NCERT Solutions for class 11 Maths | Chapter 7 - Permutations and Combinations

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Questions
1 Four dice are rolled. The number of possible outcomes in which at least one dice show 2 is
A 1296
B 671
C 625
D 585

Answer:671
2 How many ways are here to arrange the letters in the word GARDEN with the vowels in alphabetical order?
A 120
B 240
C 360
D 480

Answer:360
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3 The number of ways can the letters of the word ASSASSINATION be arranged so that all the S are together is
A 152100
B 1512
C 15120
D 151200

Answer:151200
4 In how many ways can 4 different balls be distributed among 5 different boxes when any box can have any number of balls?
A 54 – 1
B 54
C 45 – 1
D 45

Answer:54
5 The number of combination of n distinct objects taken r at a time be x is given by
A n/2Cr
B n/2Cr/2
C n/2/2
D nCr

Answer:nCr
6 The value of P(n, n – 1) is
A n
B 2n
C n!
D 2n!

Answer:n!
7 Four dice are rolled. The number of possible outcomes in which at least one dice show 2 is
A 1296
B 671
C 625
D 585

Answer:671
8 There are 12 points in a plane out of which 5 are collinear. The number of triangles formed by the points as vertices is
A 185
B 210
C 220
D 175

Answer:210
9 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:1
10 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:450
11 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:450
12 The number of squares that can be formed on a chess board is
A 64
B 160
C 224
D 204

Answer:204
13 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:196
14 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:720
15 In how many ways in which 8 students can be sated in a line is
A 40230
B 40320
C 5040
D 50400

Answer:40320
16 The number of ways in which 8 distinct toys can be distributed among 5 children is
A 58
B 85
C 8P5
D 5P5

Answer: 58
17 Out of 5 apples, 10 mangoes and 13 oranges, any 15 fruits are to be distributed among 2 persons. Then the total number of ways of distribution is
A 1800
B 1080
C 1008
D 8001

Answer:1008
18 6 men and 4 women are to be seated in a row so that no two women sit together. The number of ways they can be seated is
A 604800
B 17280
C 120960
D 518400

Answer:604800
19 Let Tn denote the number of triangles which can be formed using the vertices of a regular polygon on n sides. If Tn+1 – Tn = 21, then n equals
A 5
B 7
C 6
D 4

Answer:7
20 How many factors are 25 × 36 × 52 are perfect squares
A 24
B 12
C 16
D 22

Answer:24

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