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:

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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7 496
Q:

For  and  , then which one of the following is correct?

A) P < Q B) P = Q
C) P > Q D) can't be determined
 
Answer & Explanation Answer: C) P > Q

Explanation:

 for (k,l) > 0 and  k > l

Let     k = x+1    and   l = x

 

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6 469
Q:

The Value of   is 

A) -1 B) 0
C) 1/2 D) 1
 
Answer & Explanation Answer: B) 0

Explanation:

                                                                 

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6 512
Q:

What is the number of digits in ? Given that log3 = 0.47712?

A) 12 B) 13
C) 14 D) 15
 
Answer & Explanation Answer: B) 13

Explanation:

 Let   

Then ,    

= 27 x 0.47712 = 12.88224

Since the characteristic in the resultant value of log x is 12

 The number of digits in x is (12 + 1) = 13

Hence the required number of digits in  is 13.

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4 541
Q:

Find value of 

A) 1/2 B) 3/2
C) 2 D) 2/3
 
Answer & Explanation Answer: B) 3/2

Explanation:

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5 521