Question
Statement-I : If a, b, c are three positive numbers in G.P., then 
Statement-II : (A.M.) (H.M.) = (G.M.)2 is true for any set of positive numbers.
- Statement-I is true, Statement-II is true ; Statement-II is correct explanation for Statement-I.
- Statement-I is true, Statement-II is true ; Statement-II is NOT a correct explanation for statement-I.
- Statement-I is true, Statement-II is false.
- Statement-I is false, Statement-II is true.
Hint:
the property is valid for all numbers in GP
The correct answer is: Statement-I is true, Statement-II is true ; Statement-II is correct explanation for Statement-I.
Statement-I is true, Statement-II is false.
From the property of sequences, we know that
(AM)(HM)=GM2 when numbers are in GP
However, the statement 2 states that it is only valid for positive numbers, which is false since it is also valid for negative numbers.
The relation between AM, GM and HM of a sequence states that (AM)(HM)=GM2
Related Questions to study
Statement-I : If x2y3 = 6(x, y > 0), then the least value of 3x + 4y is 10
Statement-II : If m1, m2 
N, a1, a2 > 0 then 
and equality holds when a1 = a2.
the AM GM rule is valid for any set of natural numbers, i.e., numbers > 0.
Statement-I : If x2y3 = 6(x, y > 0), then the least value of 3x + 4y is 10
Statement-II : If m1, m2 N, a1, a2 > 0 then and equality holds when a1 = a2.
the AM GM rule is valid for any set of natural numbers, i.e., numbers > 0.
Statement-I : If a, b, c are three distinct positive number in H.P., then 
Statement-II : Sum of any number and it's reciprocal is always greater than or equal to 2.
when some numbers are in HP, then their reciprocals are in AP.
Statement-I : If a, b, c are three distinct positive number in H.P., then
Statement-II : Sum of any number and it's reciprocal is always greater than or equal to 2.
when some numbers are in HP, then their reciprocals are in AP.
Statement-I : In any ΔABC, maximum value of r1 + r2 + r3 =9R/2.
Statement-II : In any ΔABC, R ≥ 2r.
Statement-I : In any ΔABC, maximum value of r1 + r2 + r3 =9R/2.
Statement-II : In any ΔABC, R ≥ 2r.
Statement-I : If 27 abc ≥ (a + b + c)3 and 3a + 4b + 5c = 12 then 
where a, b, c are positive real numbers.
Statement-II : For positive real numbers A.M. ≥ G.M.
a,b,c are positive real numbers
=> AM>= GM can be applied to these numbers
for real and positive numbers, we can use the property AM>=GM
Statement-I : If 27 abc ≥ (a + b + c)3 and 3a + 4b + 5c = 12 then where a, b, c are positive real numbers.
Statement-II : For positive real numbers A.M. ≥ G.M.
a,b,c are positive real numbers
=> AM>= GM can be applied to these numbers
for real and positive numbers, we can use the property AM>=GM
Statement-I : Minimum value of 
Statement-II : The least value of a sin q + b cosq is 
Statement-I : Minimum value of
Statement-II : The least value of a sin q + b cosq is
At point of intersection of the two curves shown, the conc. of B is given by …….. For,
:
At point of intersection of the two curves shown, the conc. of B is given by …….. For,:
Following is the graph between log 
and log a (a 
initial concentration) for a given reaction at 27oC. Hence, order is
Following is the graph between log and log a (a initial concentration) for a given reaction at 27oC. Hence, order is
Statement-I : Circumradius and inradius of a triangle can not be 12 and 8 respectively.
Statement-II : Circumradius ≥ 2 (inradius)
The circumradius of a cyclic polygon is a radius of the circle inside which the polygon can be inscribed
inradius is the radius of the circle inscribed inside a polygon.
Statement-I : Circumradius and inradius of a triangle can not be 12 and 8 respectively.
Statement-II : Circumradius ≥ 2 (inradius)
The circumradius of a cyclic polygon is a radius of the circle inside which the polygon can be inscribed
inradius is the radius of the circle inscribed inside a polygon.
Statement-I : For n N, 2n > 1 + n 
Statement-II : G.M. > H.M. and (AM) (HM) = (GM)2
for real and positive numbers, we can use the property AM>=GM
the statement 2 doesn't have any connection with statement 1
Statement-I : For n N, 2n > 1 + n
Statement-II : G.M. > H.M. and (AM) (HM) = (GM)2
for real and positive numbers, we can use the property AM>=GM
the statement 2 doesn't have any connection with statement 1
Statement-I : 1, 2, 4, 8, ......... is a G.P., 4, 8, 16, 32 is a G.P. and 1 + 4, 2 + 8, 4 + 16, 8 + 32, ....... is also a G.P.
Statement-II : Let general term of a G.P. (with positive terms) with common ratio r be Tk + 1 and general term of another G.P. (with positive terms) with common ratio r be T'k + 1, then the series whose general term T''k + 1 = Tk + 1 + T'k + 1 is also a G.P. with common ratio r.
the mathematical reasoning can be proved by observing the term of the sequences
Statement-I : 1, 2, 4, 8, ......... is a G.P., 4, 8, 16, 32 is a G.P. and 1 + 4, 2 + 8, 4 + 16, 8 + 32, ....... is also a G.P.
Statement-II : Let general term of a G.P. (with positive terms) with common ratio r be Tk + 1 and general term of another G.P. (with positive terms) with common ratio r be T'k + 1, then the series whose general term T''k + 1 = Tk + 1 + T'k + 1 is also a G.P. with common ratio r.
the mathematical reasoning can be proved by observing the term of the sequences
Let p, q, r R+ and 27 pqr ≥ (p + q + r)3 and 3p + 4q + 5r = 12 then p3 + q4 + r5 is equal to -
for real and positive numbers, we can use the property AM>=GM
Let p, q, r R+ and 27 pqr ≥ (p + q + r)3 and 3p + 4q + 5r = 12 then p3 + q4 + r5 is equal to -
for real and positive numbers, we can use the property AM>=GM
, the rate of formation of 
is 0.04 mole lit-1sec-1. Determine the rate of disappearance of 
and 
then which of the following indicates the relative ease with which the reaction moves?
(g), at 900 K. following data are observed.
the number of 
emitted is
