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

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1. A
   $\Delta H^\circ = T\Delta S^\circ$
2. B
   $\Delta H^\circ = \frac{\Delta S^\circ}{T}$
3. C
   $\Delta H^\circ = T\Delta S^\circ$
4. D
   $\Delta H^\circ = \frac{1}{T}\Delta S^\circ$

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1. A
   $0.195$ m
2. B
   $0.174$ m
3. C
   $0.156$ m
4. D
   $0.113$ m

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1. A
   Monomolecular and $\frac{1}{2}$
2. B
   Monomolecular and $1$
3. C
   Monomolecular and $\frac{3}{2}$
4. D
   Bimolecular and $\frac{3}{2}$

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1. A
   $-4$
2. B
   $4$
3. C
   $-3$
4. D
   $3$

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

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1. A
   $38$
2. B
   $36$
3. C
   $33$
4. D
   $34$

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1. A
   $\tan^{-1}\frac{22}{19}$
2. B
   $\tan^{-1}\frac{22}{13}$
3. C
   $\tan^{-1}\frac{21}{19}$
4. D
   $\tan^{-1}\frac{19}{22}$

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1. A
   $\left(\frac{48}{19}, \frac{23}{19}, -\frac{13}{19}\right)$
2. B
   $\left(-\frac{48}{19}, \frac{23}{19}, -\frac{13}{19}\right)$
3. C
   $\left(-\frac{48}{19}, -\frac{23}{19}, -\frac{13}{19}\right)$
4. D
   $\left(\frac{48}{19}, -\frac{23}{19}, -\frac{13}{19}\right)$

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1. A
   $y = \tan^{-1}(\log_e x)$
2. B
   $y = x^2\tan^{-1}(\log_e x)$
3. C
   $y = x\tan^{-1}(\log_e x)$
4. D
   $y = \frac{1}{x}\tan^{-1}(\log_e x)$

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1. A
   $\frac{63}{65}$
2. B
   $\frac{56}{65}$
3. C
   $\frac{48}{65}$
4. D
   $\frac{36}{65}$

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1. A
   $0.1$
2. B
   $0.5$
3. C
   $1$
4. D
   $2$

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

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1. A
   T, F
2. B
   F, T
3. C
   T, T
4. D
   F, F

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

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1. A
   A$(-8,6,-7)$, B$(-6,-2,-3)$
2. B
   A$(8,6,7)$, B$(6,2,3)$
3. C
   A$(8,6,7)$, B$(6,-2,-3)$
4. D
   A$(7,6,8)$, B$(-3,-2,6)$

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1. A
   $1$
2. B
   $2$
3. C
   $3$
4. D
   $4$

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1. A
   $\frac{8}{3}$
2. B
   $4$
3. C
   $2$
4. D
   $5$

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1. A
   $0$
2. B
   $\frac{1}{2\sqrt{2}}$
3. C
   $\frac{1}{4\sqrt{2}}$
4. D
   $\frac{1}{2\sqrt{2}(\sqrt{2}+1)}$

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1. A
   $4\sqrt{3}$
2. B
   $6\sqrt{3}$
3. C
   $24\sqrt{3}$
4. D
   $12\sqrt{3}$

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1. A
   $45$
2. B
   $44$
3. C
   $48$
4. D
   $40$

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1. A
   $\frac{19}{25}$
2. B
   $\frac{18}{25}$
3. C
   $\frac{16}{25}$
4. D
   $\frac{7}{25}$

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1. A
   $\frac{1}{\sqrt{6}}(-\hat{i}+2\hat{j}-\hat{k})$
2. B
   $\frac{1}{\sqrt{6}}(\hat{i}+2\hat{j}+\hat{k})$
3. C
   $\frac{1}{\sqrt{6}}(2\hat{i}-\hat{j}-\hat{k})$
4. D
   $\frac{1}{\sqrt{6}}(-\hat{i}-2\hat{j}+\hat{k})$

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1. A
   $\frac{87}{90^4}$
2. B
   $\frac{348}{90^4}$
3. C
   $\frac{874}{90^4}$
4. D
   $\frac{4}{10^4}$

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1. A
   $1$
2. B
   $2$
3. C
   $-1$
4. D
   $0$

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