1. A
   $A \land (A \vee B)$
2. B
   $B \rightarrow \lbrack A \land (A \rightarrow B)\rbrack$
3. C
   $A \vee (A \land B)$
4. D
   $\lbrack A \land (A \rightarrow B)\rbrack \rightarrow B$

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1. A
   both one-one and onto
2. B
   onto but not one-one
3. C
   neither one-one nor onto
4. D
   one-one but not onto

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1. A
   discontinuous only at $x = 1$
2. B
   discontinuous at all integral values of $x$ except at $x = 1$
3. C
   continuous only at $x = 1$
4. D
   continuous for every real $x$

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1. A
   increases in $\left\lbrack \frac{1}{2},\infty \right)$
2. B
   decreases $\left( - \infty,\frac{1}{2} \right\rbrack$
3. C
   increases in $\left( - \infty,\frac{1}{2} \right\rbrack$
4. D
   decreases $\left\lbrack \frac{1}{2},\infty \right)$

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1. A
   $\sqrt{38}$
2. B
   $19\sqrt{2}$
3. C
   $2\sqrt{19}$
4. D
   38

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1. A
   $\frac{2}{3}$
2. B
   0
3. C
   $\frac{1}{15}$
4. D
   $\frac{3}{2}$

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1. A
   25
2. B
   $20\sqrt{3}$
3. C
   30
4. D
   $25\sqrt{3}$

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1. A
   $- 2t^{3}$
2. B
   $- t^{3}$
3. C
   0
4. D
   $2t^{3}$

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

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

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

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1. A
   $2^{14}$
2. B
   $2^{13} - 13$
3. C
   $2^{16} - 1$
4. D
   $2^{13} - 14$

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1. A
   $\frac{3}{16}$
2. B
   $\frac{1}{2}$
3. C
   $\frac{5}{16}$
4. D
   $\frac{1}{32}$

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1. A
   $x^{2} - 2x + 2 = 0$
2. B
   $x^{2} - 2x + 8 = 0$
3. C
   $x^{2} - 2x + 136 = 0$
4. D
   $x^{2} - 2x + 16 = 0$

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

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1. A
   $k = 3,m = \frac{4}{5}$
2. B
   $k \neq 3,m \in R$
3. C
   $k \neq 3,m \neq \frac{4}{5}$
4. D
   $k = 3,m \neq \frac{4}{5}$

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