Question

[MULTIPLE OBJECTIVE TYPE] choices (A), (B), (C), (D) out of which ONE OR MORE may be correct. Q.12 to Q.13 has four choices (A), (B), (); Q.12 In which of the following case(s) th (A) m=(log25)2 and n=log220 the following case(s) the real number 'm' is greater than the real number'n? (B) m= log102 and n= log10 V10 (1 = and n=log1/3 (D) m=log 1/2 (C) m = log105 log1020 + (log102)2 and n=1

JEE/Engineering Exams

Maths

Solution

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i) ( m=(log 25) 2=(1.3979) 2 ) 2.796 ( x=log 220=2 cdot 342 ) ( Rightarrow quad m>n ) is. ( m=log 102=2.009 ) ( n=log 10 sqrt[3]{10}=left(log 10^{4 / 3}right)=frac{4}{3}= ) ( Rightarrow quad m>n ) ( begin{aligned} m &=log 105 cdot log 1020+[log (102)] 2 &=2.02 cdot 3.009+2 times 2 cdot 009= & 10+0.6 cdot 0.78+4 cdot 018=10 cdot 096 end{aligned} ) ( f(u) quad m=log 1 / 2left(frac{1}{3}right)=left(10-0.3 times frac{1}{3}=-0.1right. ) ( n=log 1 / 3left(frac{1}{2}right)=-0.48 times frac{1}{2}=-0.24 ) ( Rightarrow quad m>n ) hence in each foll. case mis greataten