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1. A
   $\\\frac{k^2-1}{12}$
2. B
   $\\\frac{k^2-1}{6}$
3. C
   $\\\frac{k^2+1}{12}$
4. D
   $\\\frac{k^2+1}{6}$

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1. A
   $x+2y+z=0$
2. B
   $x+2y-z=0$
3. C
   $x-2y+z=0$
4. D
   $x-2y-z=0$

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1. A
   18
2. B
   28
3. C
   27
4. D
   19

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

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

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

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1. A
   $x\log_e 2x + \log_e 2x$
2. B
   $x\log_e 2x - \log_e 2x$
3. C
   $x\log_e 2x + \log_e 2$
4. D
   $x\log_e 2x - \log_e 2$

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

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

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1. A
   $\\\frac{9}{2}$
2. B
   6
3. C
   $\\\frac{7}{2}$
4. D
   4

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1. A
   $x+3y+6=0$
2. B
   $x+3y-3=0$
3. C
   $x+3y+8=0$
4. D
   $x+3y-4=0$

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1. A
   96
2. B
   80
3. C
   42
4. D
   48

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1. A
   ₹3000
2. B
   ₹3300
3. C
   ₹2400
4. D
   ₹3500

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

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

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1. A
   -0.1
2. B
   -0.025
3. C
   0.1
4. D
   0.025

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

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

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1. A
   0.7
2. B
   0.75
3. C
   0.65
4. D
   0.6

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1. A
   $\\\frac{8}{9}$
2. B
   $\\\frac{1}{9}$
3. C
   $\\\frac{17}{9}$
4. D
   $\\\frac{\sqrt{45}}{9}$

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1. A
   150
2. B
   160
3. C
   110
4. D
   180

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1. A
   $\\\frac{e^y}{y} = e^x \sin x + c$
2. B
   $e^y \log y - e^x \cos x + c$
3. C
   $e^y \log y = e^x \sin x + c$
4. D
   $\\\frac{e^y}{y} = e^x \sin x + c$

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1. A
   $6\vec{c}$
2. B
   $-6\vec{c}$
3. C
   $\vec{c}$
4. D
   $2\vec{c}$

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1. A
   $(\sqrt{3}-1):1$
2. B
   $\sqrt{3}:\sqrt{5}$
3. C
   $\sqrt{2}:\sqrt{3}$
4. D
   $(\sqrt{3}-1):4$

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1. A
   $\\\frac{x-1}{-3}=\\\frac{y-2}{5}=\\\frac{z-3}{4}$
2. B
   $\\\frac{x-1}{-3}=\\\frac{y-2}{-5}=\\\frac{z-3}{4}$
3. C
   $\\\frac{x-1}{4}=\\\frac{y-2}{5}=\\\frac{z-3}{3}$
4. D
   $\\\frac{x-1}{5}=\\\frac{y-2}{7}=\\\frac{z-3}{1}$

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