1. A
   ${Cl}_{2}$ is more reactive than $ClF$.
2. B
   $F_{2}$ is more reactive than $ClF$.
3. C
   On hydrolysis $ClF$ froms $HOCl$ and $HF$.
4. D
   $F_{2}$ is a stronger oxidizing agent than ${Cl}_{2}$ in aqueous solution

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

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1. A
   $- \frac{11\pi}{30}$
2. B
   $\frac{\pi}{10}$
3. C
   $- \frac{7\pi}{30}$
4. D
   $- \frac{\pi}{15}$

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1. A
   $(11,26)$
2. B
   $(10.5,25)$
3. C
   $(11,25)$
4. D
   $(10.5,26)$

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1. A
   6
2. B
   12
3. C
   14
4. D
   24

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

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1. A
   $\frac{1}{3}$
2. B
   $\frac{2}{9}$
3. C
   $\frac{4}{9}$
4. D
   $\frac{5}{12}$

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1. A
   $\frac{4\pi}{9}$
2. B
   $\frac{7\pi}{18}$
3. C
   $\frac{\pi}{18}$
4. D
   $\frac{5\pi}{18}$

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1. A
   $(1 - x)^{2}f'(x) - 2(f(x))^{2} = 0$
2. B
   $(1 + x)^{2}f'(x) + 2(f(x))^{2} = 0$
3. C
   $(1 - x)^{2}f'(x) + 2(f(x))^{2} = 0$
4. D
   $(1 + x)^{2}f'(x) - 2(f(x))^{2} = 0$

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1. A
   $1 + \frac{2^{101}}{4^{101} - 1}$
2. B
   $1 + \frac{2^{100}}{4^{101} - 1}$
3. C
   $1 - \frac{2^{100}}{4^{100} - 1}$
4. D
   $1 - \frac{2^{101}}{4^{101} - 1}$

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1. A
   $420 \times 2^{19}$
2. B
   $380 \times 2^{19}$
3. C
   $380 \times 2^{18}$
4. D
   $420 \times 2^{18}$

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1. A
   $\{ 80,83,86,89\}$
2. B
   $\{ 84,86,88,90\}$
3. C
   $\{ 79,81,83,85\}$
4. D
   $\{ 84,87,90,93\}$

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1. A
   centre at $(0, - 1)$ and radius $\sqrt{2}$
2. B
   centre at $(0,1)$ and radius $\sqrt{2}$
3. C
   centre at $(0,0)$ and radius $\sqrt{2}$
4. D
   centre at $(0,1)$ and radius 2

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

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1. A
   5
2. B
   7
3. C
   $5\sqrt{3}$
4. D
   $3\sqrt{5}$

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1. A
   $\log_{e}4$
2. B
   $\log_{e}16$
3. C
   $2\log_{e}16$
4. D
   $4\log_{e}(3 + 2\sqrt{2})$

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

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1. A
   $\begin{pmatrix} \frac{1}{\sqrt{5}} & - 2021 \\ 2021 & \frac{1}{\sqrt{5}} \end{pmatrix}$
2. B
   $\begin{pmatrix} 1 & 0 \\ - 2021i & 1 \end{pmatrix}$
3. C
   $\begin{pmatrix} 1 & 0 \\ 2021i & 1 \end{pmatrix}$
4. D
   $\begin{pmatrix} 1 & - 2021i \\ 0 & 1 \end{pmatrix}$

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1. A
   $\frac{5}{2}$
2. B
   $\frac{1}{2}$
3. C
   $\frac{25}{2}$
4. D
   $\frac{9}{2}$

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

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

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

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

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

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1. A
   $- \gamma\frac{dV}{V}$
2. B
   $- \gamma\frac{V}{dV}$
3. C
   $- \frac{1}{\gamma}\frac{dV}{V}$
4. D
   $\frac{dV}{V}$

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