5
Q:

The number of solutions of the equation  is:

A) 0 B) 1
C) 2 D) 3

Answer:   D) 3



Explanation:

By changing the base to 2 the given equation becomes

         \inline \frac{\log_{2}x^{2}}{\log_{2}x/2}+\frac{40\log_{2}\sqrt{x}}{\log_{2}4x}-14\frac{\log_{2}x^{3}}{\log_{2}16x}=0

\inline \Rightarrow     \inline \frac{2\log_{2}x}{\log_{2}x-1}+20\frac{\log_{2}x}{2+\log_{2}x}-42\frac{\log_{2}x}{4+\log_{2}x}=0

Let \inline t=\log_{2}x, then we have

         \inline 2t(4+t)(2+t)-42t(t-1)(t+2)+20t(t-1)(t+4)=0

 \inline \Rightarrow    \inline 2t[t^{2}+6t+8-21t^{2}-21t+42+10t^{2}+30t-40]=0

 \inline \Rightarrow    \inline t[2t^{2}-3t-2]=0

 \inline \Rightarrow     t = 0, t = 2, t = -1/2

 \inline \Rightarrow     x = 1, x = 4, x = \inline \frac{1}{\sqrt{2}}

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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3 242
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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6 471
Q:

If  , then 

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

Explanation:

Given  

Now  = 

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7 504
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 1314
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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17 1163