6
Q:

The value of x satisfying the following relation:

A) 1/3 B) -1/3
C) 3 D) None of these

Answer:   D) None of these

Explanation:

          \inline \log_{\frac{1}{2}}x=\log_{2}(3x-2)

\inline \Rightarrow    \inline -\log_{2}x = \log_{2}(3x-2)

\inline \Rightarrow    \inline \log_{2}(x^{-1})= \log_{2}(3x-2)

\inline \Rightarrow        \inline x^{-1}=(3x-2)

\inline \Rightarrow      \inline 3x^{2}-2x-1=0

\inline \Rightarrow      \inline 3x^{2}-3x+x-1=0

\inline \Rightarrow     \inline 3x(x-1)+1(x-1)=0

\inline \Rightarrow      x = 1, x= -1/3

but at x=-1/3, log x is not defined.

The only admissible value of x is 1.

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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1 31
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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3 238
Q:

If  , then 

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

Explanation:

Given  

Now  = 

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5 295
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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7 636
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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9 876