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1. A
   $2x+2y+\pi=0$
2. B
   $2x-2y-\pi=0$
3. C
   $x+y+\pi=0$
4. D
   $x+y-2\pi=0$

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1. A
   $-\frac{2}{\sqrt{5}}$
2. B
   $\frac{2}{\sqrt{5}}$
3. C
   $\frac{1}{\sqrt{10}}$
4. D
   $-\frac{1}{\sqrt{10}}$

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1. A
   8
2. B
   10
3. C
   9
4. D
   7

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1. A
   $\frac{x+3}{-3}=\frac{y-5}{-1}=\frac{z+2}{5}$
2. B
   $\frac{x-3}{3}=\frac{y+5}{1}=\frac{z-2}{-5}$
3. C
   $\frac{x-3}{-3}=\frac{y+5}{-1}=\frac{z-2}{5}$
4. D
   $\frac{x+3}{3}=\frac{y-5}{1}=\frac{z-2}{-5}$

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1. A
   $2\sqrt{5}$
2. B
   6
3. C
   4
4. D
   $4\sqrt{2}$

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1. A
   1
2. B
   1.5
3. C
   2
4. D
   0.5

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

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1. A
   $\theta=\alpha+\frac{n\pi}{2},\ n\in\mathbb{Z}$
2. B
   $\theta=\alpha+\frac{3n\pi}{2},\ n\in\mathbb{Z}$
3. C
   $\theta=n\pi+\alpha,\ n\in\mathbb{Z}$
4. D
   $\theta=\frac{n\pi}{4}+\alpha,\ n\in\mathbb{Z}$

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1. A
   0.8778
2. B
   0.7666
3. C
   0.7916
4. D
   0.8616

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1. A
   $\frac{24}{169}$
2. B
   $\frac{52}{169}$
3. C
   $\frac{25}{169}$
4. D
   $\frac{49}{169}$

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

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1. A
   $\frac{1}{36}$
2. B
   $-\frac{6}{13}$
3. C
   $\frac{1}{13}$
4. D
   $-\frac{1}{36}$

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1. A
   Option a
2. B
   Option b
3. C
   Option c
4. D
   Option d

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

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1. A
   $-\frac{1}{2}\begin{pmatrix}3&2\\-4&2\end{pmatrix}$
2. B
   $\frac{1}{14}\begin{pmatrix}3&2\\-4&2\end{pmatrix}$
3. C
   $\frac{1}{14}\begin{pmatrix}-3&-2\\4&-2\end{pmatrix}$
4. D
   $-\frac{1}{14}\begin{pmatrix}3&2\\-4&2\end{pmatrix}$

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1. A
   $\left(x+y\frac{dy}{dx}\right)^2 x^2=\left(x^2+y^2\right)^2$ (with factor 4 in numerator)
2. B
   $\left(x+y\frac{dy}{dx}\right)^2 x^2=\left(x^2+y^2\right)^2$
3. C
   $2\left(x+y\frac{dy}{dx}\right)^2 x^2=\left(x^2+y^2\right)^2$
4. D
   $\left(x+y\frac{dy}{dx}\right)^2 x^2=4\left(x^2+y^2\right)^2$

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1. A
   the valence band is completely filled.
2. B
   the conduction band is completely empty.
3. C
   the conduction band is partially filled and the valence band is partially empty.
4. D
   the valence band is completely filled and conduction band is partially empty.

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

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1. A
   OR gate
2. B
   AND gate
3. C
   NOR gate
4. D
   NAND gate

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1. A
   9:1
2. B
   34:1
3. C
   4:1
4. D
   16:1

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1. A
   1:4
2. B
   1:8
3. C
   16:1
4. D
   12:1

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1. A
   $Rn$
2. B
   $R \cdot n$
3. C
   $(n+1)R$
4. D
   $(n-1)R$

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1. A
   $P - \frac{3}{4}\rho v^2$
2. B
   $P - 2\rho v^2$
3. C
   $P - 3\rho v^2$
4. D
   $P - 4\rho v^2$

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1. A
   $\frac{1}{100}$ s
2. B
   $\frac{1}{200}$ s
3. C
   $\frac{1}{300}$ s
4. D
   $\frac{1}{400}$ s

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1. A
   10 V
2. B
   20 V
3. C
   30 V
4. D
   $-40$ V

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