Simulation: Questions And Answers

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 …show more content…

 !   2  [ C 0 2 - 2C 12 + 3C 2 2 - ... + ( - 1 )n ( n + 1 ) C n 2 ], n! where n is an even positive integer, is equal to (a) 0 (b) (-1) ( e ) none of these n/2 (n + 1)

(c) (-1) (n + 2)

n

(d) (-1) n [ IIT 1986 ]

n

( 23 )

Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4, and then the men select the chairs from amongst the remaining. The number of possible arrangements is (a)
6

C3 × C2

4

(b)

4

P2 × P3

4

(c)

4

C2 × P3

4

( d ) none of these

[ IIT 1982 ]

( 24 ) Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then, the number of words which have at least one letter repeated is ( a ) 69,760 ( b ) 30,240 ( c ) 99,748
5

( d ) none of these

[ IIT 1980 ]

( 25 ) The value of the expression (a)
47 C 5

47

C4 + (c)

j=1

∑

52 - j C 3

is equal to [ IIT 1980 ]

( b ) 52 C 5

52 C

4

( d ) none of these

( 26 ) n Cr - 1 = 36 n C r = 84 and n Cr + 1 = 126 , then r is (a) 1 (b) 2 (c) 3 ( d ) none of these [ IIT 1979 ]

( 27 )

There are 27 points in a plane. 5, 10 and 15 points are collinear on distinct lines. By joining