Practice every past-year question.

1. A
   I and II
2. B
   II and IV
3. C
   III and V
4. D
   I and III

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1. A
   $\tan^{-1}(x+y) = x + c$, where c is the constant of integration
2. B
   $x + y = \tan x + c$, where c is the constant of integration
3. C
   $x + y = \cot^{-1}x + c$, where c is the constant of integration
4. D
   $x + y = \sin^{-1}(x+y) + c$, where c is the constant of integration

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

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1. A
   $x^2 + y^2 = k^2$
2. B
   $(1+k)x^2 + y^2 = k^2$
3. C
   $x^2 + (1+k^2)y^2 = k^2$
4. D
   $x^2 + 2y^2 = 2k^2$

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

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

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

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1. A
   (2, -2, 1)
2. B
   (2, -3, 0)
3. C
   (1, -2, 3)
4. D
   (4, 1, 6)

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1. A
   $\mathbb{R}$
2. B
   $x \in \mathbb{R} - \{1\}$
3. C
   $\{1, 2, 3, 4\}$
4. D
   $\{1, 2, 3, 4, 5, 6\}$

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1. A
   $x\cos x + c$, where c is the constant of integration
2. B
   $x\tan x + c$, where c is the constant of integration
3. C
   $x\tan\frac{x}{2} + c$, where c is the constant of integration
4. D
   $x\sec^2\frac{x}{2} + c$, where c is the constant of integration

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1. A
   83
2. B
   166
3. C
   249
4. D
   105

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1. A
   140
2. B
   150
3. C
   165
4. D
   170

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1. A
   $\frac{9}{16}$ units
2. B
   $\frac{3}{4}$ units
3. C
   $\frac{1}{4}$ units
4. D
   $\frac{1}{2}$ units

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

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1. A
   $\log\left(\frac{x-1}{x-2}\right) + c$, where c is the constant of integration
2. B
   $\log\left(\frac{x-2}{(x-1)^2}\right) + c$, where c is the constant of integration
3. C
   $\log\left(\frac{x-2}{x-1}\right) + c$, where c is the constant of integration
4. D
   $\log\left(\frac{(x-2)^2}{x-1}\right) + c$, where c is the constant of integration

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1. A
   $4x^2 - 7x + 3 = 0$
2. B
   $4x^2 + 7x + 3 = 0$
3. C
   $4x^2 - 3x - 7 = 0$
4. D
   $6x^2 - 5x + 1 = 0$

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

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1. A
   $\frac{1}{3}$
2. B
   $\frac{2}{3}$
3. C
   $\frac{3}{7}$
4. D
   $\frac{4}{9}$

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1. A
   85
2. B
   95
3. C
   185
4. D
   195

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

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1. A
   4
2. B
   6
3. C
   8
4. D
   3

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1. A
   2
2. B
   16
3. C
   $\frac{1}{\sqrt{2}}$
4. D
   4

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