1. A
   $\frac{4}{9}$
2. B
   $\frac{17}{36}$
3. C
   $\frac{5}{12}$
4. D
   $\frac{1}{2}$

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

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1. A
   P and Q
2. B
   $P$ and $R$
3. C
   None of these
4. D
   Q and R

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1. A
   $- \frac{32}{4}$
2. B
   $- \frac{31}{4}$
3. C
   $- \frac{30}{4}$
4. D
   $- \frac{33}{4}$

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1. A
   1
2. B
   $\frac{1}{2}|z|^{2}$
3. C
   $\frac{1}{2}$
4. D
   $\frac{1}{2}|z + iz|^{2}$

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

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

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1. A
   $2 + \frac{2}{5}\sqrt{30}$
2. B
   $2 + \frac{4}{\sqrt{5}}\sqrt{30}$
3. C
   $4 + \frac{4}{\sqrt{5}}\sqrt{30}$
4. D
   $5 + \frac{2}{5}\sqrt{30}$

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1. A
   Distance between the two centres is the average of the radii of both circles.
2. B
   Both circles' centres lie inside the region of one another.
3. C
   Both circles pass through the centre of each other.
4. D
   The circles have two intersection points.

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1. A
   $g(\alpha)$ is a strictly increasing function
2. B
   $g(\alpha)$ has an inflection point at $\alpha = - \frac{1}{2}$
3. C
   $g(\alpha)$ is a strictly decreasing function
4. D
   $g(\alpha)$ is an even function

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1. A
   $y(1) = e^{- \frac{1}{2}} - 1$
2. B
   $y(1) = e^{\frac{1}{2}} - e^{- \frac{1}{2}}$
3. C
   $y(1) = 1$
4. D
   $y(1) = e^{\frac{1}{2}} - 1$

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

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1. A
   NOR Gate
2. B
   OR Gate
3. C
   AND Gate
4. D
   NAND Gate

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1. A
   $841.4\text{ }m/s$
2. B
   $811.4\text{ }m/s$
3. C
   $831.4\text{ }m/s$
4. D
   $821.4\text{ }m/s$

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

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1. A
   Unsteady to steady flow
2. B
   Remains steady flow
3. C
   Remains turbulent flow
4. D
   Steady flow to unsteady flow

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1. A
   $\tan^{- 1}\left( \frac{2}{3} \right)$ from $x$-axis
2. B
   $\tan^{- 1}\left( \frac{2}{3} \right)$ from $y$-axis
3. C
   $\tan^{- 1}\left( \frac{5}{2} \right)$ from $y$-axis
4. D
   $\tan^{- 1}\left( \frac{5}{2} \right)$ from $x$-axis

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1. A
   $0.424nCm^{- 2}$
2. B
   $47.88C/m$
3. C
   $0.07nCm^{- 2}$
4. D
   $4.0nCm^{- 2}$

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1. A
   $1860:1$
2. B
   $(1860)^{2}:1$
3. C
   $41.4:1$
4. D
   $43:1$

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1. A
   Auxilliary transformer
2. B
   Auto transformer
3. C
   Step-up transformer
4. D
   Step down transformer

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1. A
   $240Ci$
2. B
   $357Ci$
3. C
   $535Ci$
4. D
   $252Ci$

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1. A
   $58\text{ }nm$
2. B
   $32\text{ }nm$
3. C
   $86\text{ }nm$
4. D
   $102\text{ }nm$

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1. A
   1
2. B
   Infinite
3. C
   $\frac{R_{1}R_{2}}{R_{1} - R_{2}}$
4. D
   Zero

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1. A
   $0.14\%$
2. B
   $0.9\%$
3. C
   $9\%$
4. D
   $1.4\%$

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1. A
   Bend towards the right
2. B
   Not bend but shrink
3. C
   Neither bend nor shrink
4. D
   Bend towards the left

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