1. A
   $19$
2. B
   $18$
3. C
   $17$
4. D
   $11$

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

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1. A
   Zero
2. B
   One
3. C
   Two
4. D
   Infinitely many

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1. A
   $0$
2. B
   $1$
3. C
   $3$
4. D
   $71$

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1. A
   $(4,4,1)$
2. B
   $(2,4,1)$
3. C
   $(4,1,4)$
4. D
   $(3,4,7)$

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

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1. A
   $\dfrac{1}{101}$
2. B
   $\dfrac{29}{101}$
3. C
   $\dfrac{41}{101}$
4. D
   $\dfrac{92}{101}$

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1. A
   $3x+y=10xy$
2. B
   $x+3y=10xy$
3. C
   $3x+y=10$
4. D
   $x+3y=10$

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

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1. A
   $\left(1+\frac{2}{\sqrt{5}},5+\frac{4}{\sqrt{5}}\right),\left(1-\frac{2}{\sqrt{5}},5-\frac{4}{\sqrt{5}}\right)$
2. B
   $\left(3+\frac{2}{\sqrt{5}},5+\frac{4}{\sqrt{5}}\right),\left(-1-\frac{2}{\sqrt{5}},5-\frac{4}{\sqrt{5}}\right)$
3. C
   $\left(1-\frac{2}{\sqrt{5}},5+\frac{4}{\sqrt{5}}\right),\left(1+\frac{2}{\sqrt{5}},5-\frac{4}{\sqrt{5}}\right)$
4. D
   $\left(3-\frac{2}{\sqrt{5}},5+\frac{4}{\sqrt{5}}\right),\left(-1+\frac{2}{\sqrt{5}},5-\frac{4}{\sqrt{5}}\right)$

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1. A
   $6.05$
2. B
   $6.15$
3. C
   $6.25$
4. D
   $6.35$

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1. A
   $\left(\dfrac{8}{3},\dfrac{11}{3}\right)$
2. B
   $\left(\dfrac{7}{3},\dfrac{7}{3}\right)$
3. C
   $\left(2,\dfrac{8}{3}\right)$
4. D
   $\left(\dfrac{8}{3},2\right)$

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

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

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

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1. A
   $8$
2. B
   $7$
3. C
   $6$
4. D
   $0$

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

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

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1. A
   $\vec{0}$
2. B
   $\vec{r}$
3. C
   $2\vec{r}$
4. D
   $3\vec{r}$

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

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1. A
   No point
2. B
   One point
3. C
   Two points
4. D
   More than two points

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1. A
   $\dfrac{d^2y}{dx^2}+2y=0$
2. B
   $\dfrac{d^2y}{dx^2}+2\dfrac{dy}{dx}+2y=0$
3. C
   $\dfrac{d^2y}{dx^2}-2\dfrac{dy}{dx}+2y=0$
4. D
   $\dfrac{d^2y}{dx^2}+y=0$

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1. A
   $f(d)=g(b)$
2. B
   $f(b)+g(d)=0$
3. C
   $f(a)+g(c)=2a$
4. D
   $f(d)+g(b)=2d$

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

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1. A
   $2,2$
2. B
   $2,3$
3. C
   $5,2$
4. D
   $2,5$

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