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1. A
   $-\frac{45}{2}\pi^{2}$
2. B
   $-\frac{45}{2}\pi$
3. C
   $-\frac{\pi^{2}}{1440}$
4. D
   $-\frac{\pi^{2}}{2880}$

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1. A
   $\frac{13}{2}$
2. B
   $\frac{15}{2}$
3. C
   $\frac{17}{4}$
4. D
   $\frac{17}{2}$

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

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1. A
   $\frac{70}{11}$
2. B
   $\frac{11}{70}$
3. C
   $-\frac{70}{11}$
4. D
   $-\frac{11}{70}$

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

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1. A
   $\left(\frac{18}{5},\frac{8}{5}\right)$
2. B
   $\left(-\frac{8}{5},\frac{18}{5}\right)$
3. C
   $\left(\frac{8}{5},\frac{18}{5}\right)$
4. D
   $\left(-\frac{18}{5},-\frac{8}{5}\right)$

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1. A
   $3x^{2}-3y^{2}+8xy+20x+10y+25=0$
2. B
   $3x^{2}-3y^{2}+8xy-20x-10y+25=0$
3. C
   $3x^{2}-3y^{2}+8xy+10x+15y+20=0$
4. D
   $3x^{2}-3y^{2}-8xy-10x-15y-20=0$

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1. A
   $4 \text{ ms}^{-1}$
2. B
   $8 \text{ ms}^{-1}$
3. C
   $12 \text{ ms}^{-1}$
4. D
   $16 \text{ ms}^{-1}$

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1. A
   $\frac{1}{2\pi}\sqrt{\frac{A\rho g}{m}}$
2. B
   $2\pi\sqrt{\frac{A\rho g}{m}}$
3. C
   $\frac{1}{2\pi}\sqrt{\frac{m}{a\rho g}}$
4. D
   $2\pi\sqrt{\frac{m}{a\rho g}}$

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

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1. A
   $1.13 \text{ V}$
2. B
   $2.87 \text{ V}$
3. C
   $3.97 \text{ V}$
4. D
   $4.23 \text{ V}$

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1. A
   $4\pi R^2\left(n^{2/3}-1\right)T$
2. B
   $4\pi R^2\left(n^{1/3}-1\right)T$
3. C
   $4\pi R^2\left(1-n^{1/3}\right)t$
4. D
   $4\pi R^2\left(1-n^{2/3}\right)T$

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

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1. A
   $\frac{1}{\alpha} - \frac{1}{\beta}$
2. B
   $Q_2 = Q_1$
3. C
   $Q_2 = \frac{Q_1}{2}$
4. D
   $Q_2 = \frac{Q_1}{4}$

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1. A
   81 times.
2. B
   27 times.
3. C
   9 times.
4. D
   3 times.

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1. A
   $\sqrt{\frac{2qE}{mL}}$
2. B
   $\sqrt{\frac{2qEL}{m}}$
3. C
   $\sqrt{\frac{2qE}{mqL}}$
4. D
   $\sqrt{\frac{qE}{mL}}$

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

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1. A
   Reducing the separation between the slits.
2. B
   Using blue light instead of green light.
3. C
   Using red light instead of green light.
4. D
   Moving the screen away from the slits.

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1. A
   $\frac{\mu_0 l}{32r}$
2. B
   $\frac{\mu_0 I}{16r}$
3. C
   $\frac{\mu_0 I}{64r}$
4. D
   $\frac{\mu_0 I}{8r}$

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1. A
   $-\frac{\Delta\phi}{\Delta t} + R$
2. B
   $\frac{\Delta\phi}{R}$
3. C
   $\frac{\Delta\phi}{\Delta t}$
4. D
   $\frac{\Delta\phi}{\Delta t} \times R$

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1. A
   $\frac{13MR^2}{32}$
2. B
   $\frac{11MR^2}{32}$
3. C
   $\frac{9MR^2}{32}$
4. D
   $\frac{7MR^2}{32}$

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1. A
   60 m
2. B
   90 m
3. C
   120 m
4. D
   180 m

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1. A
   0.125 m
2. B
   0.150 m
3. C
   0.175 m
4. D
   0.200 m

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1. A
   5 : 1
2. B
   3 : 2
3. C
   1 : 2
4. D
   1 : 5

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1. A
   $\left(\frac{gR^2}{\omega^2}\right)^{1/3}$
2. B
   $\left(\frac{gR^2}{\omega^2}\right)^{2/3}$
3. C
   $\left(\frac{gR^2}{\omega^2}\right)^{1/2}$
4. D
   $\frac{gR^2}{\omega^2}$

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