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

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1. A
   $\dfrac{4n+1}{2}$
2. B
   $\dfrac{2n+1}{2}$
3. C
   $\dfrac{1}{2}$
4. D
   1

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1. A
   I only
2. B
   II only
3. C
   Both I and II
4. D
   Neither I nor II

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1. A
   $y+x=\tan(x+c)+k$
2. B
   $x+y=k\tan\!\left(\dfrac{y-c}{k}\right)$
3. C
   $x-y=k\tan\!\left(\dfrac{y-c}{k}\right)$
4. D
   $y-x=\tan(x+c)+k$

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1. A
   $\tan^{-1}(10^x)+c$
2. B
   $(\ln10)\tan^{-1}(10^x)+c$
3. C
   $\dfrac{1}{\ln10}\tan^{-1}(10^x)+c$
4. D
   $\ln(10^x+10^{-x})+c$

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1. A
   I only
2. B
   II only
3. C
   Both I and II
4. D
   Neither I nor II

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1. A
   $I_1-I_2=0$
2. B
   $I_1+I_2=0$
3. C
   $I_1-2I_2=0$
4. D
   $2I_1-I_2=0$

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1. A
   $2k^2$
2. B
   $4k^2$
3. C
   $5k^2$
4. D
   $8k^2$

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1. A
   Both Statement-I and Statement-II are correct and Statement-II explains Statement-I
2. B
   Both Statement-I and Statement-II are correct but Statement-II does not explain Statement-I
3. C
   Statement-I is correct but Statement-II is not correct
4. D
   Statement-I is not correct but Statement-II is correct

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1. A
   Both Statement-I and Statement-II are correct and Statement-II explains Statement-I
2. B
   Both Statement-I and Statement-II are correct but Statement-II does not explain Statement-I
3. C
   Statement-I is correct but Statement-II is not correct
4. D
   Statement-I is not correct but Statement-II is correct

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1. A
   3150/19
2. B
   4000/19
3. C
   252
4. D
   225

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1. A
   0.000216
2. B
   0.064
3. C
   0.216
4. D
   0.512

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1. A
   0.80
2. B
   0.76
3. C
   0.36
4. D
   0.28

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1. A
   2/21
2. B
   1/7
3. C
   4/21
4. D
   3/7

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1. A
   28/91
2. B
   2/7
3. C
   24/91
4. D
   23/91

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1. A
   II only
2. B
   III only
3. C
   I and II
4. D
   II and III

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1. A
   3/10
2. B
   1/15
3. C
   1/6
4. D
   7/10

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1. A
   11/15
2. B
   13/15
3. C
   14/15
4. D
   1

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1. A
   I only
2. B
   II only
3. C
   Both I and II
4. D
   Neither I nor II

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1. A
   1/36
2. B
   1/6
3. C
   7/36
4. D
   5/36

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1. A
   1/8
2. B
   3/8
3. C
   7/16
4. D
   1/2

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

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1. A
   7/10
2. B
   18/25
3. C
   37/50
4. D
   19/25

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1. A
   1/2
2. B
   24/49
3. C
   1/4
4. D
   25/49

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1. A
   10
2. B
   15
3. C
   20
4. D
   25

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