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

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1. A
   $30^\circ$
2. B
   $60^\circ$
3. C
   $75^\circ$
4. D
   $45^\circ$

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1. A
   $0.1$ cm$^3$/cm$^2$
2. B
   $\frac{1}{2}$ cm$^3$/cm$^2$
3. C
   $1$ cm$^3$/cm$^2$
4. D
   $2$ cm$^3$/cm$^2$

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1. A
   $\frac{\pi}{6}$
2. B
   $\frac{7\pi}{6}$
3. C
   $\frac{5\pi}{6}$
4. D
   $\frac{11\pi}{6}$

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1. A
   $\sqrt{3}$ sq. units
2. B
   $\sqrt{6}$ sq. units
3. C
   $\sqrt{5}$ sq. units
4. D
   $\sqrt{7}$ sq. units

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

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1. A
   $x - \sqrt{3}y = -5$
2. B
   $x + \sqrt{3}y = 10$
3. C
   $\sqrt{3}x + y = 5\sqrt{3}$
4. D
   $\sqrt{3}x - y = 0$

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

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

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1. A
   7
2. B
   5
3. C
   3
4. D
   1

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1. A
   $\frac{9}{4}$
2. B
   $\frac{4}{9}$
3. C
   $\frac{27}{4}$
4. D
   $\frac{4}{27}$

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

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

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1. A
   $\log(\sin x) - \sin x + c$
2. B
   $\log(\sin x) - \cos x + c$
3. C
   $\log(\sin x) + \sin x + c$
4. D
   $\log(\cos x) - \cos x + c$

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

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1. A
   $\frac{36}{65}$
2. B
   $\frac{12}{65}$
3. C
   $\frac{33}{65}$
4. D
   $\frac{3}{65}$

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1. A
   $e^{\sin^{-1}x} + c$
2. B
   $e^{\sin^{-1}x}\cdot\sin x + c$
3. C
   $e^{\sin^{-1}x}\cdot\cos x + c$
4. D
   $e^{\sin^{-1}x}\cdot x + c$

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1. A
   0.2762
2. B
   0.1852
3. C
   0.2074
4. D
   0.7235

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

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

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1. A
   $2\,\Omega$
2. B
   $4\,\Omega$
3. C
   $6\,\Omega$
4. D
   $10\,\Omega$

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1. A
   $\frac{I_0}{2}$
2. B
   $\frac{I_0}{\sqrt{2}}$
3. C
   $\sqrt{2}\,I_0$
4. D
   $\sqrt{3}\,I_0$

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1. A
   $E_x > E_y > E_z$
2. B
   $E_x < E_y < E_z$
3. C
   $E_x = E_y = E_z$
4. D
   $E_y > E_x < E_z$

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

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1. A
   60 cm and 90 cm
2. B
   90 cm and 100 cm
3. C
   40 cm and 80 cm
4. D
   50 cm and 90 cm

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