Q.

Let A=110,19,18,………,13,12,1,2,3,4,…….8,9,10, then the number of ordered pairs (a,b) such that a,b∈A and

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a

logb a≤0  is  180

b

logb a>0  is  162

c

logb a<0  is  162

d

All the above

answer is D.

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Detailed Solution

logb⁡a<0 if a>1,01 Number of pairs (a,b)= 9C1×9C1×2=162logb⁡a=0 if a=1,b≠1,b>0 Number of pairs (a,b)=18logb⁡a≤0⇒ number of ordered pairs (a,b)=180logb⁡a>0 if a>1,b>1 (or) 0
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Let A=110,19,18,………,13,12,1,2,3,4,…….8,9,10, then the number of ordered pairs (a,b) such that a,b∈A and