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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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1. A
   $\rightarrow , \rightarrow$
2. B
   $\land , \vee$
3. C
   $\vee , \rightarrow$
4. D
   $\land , \rightarrow$

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1. A
   20
2. B
   19
3. C
   18
4. D
   21

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1. A
   $- 15 - 20\sqrt{3},15 - 20\sqrt{3}$
2. B
   $15 + 20\sqrt{3},15 - 20\sqrt{3}$
3. C
   $15 - 20\sqrt{3},15 + 20\sqrt{3}$
4. D
   $- 15 + 20\sqrt{3},15 + 20\sqrt{3}$

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

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1. A
   1.03
2. B
   1.30
3. C
   1.37
4. D
   10.3

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1. A
   $v_{n} \propto n$
2. B
   $v_{n} \propto \frac{1}{n}$
3. C
   $v_{n} \propto n^{2}$
4. D
   $v_{n} \propto \frac{1}{n^{2}}$

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1. A
   $\frac{1}{c}\left( \frac{2\text{ }m}{E} \right)^{1/2}$
2. B
   $\frac{1}{c}\left( \frac{E}{2\text{ }m} \right)^{1/2}$
3. C
   $\left( \frac{E}{2m} \right)^{1/2}$
4. D
   $c(2mE)^{1/2}$

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1. A
   $\frac{2{\text{ }K}_{1}{\text{ }K}_{2}}{{\text{ }K}_{1} + K_{2}}$
2. B
   $\frac{K_{1} + K_{2}}{2{\text{ }K}_{1}{\text{ }K}_{2}}$
3. C
   $\frac{K_{1} + K_{2}}{{\text{ }K}_{1}{\text{ }K}_{2}}$
4. D
   $\frac{K_{1}{\text{ }K}_{2}}{{\text{ }K}_{1} + K_{2}}$

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1. A
   $8.36\text{ }cm$
2. B
   $8.54\text{ }cm$
3. C
   $8.58\text{ }cm$
4. D
   $8.56\text{ }cm$

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

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1. A
   $m\left( \frac{v^{2}}{\mu_{s}R} + g \right)$
2. B
   $m\left( \frac{v^{2}}{\mu_{s}R} - g \right)$
3. C
   $m\left( g - \frac{v^{2}}{\mu_{s}R} \right)$
4. D
   $- m\left( g + \frac{v^{2}}{\mu_{s}R} \right)$

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1. A
   $\frac{4\alpha\beta}{(\alpha + \beta)}t^{2}$
2. B
   $\frac{2\alpha\beta}{(\alpha + \beta)}t^{2}$
3. C
   $\frac{\alpha\beta}{2(\alpha + \beta)}t^{2}$
4. D
   $\frac{\alpha\beta}{4(\alpha + \beta)}t^{2}$

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1. A
   $\pi T$
2. B
   $2 \times 10^{- 3}\pi T$
3. C
   $\frac{\pi}{5}\text{ }T$
4. D
   $10^{- 4}\pi T$

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1. A
   $L_{A}$ and $L_{B}$ are both constant in magnitude and direction
2. B
   $L_{B}$ is constant in direction with varying magnitude
3. C
   $L_{B}$ is constant, both in magnitude and direction
4. D
   $L_{A}$ is constant, both in magnitude and direction

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1. A
   $x = 0$
2. B
   $x = \pm A$
3. C
   $x = \pm \frac{A}{\sqrt{2}}$
4. D
   $x = \frac{A}{2}$

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1. A
   $3200\text{ }J$
2. B
   $1800\text{ }J$
3. C
   $1600\text{ }J$
4. D
   $2400\text{ }J$

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1. A
   $0.30\text{ }cm$
2. B
   $15\text{ }cm$
3. C
   $1.5\text{ }cm$
4. D
   $30\text{ }cm$

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1. A
   XOR Gate
2. B
   NAND Gate
3. C
   AND Gate
4. D
   NOR Gate

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1. A
   $19.0{\text{ }ms}^{- 1}$
2. B
   $4.47{\text{ }ms}^{- 1}$
3. C
   $14.41{\text{ }ms}^{- 1}$
4. D
   $1.00{\text{ }ms}^{- 1}$

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