MCQ | Class 11 | Chapter 06
Permutations & Combinations
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
bQuestion : 2 The number of
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
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
cQuestion : 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
dQuestion : 8 How many 5-digit
numbers are possible without repetition of digits?
a) 27216 b) 50400 c) 100000 d) 90000
Answer
aQuestion : 9 How many 5-digit
numbers are possible if repetition of digits is allowed?
a) 27216 b) 50400 c) 100000 d) 90000
Answer
dQuestion : 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
dQuestion : 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
dQuestion : 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
cQuestion : 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 bQuestion : 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
aQuestion : 19: If 4Pr = 4 x 5Pr-1. Find r.
a) 1 b) 2 c) 3 d) 4
Answer
aQuestion : 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
bQuestion : 21 If nP3 = 4 x nP2. Find n.
a) 3 b) 2 c) 6 d) 5
Answer
cQuestion : 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
cQuestion : 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
cQuestion : 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
dQuestion : 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
bQuestion : 27 Determine n if 2nC3: nC3 = 9:1.
a) 7 b) 14 c) 28 d) 32
Answer
bQuestion : 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
cQuestion : 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
aQuestion : 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
cQuestion : 31 If 14Cr = 14
and 15Cr = 15. Find
the value of 14Cr-1.
a) 1 b) 14 c) 15 d) 3
Answer
aQuestion : 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
1Question : 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!
= 40320Question : 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 = 204Question : 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
cQuestion : 41 Permutation is also
known as selection.
a) True
b) False
Answer
bQuestion : 42 Order matters in
combination.
a) True
b) False
Answer
b
Question : 43 Is nCr = nCn-r true?
a) True
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