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

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

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1. A
   $d^{2}{sp}^{3}$ and paramagnetic
2. B
   ${sp}^{3}d^{2}$ and paramagnetic
3. C
   $d^{2}sp^{3}$ and diamagnetic
4. D
   ${sp}^{3}{\text{ }d}^{2}$ and diamagnetic

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

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

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1. A
   $0.625 \times 10^{- 6}$
2. B
   $1.6 \times 10^{- 6}$
3. C
   $2.2 \times 10^{- 16}$
4. D
   $1.9 \times 10^{- 5}$

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1. A
   $\frac{1}{54}$
2. B
   $\frac{1}{72}$
3. C
   $\frac{1}{36}$
4. D
   $\frac{5}{216}$

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

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1. A
   $\frac{1}{18}\left\lbrack 9 - 2\sin^{6}\theta - 3\sin^{4}\theta - 6\sin^{2}\theta \right\rbrack^{\frac{3}{2}} + c$
2. B
   $\frac{1}{18}\left\lbrack 11 - 18\sin^{2}\theta + 9\sin^{4}\theta - 2\sin^{6}\theta \right\rbrack^{\frac{3}{2}} + c$
3. C
   $\frac{1}{18}\left\lbrack 11 - 18\cos^{2}\theta + 9\cos^{4}\theta - 2\cos^{6}\theta \right\rbrack^{\frac{3}{2}} + c$
4. D
   $\frac{1}{18}\left\lbrack 9 - 2\cos^{6}\theta - 3\cos^{4}\theta - 6\cos^{2}\theta \right\rbrack^{\frac{3}{2}} + c$

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1. A
   $10(\sqrt{3} - 1)$
2. B
   $10\sqrt{3}$
3. C
   10
4. D
   $10(\sqrt{3} + 1)$

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1. A
   $xyz = 4$
2. B
   $xy - z = (x + y)z$
3. C
   $xy + yz + zx = z$
4. D
   $xy + z = (x + y)z$

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1. A
   $\frac{x}{- 3} = \frac{y - 1}{4} = \frac{z - 2}{3}$
2. B
   $\frac{x}{3} = \frac{y - 1}{4} = \frac{z - 2}{3}$
3. C
   $\frac{x}{3} = \frac{y - 1}{- 4} = \frac{z - 2}{3}$
4. D
   $\frac{x}{3} = \frac{y - 1}{4} = \frac{z - 2}{- 3}$

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1. A
   $A \rightarrow (A \land B)$
2. B
   $A \rightarrow (A \vee B)$
3. C
   $A \rightarrow (A \rightarrow B)$
4. D
   $A \rightarrow (A \leftrightarrow B)$

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

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1. A
   $(0,3)$
2. B
   $( - 6,0)$
3. C
   $(4,5)$
4. D
   $(5,4)$

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1. A
   $f$ is one-one
2. B
   If fog is one-one, then $g$ is one-one
3. C
   If $g$ is onto, then fog is one-one
4. D
   If $f$ is onto, then $f(n) = n\forall n \in N$

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

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1. A
   $\left( 0,\frac{\pi}{2} \right) \cup \left( \pi,\frac{3\pi}{2} \right)$
2. B
   $\left( 0,\frac{\pi}{4} \right) \cup \left( \frac{\pi}{2},\frac{3\pi}{4} \right) \cup \left( \pi,\frac{5\pi}{4} \right) \cup \left( \frac{3\pi}{2},\frac{7\pi}{4} \right)$
3. C
   $\left( 0,\frac{\pi}{2} \right) \cup \left( \frac{\pi}{2},\frac{3\pi}{4} \right) \cup \left( \pi,\frac{7\pi}{6} \right)$
4. D
   $\left( 0,\frac{\pi}{4} \right) \cup \left( \frac{\pi}{2},\frac{3\pi}{4} \right) \cup \left( \frac{3\pi}{2},\frac{11\pi}{6} \right)$

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1. A
   $(x - 2)^{2} + (y - 4)^{2} = 4$
2. B
   $(x - 4)^{2} + (y + 2)^{2} = 16$
3. C
   $(x - 4)^{2} + (y - 4)^{2} = 8$
4. D
   $(x - 2)^{2} + (y - 2)^{2} = 12$

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1. A
   $( - 5,8)$
2. B
   $(5,8)$
3. C
   $(5, - 8)$
4. D
   $( - 5, - 8)$

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1. A
   $a + b = c + d$
2. B
   $a - b = c - d$
3. C
   $ab = \frac{c + d}{a + b}$
4. D
   $a - c = b + d$

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

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1. A
   36
2. B
   45
3. C
   24
4. D
   30

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

Tap an option to check your answer.

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

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