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

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

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1. A
   $\cot^2\frac{\alpha}{2}$
2. B
   $\tan^2\frac{\alpha}{2}$
3. C
   $\tan\alpha$
4. D
   $\cot\frac{\alpha}{2}$

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1. A
   $x \in (2,4]$
2. B
   $x \in [2,4]$
3. C
   $x \in [2,4)$
4. D
   $x \in (2,4)$

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

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1. A
   $\frac{n^2-1}{12}$
2. B
   $\frac{(n-1)^2}{12}$
3. C
   $\frac{n^2}{12}-1$
4. D
   $\frac{n^2-1}{12}$

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1. A
   Table (a): P(0)=2/8, P(1)=2/8, P(2)=3/8, P(3)=1/8
2. B
   Table (b): P(0)=1/8, P(1)=3/8, P(2)=3/8, P(3)=1/8
3. C
   Table (c): P(1)=3/8, P(2)=3/8, P(3)=2/8
4. D
   Table (d): P(0)=1/8, P(1)=1/8, P(2)=3/8, P(3)=3/8

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1. A
   11
2. B
   12
3. C
   9
4. D
   10

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

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

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1. A
   $\vec{r}=(2\hat{i}-\hat{j}+\hat{k})+\lambda(-2\hat{i}+2\hat{j}-\hat{k})$
2. B
   $\vec{r}=(2\hat{i}-\hat{j}+\hat{k})+\lambda(2\hat{i}+6\hat{j}+3\hat{k})$
3. C
   $\vec{r}=(2\hat{i}-\hat{j}+\hat{k})+\lambda(2\hat{i}-2\hat{j}-\hat{k})$
4. D
   $\vec{r}=(2\hat{i}-\hat{j}+\hat{k})+\lambda(2\hat{i}-6\hat{j}-3\hat{k})$

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1. A
   $\vec{r}\cdot(2\hat{i}+\hat{j}-2\hat{k})=9$
2. B
   $\vec{r}\cdot(-2\hat{i}-\hat{j}-2\hat{k})=7$
3. C
   $\vec{r}\cdot(2\hat{i}-\hat{j}-2\hat{k})=9$
4. D
   $\vec{r}\cdot(2\hat{i}-\hat{j}-\hat{k})=7$

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1. A
   12
2. B
   30
3. C
   15
4. D
   33

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1. A
   $\frac{1}{b+c}$
2. B
   $\frac{1}{b}$
3. C
   $\frac{1}{c}$
4. D
   $\frac{1}{a}$

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1. A
   $\frac{x}{2}+\frac{1}{2}\log|2x+1|+c$
2. B
   $\frac{x}{2}-\frac{1}{4}\log|2x+1|+c$
3. C
   $\frac{x}{2}-\frac{1}{2}\log|2x+1|+c$
4. D
   $\frac{x}{2}+\frac{1}{4}\log|2x+1|+c$

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1. A
   $(p\wedge q)\to r$ has truth value False.
2. B
   $(p\to q)\to r$ has truth value True.
3. C
   $(p\vee q)\leftrightarrow r$ has truth value False.
4. D
   $(p\to q)\to(q\to p)$ has truth value True.

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

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

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1. A
   $\frac{1}{3}$
2. B
   $\frac{4}{11}$
3. C
   $\frac{5}{18}$
4. D
   $\frac{5}{36}$

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1. A
   160 cm/s
2. B
   80 cm/s
3. C
   320 cm/s
4. D
   480 cm/s

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

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1. A
   $\frac{L^{2}\omega^{2}}{3g}$
2. B
   $\frac{L^{2}\omega^{2}}{2g}$
3. C
   $\frac{L^{2}\omega^{2}}{6g}$
4. D
   $\frac{L^{2}\omega^{2}}{4g}$

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1. A
   1.5 times
2. B
   two times
3. C
   Nine times
4. D
   four times

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1. A
   20 cal
2. B
   35 cal
3. C
   45 cal
4. D
   65 cal

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

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