15
Q:

The least value of expression  for x>1 is:

A) 2 B) 3
C) 4 D) 5

Answer:   C) 4



Explanation:

   \inline 2\log_{10}x-\log_{x}\frac{1}{100}=2\log_{10}x-\frac{\log_{10}10^{-2}}{\log_{10}x}

                                    \inline =2\log_{10}x+\frac{2}{\log_{10}x}

                                    \inline =2\left [ \log_{10}x-\frac{1}{\log_{10}x} \right ]

Since       x >1     \inline \Rightarrow \log_{10}x>0

But since \inline AM\geq GM

\therefore  \inline \frac{\log_{10}x+\frac{1}{\log_{10}x}}{2}\geq \sqrt{\log_{10}x\times \frac{1}{\log_{10}x}}

\inline \Rightarrow   \inline \log_{10}x+\frac{1}{\log_{10}x}\geq 2

\Rightarrow   \inline 2\left [ \log_{10}x+\frac{1}{\log_{10}x} \right ]\geq 4

For x= 10,  \inline 2\left [ \log_{10}x+\frac{1}{\log_{10}x} \right ]\geq 4

Hence the least value of \inline \left [ \log_{10}x-\log_{x}\frac{1}{100} \right ] is 4

Q:

Solve the equation   ?

A) -1/2 B) 1/2
C) 1 D) -1
 
Answer & Explanation Answer: A) -1/2

Explanation:

Rewrite equation as

Leads to 2x + 1 = 0 

Solve for x : x = -1/2

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3 189
Q:

If  = m, then  is equal to ?

A) 1/(1+2m) B) (1+2m)/2
C) 2m/(2m+1) D) (2m+1)/2m
 
Answer & Explanation Answer: B) (1+2m)/2

Explanation:

=
=

.

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6 418
Q:

If  , then 

A) 1 B) 2
C) 4 D) 8
 
Answer & Explanation Answer: B) 2

Explanation:

Given  

Now  = 

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7 437
Q:

If log 64 = 1.8061, then the value of log 16 will be (approx)?

A) 1.9048 B) 1.2040
C) 0.9840 D) 1.4521
 
Answer & Explanation Answer: B) 1.2040

Explanation:

Given that, 

 

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11 1042
Q:

A fast moving superfast express crosses another pasenger train in 20 seconds. The speed of faster train is 72 km/hr and speeds of slower train is 27 km/h. Also the length of faster ntrain is 100m, then find the length of the slower train if they are moving in the same direction.

A) 100 m B) 125 m
C) 150 m D) 175 m
 
Answer & Explanation Answer: C) 150 m

Explanation:

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14 1089