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1. A
   Alcohols < Amines < Carboxylic acids
2. B
   Amines < Carboxylic acids < Alcohols
3. C
   Amine < Alcohols < Carboxylic acids
4. D
   Carboxylic acids < Alcohols < Amines

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1. A
   Group-12, Period-3
2. B
   Group-11, Period-4
3. C
   Group-8, Period-4
4. D
   Group-11, Period-5

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1. A
   846.4 pm
2. B
   211.6 pm
3. C
   476.1 pm
4. D
   1322.5 pm

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

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

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

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1. A
   $\\\frac{8}{\sqrt{35}}$
2. B
   $\\\frac{1}{\sqrt{35}}$
3. C
   $\\\frac{7}{\sqrt{35}}$
4. D
   $\\\frac{2}{\sqrt{35}}$

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

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1. A
   $\\\frac{1}{9x^4}$
2. B
   $-\\\frac{1}{3x^3}$
3. C
   $-\\\frac{1}{27x^9}$
4. D
   $\\\frac{1}{27x^6}$

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

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1. A
   $2\sqrt{\tan x} + \\\frac{1}{5}(\tan x)^{5/2} + c$
2. B
   $\sqrt{\tan x} + \\\frac{2}{5}(\tan x)^{5/2} + c$
3. C
   $\\\frac{1}{2}\sqrt{\tan x} + \\\frac{2}{5}(\tan x)^{5/2} + c$
4. D
   $2\sqrt{\tan x} + \\\frac{1}{5}(\tan x)^{5/2} + c$

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

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

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

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1. A
   $\\\frac{8\hat{i}-3\hat{j}+3\hat{k}}{\sqrt{82}}$
2. B
   $\\\frac{-8\hat{i}-3\hat{j}+3\hat{k}}{\sqrt{82}}$
3. C
   $\\\frac{-8\hat{i}+3\hat{j}+3\hat{k}}{\sqrt{82}}$
4. D
   $\\\frac{-8\hat{i}+3\hat{j}+3\hat{k}}{\sqrt{82}}$

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1. A
   0
2. B
   -2
3. C
   2
4. D
   5

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

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

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1. A
   $2\log\\\frac{x+2}{\sqrt{x^2+1}}+4\tan^{-1}x+c$
2. B
   $\log\\\frac{x+2}{\sqrt{x^2+1}}+4\tan^{-1}x+c$
3. C
   $\log\\\frac{(x+2)^2}{x^2+1}+4\tan^{-1}x+c$
4. D
   $\log\\\frac{(x+2)}{\sqrt{(x^2+1)^2}}+4\tan^{-1}x+c$

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

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1. A
   0
2. B
   $\\\frac{\pi}{2}$
3. C
   $\\\frac{\pi}{4}$
4. D
   $\\\frac{\pi}{6}$

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1. A
   0
2. B
   0.25
3. C
   0.5
4. D
   3

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1. A
   $5 \times 7!$
2. B
   $\\\frac{9!}{8}$
3. C
   $\\\frac{5 \times 7!}{2}$
4. D
   $20 \times 7!$

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1. A
   -8
2. B
   2
3. C
   -2
4. D
   8

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1. A
   centroid
2. B
   circumcenter
3. C
   incentre
4. D
   orthocentre

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