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

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

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

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1. A
   $mn - 1 = 0$
2. B
   $mn + 1 = 0$
3. C
   $m + n = 0$
4. D
   $m - n = 0$

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

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

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

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1. A
   $3x + 4y - 18 = 0$
2. B
   $4x + 3y - 1 = 0$
3. C
   $4x - 3y + 26 = 0$
4. D
   $3x - 4y + 30 = 0$

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1. A
   $x^2 + y^2 = 1$
2. B
   $x^2 + y^2 = 25$
3. C
   $x^2 + y^2 = 100$
4. D
   $x^2 + y^2 - 2x - 2y - 23 = 0$

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1. A
   $(-2, 2)$
2. B
   $(-2, -2)$
3. C
   $\left(-1+\frac{1}{\sqrt{2}}, -1-\frac{1}{\sqrt{2}}\right)$
4. D
   None of the above

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1. A
   $(1, 1)$
2. B
   $(2, 2\sqrt{2})$
3. C
   $\left(\frac{1}{2}, \frac{1}{\sqrt{2}}\right)$
4. D
   $(1, 2)$

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

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

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1. A
   $\cos^2\gamma$
2. B
   $-\cos^2\gamma$
3. C
   $\sin^2\gamma$
4. D
   $-\sin^2\gamma$

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1. A
   $8$ square units
2. B
   $9$ square units
3. C
   $\sqrt{66}$ square units
4. D
   $\sqrt{68}$ square units

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

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1. A
   $-\frac{31}{49}$
2. B
   $-\frac{37}{49}$
3. C
   $\frac{31}{49}$
4. D
   $\frac{37}{49}$

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1. A
   $x + 2y + 3z = 6$
2. B
   $3x + 2y + z = 6$
3. C
   $x + y + z = 3$
4. D
   $3x + 2y + z = 0$

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

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1. A
   I only
2. B
   II only
3. C
   Both I and II
4. D
   Neither I nor II

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

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1. A
   $\vec{0}$
2. B
   $2\vec{c}$
3. C
   $3\vec{c}$
4. D
   Unit vector

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

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