15
Q:

For ,  and  $p={\mathrm{log}}_{x}\left(x+1\right)$, $q={\mathrm{log}}_{x+1}\left(x+2\right)$ then which one of the following is correct?

 A) p < q B) p = q C) p > q D) can't be determined

Answer:   C) p > q

Explanation:

$\frac{k}{l}>\frac{k+1}{l+1}$ for (k,l) > 0 and  k > l

Let     k = x+1    and   l = x

Therefore, $\frac{x+1}{x}>\frac{\left(x+1\right)+1}{\left(x\right)+1}$

(x + 1) > x

Therefore, $\frac{\mathrm{log}\left(x+1\right)}{\mathrm{log}\left(x\right)}>\frac{\mathrm{log}\left(x+2\right)}{\mathrm{log}\left(x+1\right)}$

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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11 1488
Q:

If ${\mathrm{log}}_{7}\left(2\right)$ = m, then ${\mathrm{log}}_{49}\left(28\right)$ 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:

= $\frac{1}{2}+\frac{1}{2}\left(2{\mathrm{log}}_{7}\left(2\right)\right)$
= $\frac{1}{2}+{\mathrm{log}}_{7}\left(2\right)$

$\frac{1+2m}{2}$.

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16 2184
Q:

If  , then

 A) 1 B) 2 C) 4 D) 8

Answer & Explanation Answer: B) 2

Explanation:

Given

Now

${\mathrm{log}}_{b}\left({c}^{2}-{a}^{2}\right)$

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12 1700
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, log 64 = 1.8061

i.e $\mathrm{log}\left({4}^{3}\right)=1.8061$

--> 3 log 4 = 1.8061

--> log 4 = 0.6020

--> 2 log 4 = 1.2040

$⇒\mathrm{log}\left({4}^{2}\right)=1.2040$

Therefore, log 16 = 1.2040

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21 4149
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:

$20=\frac{\left(100+x\right)}{25}{2}}$

$⇒$ X=150m

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22 2677
Q:

The Value of  $\left[\mathrm{log}\left(\mathrm{tan}\left({1}^{0}\right)\right)+\mathrm{log}\left(\mathrm{tan}\left({2}^{0}\right)\right)+\cdots \cdots +\mathrm{log}\left(\mathrm{tan}\left({89}^{0}\right)\right)\right]$ is

 A) -1 B) 0 C) 1/2 D) 1

Answer & Explanation Answer: B) 0

Explanation:

= log 1 + log 1 +.....+log 1

= 0.

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15 1760
Q:

What is the number of digits in ${3}^{{3}^{3}}$? Given that log3 = 0.47712?

 A) 12 B) 13 C) 14 D) 15

Answer & Explanation Answer: B) 13

Explanation:

Let   ${\left({3}^{3}\right)}^{3}$

Then,

= 27 x 0.47712 = 12.88224

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

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

Hence the required number of digits in ${3}^{{3}^{3}}$is 13.

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16 2069
Q:

Find value of

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

Answer & Explanation Answer: B) 3/2

Explanation:

= $\frac{3}{2}$

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13 1670