Permutation & Combination Mcq Practice Set
05 - PERMUTATIONS AND COMBINATIONS
( Answers at the end of all questions )
Page 1
(1)
If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word ‘SACHIN’ appears at serial number ( a ) 601 ( b ) 600 ( c ) 603 ( d ) 602 [ AIEEE 2005 ]
(2)
The value of
50
C4 +
55
r =1
∑
6
56
-r C 3
is
( a ) 55 C 4
(b)
C3
( c ) 56 C 3
(d)
56
C4
[ AIEEE 2005 ]
(3)
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 [ AIEEE 2004 ]
(4)
The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is (a) 5 ( b ) 21 (c) 3
8
( d ) 8 C3
[ AIEEE 2004 ]
(5)
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 ) 140 ( b ) 196 ( c ) 280 ( d ) 346 [ AIEEE 2003 ]
(6)
The number of ways in which 6 men and 5 women can dine at a round table, if no two women are to sit together, is given by ( a ) 30 (b) 5! × 5! (c) 5! × 4! (d) 7! ×5! [ AIEEE 2003 ]
(7)
If n C r
denotes the number of combinations of n things taken r at a time, then the is ( d ) n + 1Cr + 1 [ AIEEE 2003 ]
value of expression n C r + 1 + n Cr - 1 + 2 n C r ( a ) n + 2 Cr ( b ) n + 2 Cr + 1 ( c ) n + 1C r
05 - PERMUTATIONS AND COMBINATIONS
( Answers at the end of all questions ) (8)
Page 2
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 [ AIEEE 2002 ]
(9)
If n + 1 C 3 = 2 n C 2 , then the value of n is (a) 3 (b) 4 (c) 5 (d) 6 [ AIEEE 2002 ]
( 10 ) If n Cr - 1 = 36, n Cr = 84 and n C r + 1 = 126, then n and r are respectively ( a ) 9, 6 ( b ) 9, 3 ( c ) 6, 3 ( d ) 6, 2 [ AIEEE 2002 ]
( 11 ) If ( 1 + x )
= C 0 + C1 x + C 2 x 2 + ... + Cn x n , then the value of 3C 3 C1 2C 2
( Answers at the end of all questions )
Page 1
(1)
If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word ‘SACHIN’ appears at serial number ( a ) 601 ( b ) 600 ( c ) 603 ( d ) 602 [ AIEEE 2005 ]
(2)
The value of
50
C4 +
55
r =1
∑
6
56
-r C 3
is
( a ) 55 C 4
(b)
C3
( c ) 56 C 3
(d)
56
C4
[ AIEEE 2005 ]
(3)
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 [ AIEEE 2004 ]
(4)
The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is (a) 5 ( b ) 21 (c) 3
8
( d ) 8 C3
[ AIEEE 2004 ]
(5)
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 ) 140 ( b ) 196 ( c ) 280 ( d ) 346 [ AIEEE 2003 ]
(6)
The number of ways in which 6 men and 5 women can dine at a round table, if no two women are to sit together, is given by ( a ) 30 (b) 5! × 5! (c) 5! × 4! (d) 7! ×5! [ AIEEE 2003 ]
(7)
If n C r
denotes the number of combinations of n things taken r at a time, then the is ( d ) n + 1Cr + 1 [ AIEEE 2003 ]
value of expression n C r + 1 + n Cr - 1 + 2 n C r ( a ) n + 2 Cr ( b ) n + 2 Cr + 1 ( c ) n + 1C r
05 - PERMUTATIONS AND COMBINATIONS
( Answers at the end of all questions ) (8)
Page 2
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 [ AIEEE 2002 ]
(9)
If n + 1 C 3 = 2 n C 2 , then the value of n is (a) 3 (b) 4 (c) 5 (d) 6 [ AIEEE 2002 ]
( 10 ) If n Cr - 1 = 36, n Cr = 84 and n C r + 1 = 126, then n and r are respectively ( a ) 9, 6 ( b ) 9, 3 ( c ) 6, 3 ( d ) 6, 2 [ AIEEE 2002 ]
( 11 ) If ( 1 + x )
= C 0 + C1 x + C 2 x 2 + ... + Cn x n , then the value of 3C 3 C1 2C 2