# AMCAT Numbers and Divisibility Quiz-1

Question 1

Time: 00:00:00
Find the inverse function of $f(x) = \frac{2x-1}{x+4}$.

$f^{-2}(x) = \frac{4x-1}{x-2}$

$f^{-2}(x) = \frac{4x-1}{x-2}$

$f^{-1}(x) = \frac{-4x-2}{x-2}$

$f^{-1}(x) = \frac{-4x-2}{x-2}$

$f^{-1}(x) = \frac{-4x-1}{x-2}$

$f^{-1}(x) = \frac{-4x-1}{x-2}$

$f^{-1}(x) = \frac{-4x-1}{-x-1}$

$f^{-1}(x) = \frac{-4x-1}{-x-1}$

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Question 2

Time: 00:00:00
$(125)^{7} × (125)^{x} = (125)^{11.5}$

2.5

2.5

3.5

3.5

4.5

4.5

5.5

5.5

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Question 3

Time: 00:00:00
Evaluate $\frac{5.45^{2}-3.32^{2}}{5.45 - 3.32}$

5.24

5.24

6.87

6.87

5.45

5.45

8.77

8.77

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Question 4

Time: 00:00:00
What is the inverse function of $g(x) = e^x$?

$g^{-1}(x) = log(x)$

$g^{-1}(x) = log(x)$

$g^{-1}(x) = ln(x)$

$g^{-1}(x) = ln(x)$

$g^{-1}(x)= e^x$

$g^{-1}(x)= e^x$

$g^{-1}(x) = x^2$

$g^{-1}(x) = x^2$

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Question 5

Time: 00:00:00
$\left ( \frac{a}{b} \right )^{x-2} = \left ( \frac{b}{a} \right )^{x-4}$
What is the value of x ?

8

8

3

3

5

5

2

2

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Question 6

Time: 00:00:00
Convert 5.46 + 2.23 + 1.96 into fraction

65/54

65/54

144/45

144/45

193/20

193/20

180/54

180/54

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Question 7

Time: 00:00:00
Find the inverse function of $f(x) = e^{2x}$

$f^{-1}(x) = \frac{x}{2}$

$f^{-1}(x) = \frac{x}{2}$

$f^{-1}(x) = ln(x)$

$f^{-1}(x) = ln(x)$

$f^{-1}(x) = \frac{ln(x)}{2}$

$f^{-1}(x) = \frac{ln(x)}{2}$

None of these

None of these

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Question 8

Time: 00:00:00
$3^{x-y}=729$ and $4^{x-y}=2187$
Find the value of x and y.

5,2

5,2

3,4

3,4

6.5,0.5

6.5,0.5

4,8

4,8

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Question 9

Time: 00:00:00
Find the value of $\frac{5.45 + 6.23 * 9.7}{3.42 + 5.23 * 8.6}$

65.188 / 48.389

65.188 / 48.389

65.881 / 48.398

65.881 / 48.398

54.65 / 56.32

54.65 / 56.32

55.654 / 65.456

55.654 / 65.456

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Question 10

Time: 00:00:00
Find the inverse function of f(x) = ln(3x).

$f^{-1}(x) = \frac{lnx}{3}$

$f^{-1}(x) = \frac{lnx}{3}$

$f^{-1}(x) = 3e^{x}$

$f^{-1}(x) = 3e^{x}$

$f^{-1}(x) = \frac{e^{x}}{3}$

$f^{-1}(x) = \frac{e^{x}}{3}$

$f^{-1}(x) = {e^{x}$

$f^{-1}(x) = {e^{x}$

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