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...

( 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...

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