1. A
   25 m
2. B
   $25\sqrt{3}$ m
3. C
   50 m
4. D
   $50\sqrt{3}$ m

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

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

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1. A
   $\dfrac{(p+q)\sin\alpha}{p-q}$
2. B
   $\dfrac{p\sin\alpha}{p+q}$
3. C
   $\dfrac{p\sin\alpha}{p-q}$
4. D
   $\dfrac{(p-q)\sin\alpha}{p+q}$

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

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1. A
   1 and 3 only
2. B
   2 and 3 only
3. C
   1 and 2 only
4. D
   1, 2 and 3

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

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1. A
   $\dfrac{3\pi}{2} < A < \dfrac{5\pi}{2}$ only
2. B
   $\dfrac{\pi}{2} < A < \dfrac{3\pi}{2}$ only
3. C
   $\dfrac{3\pi}{2} < A < \dfrac{7\pi}{2}$
4. D
   $0 < A < \dfrac{3\pi}{2}$

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1. A
   right-angled
2. B
   equilateral
3. C
   isosceles
4. D
   obtuse-angled

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1. A
   $\left(-\dfrac{\pi}{2},\dfrac{\pi}{2}\right)$
2. B
   $\left[-\dfrac{\pi}{2},\dfrac{\pi}{2}\right]$
3. C
   $\left[0,\dfrac{\pi}{2}\right]$
4. D
   $[0,\pi]$

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1. A
   the vertices of a parallelogram
2. B
   the vertices of a rectangle
3. C
   the vertices of a square
4. D
   collinear

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

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1. A
   1 and 2 only
2. B
   2 and 3 only
3. C
   1 and 3 only
4. D
   1, 2 and 3

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1. A
   $\alpha = \beta$
2. B
   $\alpha > \beta$
3. C
   $\alpha < \beta$
4. D
   $\alpha = 2\beta$

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

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1. A
   $(\hat{a}-\hat{b})$
2. B
   $(\hat{a}+\hat{b})$
3. C
   $(2\hat{a}-\hat{b})$
4. D
   $(2\hat{a}+\hat{b})$

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1. A
   5 units
2. B
   7 units
3. C
   9 units
4. D
   10 units

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1. A
   $|\vec{a}|^2$
2. B
   $2|\vec{a}|^2$
3. C
   $3|\vec{a}|^2$
4. D
   $4|\vec{a}|^2$

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1. A
   $18\pi$ square metres
2. B
   $15\pi$ square metres
3. C
   $12\pi$ square metres
4. D
   $8\pi$ square metres

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1. A
   $\dfrac{5}{\sqrt{13}}$ units
2. B
   $\dfrac{3}{\sqrt{17}}$ unit
3. C
   $\sqrt{17}$ units
4. D
   $\dfrac{\sqrt{17}}{2}$ units

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1. A
   0
2. B
   1
3. C
   $a+b+c$
4. D
   $abc$

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1. A
   $\left(\dfrac{7}{3}, -\dfrac{8}{3}, 0\right)$
2. B
   $\left(-\dfrac{7}{3}, -\dfrac{8}{3}, 0\right)$
3. C
   $\left(-\dfrac{7}{3}, \dfrac{8}{3}, 0\right)$
4. D
   $\left(\dfrac{7}{3}, \dfrac{8}{3}, 0\right)$

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1. A
   52
2. B
   4
3. C
   2
4. D
   1

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1. A
   outside the ellipse
2. B
   inside the ellipse but not at the focus
3. C
   on the ellipse
4. D
   at the focus

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

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