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1. A
   $\frac{1}{5}\left[\frac{\pi}{4}-\tan^{-1}\!\left(\frac{1}{3\sqrt{3}}\right)\right]$
2. B
   $\frac{1}{2}\left[\frac{\pi}{4}-\tan^{-1}\!\left(\frac{1}{9\sqrt{3}}\right)\right]$
3. C
   $\frac{1}{10}\left[\frac{\pi}{4}-\tan^{-1}\!\left(\frac{1}{9\sqrt{3}}\right)\right]$
4. D
   $\frac{1}{10}\left[\frac{\pi}{4}-\tan^{-1}\!\left(\frac{1}{3\sqrt{3}}\right)\right]$

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1. A
   $C\equiv(3,0), r=4$
2. B
   $C\equiv(6,0), r=2$
3. C
   $C\equiv(0,3), r=8$
4. D
   $C\equiv(0,0), r=2\sqrt{2}$

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1. A
   $-n^2y$
2. B
   $n^2y$
3. C
   $n^2x$
4. D
   $n^2x^2$

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1. A
   $\frac{1}{7}$
2. B
   $\frac{2}{7}$
3. C
   $\frac{6}{7}$
4. D
   $\frac{4}{7}$

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1. A
   7
2. B
   12
3. C
   6
4. D
   5

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1. A
   $\frac{\pi}{4}x - x + c$
2. B
   $\frac{\pi}{4}-\frac{x}{2}+c$
3. C
   $\frac{\pi}{4}x-\frac{x^2}{4}+c$
4. D
   $\frac{\pi}{4}x+\frac{x^2}{4}+c$

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

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1. A
   $x-3y=0$
2. B
   $x+3y=0$
3. C
   $x+2y=0$
4. D
   $3x+y=0$

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1. A
   $x-2\log|x+1|-\frac{1}{x+1}+c$
2. B
   $x-2\log|x+1|-\frac{2}{x+1}+c$
3. C
   $x-\log|x+1|-\frac{2}{x+1}+c$
4. D
   $x-\log|x+1|-\frac{x}{x+1}+c$

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1. A
   $x^2+y^2-4x-6y+77=0$
2. B
   $x^2+y^2-4x-6y-89=0$
3. C
   $x^2+y^2-4x-6y+97=0$
4. D
   $x^2+y^2-4x-6y-87=0$

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1. A
   $75°$
2. B
   30°
3. C
   60°
4. D
   45°

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1. A
   $0.7934, \frac{\pi}{9}$
2. B
   $\frac{1}{2}, \frac{\pi}{4}$
3. C
   $\frac{5}{8}, \frac{\pi}{3}$
4. D
   $0.75, \frac{\pi}{8}$

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1. A
   $\frac{256\cdot49^4}{7^{18}}$
2. B
   $\frac{1966\cdot49^4}{7^{18}}$
3. C
   $\frac{1710\cdot49^4}{7^{18}}$
4. D
   $\frac{1726\cdot49^4}{7^{18}}$

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1. A
   $\frac{1}{y}-\frac{1}{x}$
2. B
   $\frac{1}{x}-\frac{1}{y}$
3. C
   $\frac{1}{x}+\frac{1}{y}$
4. D
   $\frac{xy}{x-y}$

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1. A
   $\frac{9}{2}R$
2. B
   $\frac{5}{2}R$
3. C
   $\frac{3}{2}R$
4. D
   $\frac{7}{2}R$

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1. A
   3.8 pF
2. B
   20.25 pF
3. C
   40.5 pF
4. D
   45 pF

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1. A
   0.25 mA
2. B
   0.05 mA
3. C
   0.12 mA
4. D
   0.02 mA

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1. A
   22
2. B
   44
3. C
   66
4. D
   88

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1. A
   $\tan^{-1}\!\left(\frac{1}{2}\right)$
2. B
   $\tan^{-1}(2)$
3. C
   $\tan^{-1}\!\left(\frac{1}{4}\right)$
4. D
   $\tan^{-1}(4)$

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1. A
   The r.m.s. current in circuit (B) can never be greater than that in circuit (A)
2. B
   The r.m.s. current in circuit (A) is always equal to that in circuit (B)
3. C
   The r.m.s. current in circuit (B) can be greater than in circuit (A)
4. D
   At resonance, current in (B) is less than that in circuit (A)

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

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

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1. A
   $1\,\Omega$
2. B
   $2\,\Omega$
3. C
   $3\,\Omega$
4. D
   $4\,\Omega$

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1. A
   $\left(1-\frac{d}{R}\right)^{-1}$
2. B
   $1-\frac{d}{R}$
3. C
   $\left(1+\frac{d}{R}\right)^{-1}$
4. D
   $1+\frac{d}{R}$

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1. A
   $50^\circ$
2. B
   $40^\circ$
3. C
   $25^\circ$
4. D
   $20^\circ$

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