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
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
combination of n distinct objects taken r at a time is given by
(a) n/2Cr
(b) n/2Cr/2
(c) nCr/2
(d) nCr
Answer d
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
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
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.
letter words which can be formed from word PULSE without repetition.
a) 20
b) 60
c) 120
d) 240
Answer
c
letter words which can be formed from word PULSE if repetition is allowed.
a) 25
b) 120
c) 125
d) 3125
Answer
d
numbers are possible without repetition of digits?
a) 27216
b) 50400
c) 100000
d) 90000
Answer
a
numbers are possible if repetition of digits is allowed?
a) 27216
b) 50400
c) 100000
d) 90000
Answer
d
the value of n is
a) 6
b) 10
c) 12
d) 16
Answer: b
numbers are possible from digits 1 to 9 if repetition is allowed?
a) 6561
b) 2016
c) 1344
d) 2916
Answer
d
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
numbers are possible from digits 1 to 9 if repetition is allowed?
a) 6561
b) 2016
c) 1344
d) 2916
Answer
d
numbers are possible from digits 1 to 9 if repetition is not allowed?
a) 6561
b) 2016
c) 1344
d) 2916
Answer
c
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
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
permutations of word DEPENDENT.
a) 13240
b) 15120
c) 16320
d) 17400
Answer b
numbers are possible using permutations without repetition of digits if digits
are 1-9?
a) 504
b) 729
c) 1000
d) 720
Answer
a
a) 1
b) 2
c) 3
d) 4
Answer
a
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
a) 3
b) 2
c) 6
d) 5
Answer
c
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.
n.
a) 2
b) 3
c) 5
d) 6
Answer
c
letter words which can be formed from word IMAGE without
repetition using permutations.
a) 20
b) 60
c) 120
d) 240
Answer
c
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
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
a) 7
b) 14
c) 28
d) 32
Answer
b
persons, find the number of ways of selecting 3 persons.
a) 1
b) 5
c) 10
d) 15
Answer
c
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
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
and 15Cr = 15. Find
the value of 14Cr-1.
a) 1
b) 14
c) 15
d) 3
Answer
a
polygon have 15 sides. What is the possible number of diagonals it have ?
a) 90
b) 105
c) 120
d) 75
Answer
: a
possible outcomes is
a) 2n
b) 2n
c) C(n, 2)
d) P(n, 2)
Answer: (b) 2n
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
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
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
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
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
a) 1
b) 2
c) 3
d) 4
Answer
a
a) 24
b) 120
c) 720
d) 8
Answer
c
known as selection.
a) True
b) False
Answer
b
combination.
a) True
b) False
Answer
b
b) False
Answer
a
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