Practice every past-year question.

1. A
   $f(2)$
2. B
   $2f(2)$
3. C
   $2f(\sqrt{2})$
4. D
   $4f(2)$

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1. A
   $3\pi - 11$
2. B
   $4\pi - 9$
3. C
   $4\pi - 11$
4. D
   $3\pi + 1$

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1. A
   $n\left( S_{1} \right) = 2,n\left( S_{2} \right) = 2$
2. B
   $n\left( S_{1} \right) = 1,n\left( S_{2} \right) = 0$
3. C
   $n\left( S_{1} \right) = 2,n\left( S_{2} \right) = 0$
4. D
   $n\left( S_{1} \right) = 0,n\left( S_{2} \right) = 2$

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1. A
   $\left( 3,1, - \frac{1}{2} \right)$
2. B
   $\left( - 2,0, - \frac{1}{2} \right)$
3. C
   $(0,2, - 4)$
4. D
   $(4,0, - 2)$

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1. A
   $\sim (q \rightarrow p)$
2. B
   $\sim p \rightarrow \sim q$
3. C
   $\sim (p \rightarrow \sim q)$
4. D
   $\sim (p \rightarrow q)$

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1. A
   $\frac{2}{7}$
2. B
   $\frac{1}{18}$
3. C
   $\frac{1}{7}$
4. D
   $\frac{1}{9}$

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1. A
   $\frac{3}{2} - \frac{1}{\sqrt{e}}$
2. B
   $3 + \frac{1}{\sqrt{e}}$
3. C
   $3 + e$
4. D
   3 - e

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1. A
   $(3,13\pi/9)$
2. B
   $(2,2\pi/3)$
3. C
   $(2,8\pi/9)$
4. D
   $(3,5\pi/3)$

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1. A
   both (S1) and (S2) are true
2. B
   (S1) is false and (S2) is true
3. C
   both (S1) and (S2) are false
4. D
   (S1) is true and (S2) is false

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1. A
   $(15)^{2} \times 2^{42}$
2. B
   $(15)^{2} \times 2^{34}$
3. C
   $(105)^{2} \times 2^{38}$
4. D
   $(105)^{2} \times 2^{36}$

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1. A
   $2\sqrt{2}(\sqrt{2} - 1)$
2. B
   $2(\sqrt{2} + 1)$
3. C
   $4(\sqrt{2} - 1)$
4. D
   $2\sqrt{2}(\sqrt{2} + 1)$

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1. A
   $\sqrt{26}$
2. B
   $2\sqrt{5}$
3. C
   $2\sqrt{6}$
4. D
   $4\sqrt{2}$

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1. A
   $\frac{75}{8}$
2. B
   $\frac{125}{16}$
3. C
   $\frac{25}{2}$
4. D
   $\frac{15}{2}$

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1. A
   6
2. B
   2
3. C
   4
4. D
   8

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1. A
   $\frac{e - 1}{3}$
2. B
   $\frac{e - 2}{6}$
3. C
   $\frac{e}{3}$
4. D
   $\frac{e}{6}$

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1. A
   12
2. B
   419
3. C
   443
4. D
   455

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1. A
   $(0,\sqrt{5})$
2. B
   $\lbrack - 2,2\rbrack$
3. C
   $\left\lbrack \frac{1}{\sqrt{5}},\sqrt{5} \right\rbrack$
4. D
   $\lbrack 0,2\rbrack$

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1. A
   57
2. B
   72
3. C
   48
4. D
   36

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1. A
   $x + \frac{2}{3}(\pi - 2)\sin x$
2. B
   $x + (\pi + 2)\sin x$
3. C
   $x + \frac{\pi}{2}\sin x$
4. D
   $x + (\pi - 2)\sin x$

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1. A
   $\frac{5}{2\sqrt{3}}$
2. B
   $\frac{2}{\sqrt{3}}$
3. C
   $\frac{4}{\sqrt{3}}$
4. D
   2

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