Logarithms & Binary Numbers · NDA previous year questions

2020 3 questions

1. Q62020 · 6 Sept 2020

   The number $(1101101+1011011{)}_2$ can be written in decimal system as

   1. A.$(198{)}_{10}$
   2. B.$(199{)}_{10}$
   3. C.$(200{)}_{10}$
   4. D.$(201{)}_{10}$
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   Answer: C

2. Q72020 · 6 Sept 2020

   What is the value of $\frac{1}{10}{\log }_{5}1024-{\log }_{5}10+\frac{1}{5}{\log }_{5}3125$ ?

   1. A.0
   2. B.1
   3. C.2
   4. D.3
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   Answer: A

3. Q82020 · 6 Sept 2020

   If $x={\log }_c(ab)$, $y={\log }_a(bc)$, $z={\log }_b(ca)$, then which of the following is correct?

   1. A.$xyz=1$
   2. B.$x+y+z=1$
   3. C.$(1+x{)}^{-1}+(1+y{)}^{-1}+(1+z{)}^{-1}=1$
   4. D.$(1+x{)}^{-2}+(1+y{)}^{-2}+(1+z{)}^{-2}=1$
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   Answer: C