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Q.

Match the Following: 

 Column I Column II
(A)Number of ways to select n objects from 3n objects of which only n are identical and rest are distinct is  k2n1+1k(kn)!(n!)2, where k is (P)3
(B)If maximum number of points of intersection of diagonals interior to a convex polygon of n sides is  nCλ, then λ is(Q)2
(C)Five digit numbers of different digits can be made in which digits are in descending order is 10Cμ, then  μ is (R)4
(D)Number of terms in expansion of (1+20231/3)8 which are free from radical sign(s)are(S)5
  (t)1

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a

(A)  (S), (B)  (P), (C)  (P), (D)  (Q)

b

(A)  (Q), (B)  (R), (C)  (S), (D)  (P)

c

(A)  (R), (B)  (Q), (C)  (S), (D)  (P)

d

(A)  (P), (B)  (R), (C)  (Q), (D)  (R)

answer is B.

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Detailed Solution

detailed_solution_thumbnail

(A) Required number of selections  =2nC0+2nC1+........+2nCn=22n1+12(2n)!(n!)2

 (B)  nC4  (Each quadrilateral gives one point of intersection)

(C)  x4>x3>x2>x1>x0

(D) Terms is involving  20230,20233/3,20236/33

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