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

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

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1. A
   $x_1 + x_2 > 2\sqrt{x_1 x_2}$
2. B
   $\sqrt{x_1} + \sqrt{x_2} > \sqrt{2}$
3. C
   $|\sqrt{x_1} - \sqrt{x_2}| > \sqrt{2}$
4. D
   $x_1 + x_2 < 2(\sqrt{x_1 x_2}+1)$

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1. A
   3:5
2. B
   2:9
3. C
   9:1
4. D
   5:3

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1. A
   x, 6, z
2. B
   x, 4, z
3. C
   x, 2, z
4. D
   x, 1, z

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

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

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

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

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

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

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1. A
   100
2. B
   96
3. C
   84
4. D
   50

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1. A
   $\frac{1}{2}$
2. B
   $1$
3. C
   $2$
4. D
   Minimum does not exist

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

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1. A
   4 square units
2. B
   6 square units
3. C
   8 square units
4. D
   16 square units

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

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1. A
   130
2. B
   260
3. C
   2113
4. D
   4226

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1. A
   $\tan^2x = \frac{q}{p}$
2. B
   $\cot^2x = \frac{q}{p}$
3. C
   $\tan^2x = pq$
4. D
   $\cot^2x = pq$

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1. A
   A, G
2. B
   2A, G
3. C
   A, 2G
4. D
   2A, 2G

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1. A
   $\dfrac{\pi}{2}$
2. B
   $\dfrac{\pi}{4}$
3. C
   $\dfrac{\pi}{6}$
4. D
   $\dfrac{\pi}{8}$

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

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