1. A
   $\frac{1}{I_{2} + I_{4}},\frac{1}{I_{3} + I_{5}},\frac{1}{I_{4} + I_{6}}$ are in G.P.
2. B
   $\frac{1}{I_{2} + I_{4}},\frac{1}{I_{3} + I_{5}},\frac{1}{I_{4} + I_{6}}$ are in A.P.
3. C
   $I_{2} + I_{4},I_{3} + I_{5},I_{4} + I_{6}$ are in A.P.
4. D
   $I_{2} + I_{4},\left( I_{3} + I_{5} \right)^{2},I_{4} + I_{6}$ are in G.P.

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

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1. A
   $y = 273x$
2. B
   $2y = 91x$
3. C
   $y = 91x$
4. D
   $2y = 273x$

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1. A
   $\frac{\pi}{2} + \tan^{- 1}\left( \frac{1}{4} \right)$
2. B
   $\frac{\pi}{2} - \tan^{- 1}\left( \frac{1}{4} \right)$
3. C
   $\frac{\pi}{2} + \tan^{- 1}\left( \frac{1}{3} \right)$
4. D
   $\frac{\pi}{2} - \tan^{- 1}\left( \frac{1}{3} \right)$

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1. A
   $\log_{e}\left| x^{2} + 5x - 7 \right| + c$
2. B
   $\frac{1}{4}\log_{e}\left| x^{2} + 5x - 7 \right| + c$
3. C
   $4\log_{e}\left| x^{2} + 5x - 7 \right| + c$
4. D
   $\log_{e}\sqrt{x^{2} + 5x - 7} + c$

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1. A
   $\frac{x^{2}}{9} - \frac{y^{2}}{4} = 1$
2. B
   $\frac{x^{2}}{9} - \frac{y^{2}}{16} = 1$
3. C
   $x^{2} - y^{2} = 9$
4. D
   $\frac{x^{2}}{9} - \frac{y^{2}}{25} = 1$

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

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1. A
   $\frac{7}{45}$
2. B
   $\frac{8}{45}$
3. C
   $\frac{14}{45}$
4. D
   $\frac{28}{45}$

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1. A
   does not have any solution
2. B
   has a unique solution
3. C
   has a solution $(\alpha,\beta,\gamma)$ satisfying $\alpha + \beta^{2} + \gamma^{3} = 12$
4. D
   has infinitely many solutions

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

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1. A
   $\frac{19}{2}$
2. B
   $\frac{49}{2}$
3. C
   $\frac{39}{2}$
4. D
   $\frac{29}{2}$

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

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1. A
   64
2. B
   16
3. C
   80
4. D
   128

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

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1. A
   $\frac{1}{5}$
2. B
   $\frac{2}{9}$
3. C
   $\frac{97}{297}$
4. D
   $\frac{122}{297}$

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1. A
   $\frac{75}{56}$
2. B
   $\frac{65}{56}$
3. C
   $\frac{56}{33}$
4. D
   $\frac{65}{33}$

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

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1. A
   $\sim 0.86\text{ }A$
2. B
   $\sim 0.5\text{ }A$
3. C
   $\text{ }0.43\text{ }A$
4. D
   $\sim 1.5\text{ }A$

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1. A
   $41:50$
2. B
   $36:25$
3. C
   $50:41$
4. D
   $25:36$

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1. A
   $13\text{ }cm$
2. B
   $14.8\text{ }cm$
3. C
   $16.6\text{ }cm$
4. D
   $18.4\text{ }cm$

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1. A
   $3:7:2$
2. B
   $5:7:2$
3. C
   $5:7:3$
4. D
   $3:5:2$

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1. A
   Both statement I and statement II are false
2. B
   Statement I is false but statement II is true
3. C
   Statement I is true but statement II is false
4. D
   Both statement I and statement II are true

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1. A
   $\frac{18E}{55},\frac{5E}{18}$
2. B
   $\frac{5E}{18},\frac{18E}{55}$
3. C
   $\frac{5E}{18},\frac{10E}{33}$
4. D
   $\frac{10E}{33},\frac{5E}{18}$

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1. A
   $4.24 \times 10^{2}\text{ }s$
2. B
   $3.33 \times 10^{2}\text{ }s$
3. C
   $1.33 \times 10^{3}\text{ }s$
4. D
   $4.24 \times 10^{3}\text{ }s$

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1. A
   $\sqrt{\frac{v^{2} - u^{2}}{2}}$
2. B
   $\frac{v - u}{2}$
3. C
   $\sqrt{\frac{v^{2} + u^{2}}{2}}$
4. D
   $\frac{u + v}{2}$

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