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Q.

Let  A={1,2,3,4},   B={1,2,3,4,5,6,7,8}

 Column-I Column-II
P)

The number of functions f:BA,suchthat

if x1>x2, then f(x1)f(x2)x1,x2B

is N. Then the sum of digits of N  is

(1)7
Q)The number of onto functions f:BA  such that if x1>x2, then f(x1)f(x2)    x1, x2B   is  N. Then the sum of digits of N is(2)8
R)The numbers of oneone function f:AB   such that f(x)x    xA is N. Then the sum of digits of N is(3)9
S)The number of oneone function f:AB   such that there are exactly two, x,   xA for which f(x)=x is N. Then the   sum of digits of N is(4)10
  (5)12

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a

P-4;   Q-1;   R-5;   S-2

b

P-4;   Q-2;  R-3;   S-2

c

P-5;  Q-2;   R-1;   S-3

d

P-1;   Q-2;   R-3;   S-4

answer is A.

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Detailed Solution

(A)   N= 8+3C3=165
(B)   N= 84+3C3=35
(C)   N= 8C44!( 4C1 7C33! 4C2 6C22!+ 4C3 5C11)=1006
(D)  N= 4C2×4×3=72

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