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Question

List I has four entries and List II has five entries. Each entry of List I is to be matched with one or more than one entries of List II.

List IList II (A)The vertices of a triangle are (1,a),(P)a+b=13(2,b) and (c2,3). If the centroid ofthe triangle lies on the x-axis, then(B)If a,b,c (a<b<c) are the roots of(Q)ab=12x36x2+11x6=0, then(C)If a,b,c lie between 2 and 18 such that(R)(a,b)=(5,8)(i) a+b+c=25(ii) 2,a,b are in A.P.(iii) b,c,18 are in G.P., then(D)If a,b,c are in G.P. with common ratio(S)a+b=8r (r>1) such that abc=216 and ab+bc+ca=156, then(T)a+b=3

Which of the following is the only CORRECT combination?

A
(A)(Q),(R)
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B
(A)(R),(T)
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C
(B)(Q),(T)
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D
(B)(R),(T)
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Solution

The correct option is B (A)(R),(T)
(A)
Given vertices : (1,a),(2,b),(c2,3)
Centroid lies on x-axis.
a+b33=0
a+b=3
(A)(R),(T)

(B)
Given a,b,c are the roots of x36x2+11x60 (a<b<c)
By verification, x=1 is a root.
(x1)(x25x+6)=0(x1)(x2)(x3)=0x=1,x=2,x=3a=1,b=2,c=3
(B)(T)

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