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

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

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1. A
   a unique solution
2. B
   infinite many solutions
3. C
   no solution
4. D
   exactly three solutions

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1. A
   $a=b$
2. B
   $a+b=1$
3. C
   $a+b=0$
4. D
   $a-b=1$

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1. A
   $a+b+c$
2. B
   $a-b+c$
3. C
   $a+b-c$
4. D
   $a-b-c$

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1. A
   -11
2. B
   -3
3. C
   0
4. D
   3

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1. A
   $\dfrac{\pi}{3}$
2. B
   $\dfrac{2\pi}{3}$
3. C
   $\dfrac{4\pi}{3}$
4. D
   $\dfrac{5\pi}{6}$

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

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1. A
   $\log_a(\log_b a)$
2. B
   $\log_b(\log_a b)$
3. C
   $\dfrac{\log_a(\log_b a)}{2}$
4. D
   $\dfrac{\log_b(\log_a b)}{2}$

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1. A
   $a,b,c$ are in AP
2. B
   $a,b,c$ are in GP
3. C
   $a,b,c$ are in HP
4. D
   $ab,bc,ca$ are in AP

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1. A
   5
2. B
   6
3. C
   7
4. D
   $n$ cannot be determined

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

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1. A
   $\dfrac{mx(m+n)}{n-1}$
2. B
   $\dfrac{mx(m+n)}{1-n}$
3. C
   $\dfrac{nx(m+n)}{m-1}$
4. D
   $\dfrac{nx(m+n)}{1-m}$

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

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

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1. A
   Only one
2. B
   Only two
3. C
   Only three
4. D
   Infinitely many

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1. A
   $A=R\setminus\left\{-\frac{5}{3}\right\}$ and $B=R\setminus\left\{-\frac{2}{3}\right\}$
2. B
   $A=R$ and $B=R\setminus\left\{-\frac{5}{3}\right\}$
3. C
   $A=R\setminus\left\{-\frac{3}{2}\right\}$ and $B=R\setminus\{0\}$
4. D
   $A=R\setminus\left\{-\frac{5}{3}\right\}$ and $B=R\setminus\left\{\frac{2}{3}\right\}$

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

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1. A
   6
2. B
   8
3. C
   9
4. D
   10

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1. A
   9
2. B
   12
3. C
   15
4. D
   17

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

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

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1. A
   6
2. B
   7
3. C
   8
4. D
   9

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1. A
   $x=y$
2. B
   $y=2x$
3. C
   $x=4y$
4. D
   $y=4x$

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1. A
   20%
2. B
   25%
3. C
   $\dfrac{100}{3}\%$
4. D
   $\dfrac{110}{3}\%$

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