b) 729
c) 1000
d) 720

Answer a

Question : 19:  If  ⁴P_r = 4 x ⁵P_r-1. Find r.

a) 1
b) 2
c) 3
d) 4

Answer a

Question : 20 Find the number of different 8-letter arrangements that can be made from the letters of the word EDUCATION so that all vowels do not occur together.

a) 40320
b) 37440
c) 1440
d) 2880

Answer b

Question : 21 If ⁿP₃ = 4 x ⁿP₂. Find n.

a) 3
b) 2
c) 6
d) 5

Answer c

Question : 22  Find the number of words which can be made using all the letters of the word IMAGE. If these words are written as in a dictionary, what will be the rank of MAGIE?

a) 97
b) 98
c) 99
d) 100

Answer c

Explanation: Words starting with letter A comes first in dictionary.

Starting with A, number of words = 4! = 24.

Starting with E, number of words = 4! = 24.

Starting with I, number of words = 4! = 24.

Starting with G, number of words = 4! = 24.

Since our word also start with M so, we have to consider one more letter i.e. MA.

Since our word also start with MA so, we have to consider one more letter i.e. MAE.

Starting with MAE, number of words = 2! = 2.

Since our word also start with MAG so, we have to consider one more letter i.e. MAGE.

Starting with MAGE, only one letter i.e. MAGEI.

After this, MAGIE comes. Total number of words before MAGIE = 24 + 24 + 24 + 24 + 2 = 98. So, rank of MAGIE is 99.

Question : 23  If ⁿC₂ = ⁿC₃ then find n.

a) 2
b) 3
c) 5
d) 6

Answer c

Question : 24 Find the number of 5 letter words which can be formed from word IMAGE without repetition using permutations.

a) 20
b) 60
c) 120
d) 240

Answer c

Question : 25 Find the number of different 8-letter arrangements that can be made from the letters of the word EDUCATION so that all vowels occur together.

a) 40320
b) 37440
c) 1440
d) 2880

Answer d

Question : 26 In how many ways 2 red pens, 3 blue pens and 4 black pens can be arranged if same color pens are indistinguishable?

a) 362880
b) 1260
c) 24
d) 105680

Answer b

Question : 27 Determine n if ²ⁿC₃: ⁿC₃ = 9:1.

a) 7
b) 14
c) 28
d) 32

Answer b

Question : 28 Out of a group of 5 persons, find the number of ways of selecting 3 persons.

a) 1
b) 5
c) 10
d) 15

Answer c

Question : 29 How many 3-letter words with or without meaning, can be formed out of the letters of the word, LOGARITHMS, if repetition of letters is not allowed

(a) 720
(b) 420
(c) none of these
(d) 5040

Answer a

Question : 30 In a family, 5 males and 3 females are there. In how many ways we can select a group of 2 males and 2 females from the family?

a) 3
b) 10
c) 30
d) 40

Answer c

Question : 31  If ¹⁴C_r = 14 and ¹⁵C_r = 15. Find the value of ¹⁴C_r-1.

a) 1
b) 14
c) 15
d) 3

Answer a

Question : 32 A polygon have 15 sides. What is the possible number of diagonals it  have ?

a) 90                    

b) 105                   

c) 120                        

d) 75

Answer : a

Explanation : 

If a polygon have n sides then no. of diagonals a polygon can have = ⁿC₂ - n

Here number sides = 15

No of diagonals = ¹⁵C₂ - 15

=   - 15

=  - 15

=  = 105 - 15 = 90 diagonals

Question : 33 A coin is tossed n times, the number of all the possible outcomes is

a) 2n

b) 2ⁿ

c) C(n, 2)

d) P(n, 2)

Answer: (b) 2ⁿ

Question : 34 The number of ways of painting the faces of a cube with six different colors is

a) 1
b) 6
c) 6!
d) None of these

Answer a

Explanation:
Since the number of faces is same as the number of colors,
therefore the number of ways of painting them is 1

Question : 35 In how many ways in which 8 students can be seated in a line is

(a) 40230
(b) 40320
(c) 5040
(d) 50400

Answer b

Explanation:
The number of ways in which 8 students can be sated in a line = ⁸P₈  = 8!
= 40320

Question : 36 If repetition of the digits is allowed, then the number of even natural numbers having three digits is

(a) 250
(b) 350
(c) 450
(d) 550

Answer c

Explanation:
In a 3 digit number, 1st place can be filled in 5 different ways with (0, 2, 4, 6, 8)
10th place can be filled in 10 different ways.
100th place can be filled in 9 different ways.
So, the total number of ways = 5 × 10 × 9 = 450

Question : 37 The number of squares that can be formed on a chess board is

(a) 64
(b) 160
(c) 224
(d) 204

Answer  d

Explanation:

1×1 grid squares = 8×8 = 64,

2×2 grid squares = 7×7 = 49,

3×3 grid squares = 6×6 = 36 upto 8×8 grid squares = 1×1 = 1.

Hence, the total number of squares that can be formed on a chess board = 8² + 7² + 6² + … + 1²

= 1² + 2² + 3² + … + 8²

= [n(n + 1)(2n + 1)]/6

Here, n = 8

Hence,

= [8(8 + 1)(16 + 1)]/6

= (8×9×17)/6

= 12×17 = 204

Question : 38 A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is

(a) 40
(b) 196
(c) 280
(d) 346

Answer  b

Explanation:
There are two cases
1. When 4 is selected from the first 5 and rest 6 from remaining 8
Total arrangement = ⁵C₄ × ⁸C₆
= ⁵C₁ × ⁸C₂
= 5 × (8×7)/(2×1)
= 5 × 4 × 7
= 140
2. When all 5 is selected from the first 5 and rest 5 from remaining 8
Total arrangement = ⁵C₅ × ⁸C₅
= 1 × ⁸C₃
= (8×7×6)/(3×2×1)
= 8×7
= 56
Now, total number of choices available = 140 + 56 = 196

Question : 39  If       , then find the value of x

a) 1
b) 2
c) 3
d) 4

Answer a

Question : 40  Find the value of  6! 

a) 24
b) 120
c) 720
d) 8

Answer c

Question : 41 Permutation is also known as selection.

a) True
b) False

Answer b

Question : 42 Order matters in combination.

a) True
b) False

Answer b

Question : 43  Is ⁿC_r = ⁿC_n-r  true?

a) True

b) False

Answer a

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