Match the following and select the correct answer. List I List II A: xyz = 15/2 or 18/5 according as a, x, y, z, b are in A.P. or H.P. Then a + b equals, where a, b are positive integers. p: 2 B: The

Question

Match the following and select the correct answer.

List I	List II
A: xyz = 15/2 or 18/5 according as a, x, y, z, b are in A.P. or H.P. Then a + b equals, where a, b are positive integers.	p: 2
B: The product 2^(1/4)·4^(1/8)·8^(1/16)·... to infinity is equal to.	q: 1
C: If x, y, z are in A.P., then (x + 2y - z)(2y + z - x)(z + x - y) = kxyz, where k is a natural number. Then k is equal to.	r: 3
D: There are m A.M.s between 1 and 31. If the ratio of the 7th and (m - 1)th means is 5:9, then m/7 is equal to.	s: 4

TestHub · Accepted Answer

Item A: in A.P., x yz = 32 ( 3 a + b ) ( a + b ) ( a + 3 b ) ​ = 2 15 ​ . In H.P., x yz = ( a + 3 b ) ( a + b ) ( 3 a + b ) 32 ( ab ) 3 ​ = 5 18 ​ . Dividing, ( ab ) 3 = 27 , so ab = 3 and { a , b } = { 1 , 3 } . Then a + b = 4 . A matches s. Item B: the exponent is 4 1 ​ + 8 2 ​ + 16 3 ​ + ⋯ = ∑ 2 n + 1 n ​ = 1 , so the product is 2 1 = 2 . B matches p. Item C: with 2 y = x + z , the product is ( 2 x ) ( 2 z ) ( y ) = 4 x yz , so k = 4 . C matches s. Item D: d = m + 1 30 ​ and A m − 1 ​ A 7 ​ ​ = 1 + m + 1 30 ( m − 1 ) ​ 1 + m + 1 210 ​ ​ = 31 m − 29 m + 211 ​ = 9 5 ​ . So 146 m = 2044 , m = 14 and 7 m ​ = 2 . D matches p.

Mathematics - Sequence & Series Question with Solution | TestHub

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