Build a question paper in 60 seconds.

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

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1. A
   $\frac{63}{65}$
2. B
   $\frac{56}{65}$
3. C
   $\frac{48}{65}$
4. D
   $\frac{36}{65}$

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1. A
   0.1
2. B
   0.5
3. C
   1
4. D
   2

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

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1. A
   T, F
2. B
   F, T
3. C
   T, T
4. D
   F, F

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

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1. A
   A(-8, 6, -7) B(-6, -2, -3)
2. B
   A(8, 6, 7) B(6, 2, 3)
3. C
   A(8, 6, 7) B(6, -2, -3)
4. D
   A(7, 6, 8) B(-3, -2, 6)

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

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1. A
   $\cos^{-1}\frac{10}{19}$
2. B
   $\cos^{-1}\frac{11}{19}$
3. C
   $\cos^{-1}\frac{13}{19}$
4. D
   $\cos^{-1}\frac{14}{19}$

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

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

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1. A
   $4\sqrt{3}$
2. B
   $6\sqrt{3}$
3. C
   $24\sqrt{3}$
4. D
   $12\sqrt{3}$

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1. A
   45
2. B
   44
3. C
   48
4. D
   40

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1. A
   $\frac{1}{1+25x^2}$
2. B
   $\frac{5}{1+25x^2}$
3. C
   $\frac{1}{1+5x^2}$
4. D
   $\frac{5}{1+5x^2}$

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1. A
   $ad - bc > 0$
2. B
   $ad - bc < 0$
3. C
   $ab - cd > 0$
4. D
   $ab - cd < 0$

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1. A
   $\frac{19}{25}$
2. B
   $\frac{18}{25}$
3. C
   $\frac{16}{25}$
4. D
   $\frac{7}{25}$

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1. A
   $\frac{1}{\sqrt{6}}(-\hat{i} + 2\hat{j} - \hat{k})$
2. B
   $\frac{1}{\sqrt{6}}(\hat{i} + 2\hat{j} + \hat{k})$
3. C
   $\frac{1}{\sqrt{6}}(2\hat{i} - \hat{j} - \hat{k})$
4. D
   $\frac{1}{\sqrt{6}}(-\hat{i} - 2\hat{j} + \hat{k})$

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1. A
   $\frac{87}{90^4}$
2. B
   $\frac{348}{90^4}$
3. C
   $\frac{874}{90^4}$
4. D
   $\frac{4}{10^4}$

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

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

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1. A
   $\frac{244}{3}$
2. B
   $\frac{316}{3}$
3. C
   $\frac{200}{3}$
4. D
   $\frac{400}{3}$

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

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1. A
   $-\frac{4}{7}\tan^{-4/7}x + c$, where c is a constant of integration.
2. B
   $\frac{4}{7}\tan^{4/7}x + c$, where c is a constant of integration.
3. C
   $-\frac{7}{4}\tan^{-4/7}x + c$, where c is a constant of integration.
4. D
   $\frac{7}{4}\tan^{4/7}x + c$, where c is a constant of integration.

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

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1. A
   (2, 3)
2. B
   [2, 3)
3. C
   [2, 3]
4. D
   (2, 3]

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