Practice every past-year question.

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

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1. A
   $(n-1)!$
2. B
   $n!$
3. C
   $(-1)(n-1)!$
4. D
   $(-n)(n-1)!$

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1. A
   $\frac{n-k}{k-1}\cdot\frac{p}{q}$
2. B
   $\frac{n-k+1}{k+1}\cdot\frac{p}{q}$
3. C
   $\frac{n+1}{k}\cdot\frac{q}{p}$
4. D
   $\frac{n-k+1}{k}\cdot\frac{p}{q}$

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1. A
   $y = (x-1)\frac{dy}{dx} - 1$
2. B
   $x = (x-1)\frac{dy}{dx} + 1$
3. C
   $y = (x-1)\frac{dy}{dx}$
4. D
   $y = 2(x-1)\frac{dy}{dx}$

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

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1. A
   $\sqrt{14}$
2. B
   14
3. C
   $\sqrt{7}$
4. D
   2

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1. A
   $\frac{8}{3}$ sq. units
2. B
   $\frac{5}{3}$ sq. units
3. C
   $\frac{4}{3}$ sq. units
4. D
   $\frac{2}{3}$ sq. units

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1. A
   $A + B = C$
2. B
   $A + B = 2C$
3. C
   $A + B = 3C$
4. D
   $A + B = 4C$

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1. A
   $\frac{3}{10}$
2. B
   $\frac{2}{15}$
3. C
   $\frac{1}{15}$
4. D
   $\frac{3}{20}$

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1. A
   $\frac{19}{7}$ units
2. B
   $\frac{17}{7}$ units
3. C
   $\frac{11}{7}$ units
4. D
   $\frac{15}{7}$ units

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1. A
   $\sqrt[5]{\left(\frac{y}{x}\right)^3}$
2. B
   $-\sqrt[5]{\left(\frac{x}{y}\right)^3}$
3. C
   $\sqrt[5]{\left(\frac{x}{y}\right)^3}$
4. D
   $-\sqrt[5]{\left(\frac{y}{x}\right)^3}$

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1. A
   5
2. B
   2
3. C
   4
4. D
   6

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1. A
   $\frac{\pi}{12}$
2. B
   $\frac{\pi}{4}$
3. C
   $\frac{\pi}{3}$
4. D
   $\frac{\pi}{6}$

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1. A
   $a + c = b$
2. B
   $a + b = c$
3. C
   $b + c = a$
4. D
   $a + c = 2b$

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

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1. A
   0
2. B
   2
3. C
   4
4. D
   6

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

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

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1. A
   100
2. B
   0
3. C
   200
4. D
   -100

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1. A
   $\frac{1}{5}$
2. B
   1
3. C
   0
4. D
   $-\frac{1}{5}$

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

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1. A
   3926
2. B
   3296
3. C
   3692
4. D
   3269

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1. A
   $\frac{8}{3}$
2. B
   $\frac{2}{3}$
3. C
   $\frac{10}{3}$
4. D
   $\frac{1}{3}$

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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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