1. A
   Amylase and Invertase
2. B
   Invertase and Amylase
3. C
   Invertase and Zymase
4. D
   Zymase and Invertase

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1. A
   $Ca(OH)_{2}$
2. B
   ${NaHCO}_{3}$
3. C
   ${CaCl}_{2}$
4. D
   ${NH}_{4}Cl$

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

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1. A
   ${SO}_{4}^{2 -}$
2. B
   ${Ba}^{2 +}$
3. C
   ${Na}^{+}$
4. D
   ${PO}_{4}^{3 -}$

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1. A
   (A) only
2. B
   (C) only
3. C
   (B) and (D) only
4. D
   (D) only

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1. A
   Carbocation B is more stable and formed relatively at faster rate
2. B
   Carbocation A is more stable and formed relatively at slow rate
3. C
   Carbocation B is more stable and formed relatively at slow rate
4. D
   Carbocation A is more stable and formed relatively at faster rate

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1. A
   (A), (B), (C) and (D) only
2. B
   (B) and (C) only
3. C
   (A) and (E) only
4. D
   (A), (C) and (E) only

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1. A
   $\left\lbrack \frac{327}{360},\frac{329}{360} \right\rbrack$
2. B
   $\left\lbrack \frac{330}{360},\frac{331}{360} \right\rbrack$
3. C
   $\left\lbrack \frac{331}{360},\frac{334}{360} \right\rbrack$
4. D
   $\left\lbrack \frac{335}{360},\frac{336}{360} \right\rbrack$

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1. A
   0
2. B
   20
3. C
   25
4. D
   10

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1. A
   $2\log_{e}\left( \frac{2\sqrt{3} + 9}{6} \right)$
2. B
   $2\log_{e}\left( \frac{2\sqrt{3} + 10}{11} \right)$
3. C
   $2\log_{e}\left( \frac{\sqrt{3} + 7}{2} \right)$
4. D
   $2\log_{e}\left( \frac{3\sqrt{3} - 8}{4} \right)$

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1. A
   1124
2. B
   1324
3. C
   1024
4. D
   924

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1. A
   $\frac{r}{2}$
2. B
   $r$
3. C
   $2r$
4. D
   0

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1. A
   2
2. B
   0
3. C
   4
4. D
   Infinite

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1. A
   $\frac{1}{18}$
2. B
   $\frac{1}{3}$
3. C
   $\frac{1}{6}$
4. D
   $\frac{1}{9}$

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

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1. A
   is a singleton
2. B
   has exactly two elements
3. C
   has infinitely many elements
4. D
   has exactly three elements

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1. A
   $4\left( \frac{31}{3} + \frac{8}{3}\log_{e}3 \right)$
2. B
   $\left( \frac{31}{3} + \frac{8}{3}\log_{e}3 \right)$
3. C
   $4\left( \frac{31}{3} - \frac{8}{3}\log_{e}3 \right)$
4. D
   $\left( \frac{31}{3} - \frac{8}{3}\log_{e}3 \right)$

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1. A
   364
2. B
   240
3. C
   333
4. D
   360

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1. A
   72
2. B
   12
3. C
   36
4. D
   6

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1. A
   7
2. B
   9
3. C
   2
4. D
   1

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1. A
   $11:4$
2. B
   $9:4$
3. C
   $3:1$
4. D
   $2:1$

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1. A
   monotonic on $( - \infty,0) \cup (0,\infty)$
2. B
   not monotonic on $( - \infty,0)$ and $(0,\infty)$
3. C
   monotonic on $(0,\infty)$ only
4. D
   monotonic on $( - \infty,0)$ only

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1. A
   11
2. B
   14
3. C
   16
4. D
   20

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1. A
   $- \frac{1}{2}$
2. B
   $- \frac{1}{4}$
3. C
   0
4. D
   $\frac{1}{4}$

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1. A
   $\frac{529}{64}$
2. B
   $\frac{125}{72}$
3. C
   $\frac{625}{72}$
4. D
   $\frac{585}{66}$

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