1. A
   $X$ and $Y$ are metalloids and $Z$ is a metal.
2. B
   $X$ is a metalloid, $Y$ is a non-metal and $Z$ is a metal.
3. C
   $X,Y$ and $Z$ are metals.
4. D
   $X$ and $Z$ are non-metals and $Y$ is a metalloid

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1. A
   (A)-(iii), (B)-(i), (C)-(ii), (D)-(iv)
2. B
   (A)-(i), (B)-(iv), (C)-(iii), (D)-(ii)
3. C
   (A)-(iii), (B)-(i), (C)-(iv), (D)-(ii)
4. D
   (A)-(i), (B)-(ii), (C)-(iv), (D)-(iii)

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1. A
   A colloidal solution shows colligative properties.
2. B
   An ordinary filter paper can stop the flow of colloidal particles.
3. C
   The flocculating power of ${Al}^{3 +}$ is more than that of ${Na}^{+}$.
4. D
   A colloidal solution shows Brownian motion of colloidal particles.

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

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1. A
   $100\text{ }mL$ and $100\text{ }Ml$
2. B
   $100\text{ }mL$ and $50\text{ }mL$
3. C
   $100\text{ }mL$ and $200\text{ }mL$
4. D
   $50\text{ }mL$ and $50\text{ }mL$

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

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

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1. A
   $\frac{9}{56}$
2. B
   $\frac{4}{9}$
3. C
   $\frac{3}{7}$
4. D
   $\frac{11}{27}$

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1. A
   $\alpha = \frac{\pi}{\sqrt{2}}$
2. B
   $\alpha = 0$
3. C
   no such $\alpha$ exists
4. D
   $\alpha = \frac{\pi}{4}$

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1. A
   0
2. B
   3
3. C
   39
4. D
   -45

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1. A
   $9(e - 1)$
2. B
   $45(e + 1)$
3. C
   $45(e - 1)$
4. D
   $9(e + 1)$

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1. A
   $x - y = 1$
2. B
   $2x + y = 5$
3. C
   $x + 3y = 5$
4. D
   $x + 2y = 4$

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1. A
   $\frac{1}{4}\log_{e}2$
2. B
   $\left( \frac{1}{2\sqrt{2}} \right)\log_{e}2$
3. C
   $\log_{e}2$
4. D
   $\frac{1}{2}\log_{e}2$

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1. A
   5
2. B
   6
3. C
   8
4. D
   7

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1. A
   $\sqrt{11}$
2. B
   $\sqrt{7}$
3. C
   $\sqrt{6}$
4. D
   $\sqrt{10}$

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1. A
   3
2. B
   $\sqrt{5}$
3. C
   2
4. D
   8

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1. A
   795
2. B
   1173
3. C
   1890
4. D
   717

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1. A
   12
2. B
   5
3. C
   6
4. D
   10

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

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

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1. A
   $( - \infty, - 1) \cup \left( \left\lbrack \frac{1}{2},\infty \right) - \{ 1\} \right)$
2. B
   $( - \infty,\infty) - \{ - 1,1\}$
3. C
   $\left( - 1,\frac{1}{2} \right\rbrack$
4. D
   $\left( - \infty,\frac{1}{2} \right\rbrack - \{ - 1\}$

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1. A
   $\frac{205}{144}$
2. B
   $\frac{197}{144}$
3. C
   $\frac{187}{144}$
4. D
   1

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1. A
   9
2. B
   15
3. C
   7
4. D
   11

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

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

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