1. A
   22
2. B
   33
3. C
   44
4. D
   55

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1. A
   $0$
2. B
   $\frac{1}{3}$
3. C
   $\frac{1}{4}$
4. D
   $\frac{1}{8}$

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

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1. A
   $\frac{11}{14}$
2. B
   $\frac{9}{14}$
3. C
   $\frac{1}{4}$
4. D
   $\frac{1}{2}$

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1. A
   $\frac{7}{15}$
2. B
   $\frac{8}{15}$
3. C
   $\frac{11}{15}$
4. D
   $\frac{13}{15}$

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1. A
   0
2. B
   always positive
3. C
   always negative
4. D
   positive if $p, q, r$ are positive else negative

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1. A
   3
2. B
   12
3. C
   14
4. D
   15

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1. A
   1 and 2 only
2. B
   2 and 3 only
3. C
   1 and 3 only
4. D
   1, 2 and 3

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

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1. A
   Null matrix
2. B
   $-I$
3. C
   I
4. D
   2I

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1. A
   0 only
2. B
   1 only
3. C
   2 only
4. D
   Any real value

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1. A
   1 only
2. B
   1 and 2 only
3. C
   2 only
4. D
   1, 2 and 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
   1
2. B
   2
3. C
   4
4. D
   8

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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
   9
2. B
   10
3. C
   19
4. D
   20

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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
   42
2. B
   35
3. C
   28
4. D
   21

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1. A
   $C(51,25)$
2. B
   $C(51,27)$
3. C
   $C(51,51)-C(51,0)$
4. D
   $C(51,25)-C(51,27)$

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1. A
   32
2. B
   36
3. C
   40
4. D
   45

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1. A
   72
2. B
   36
3. C
   18
4. D
   12

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1. A
   $p^3+q^3+pq$
2. B
   $p^3+q^3-pq$
3. C
   $p^3+q^3+3pq$
4. D
   $p^3+q^3-3pq$

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1. A
   $x^2-\alpha x-\beta x+\alpha\beta+c=0$
2. B
   $x^2-\alpha x-\beta x+\alpha\beta-c=0$
3. C
   $x^2+\alpha x+\beta x+\alpha\beta+c=0$
4. D
   $x^2+\alpha x+\beta x+\alpha\beta-c=0$

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

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1. A
   -15
2. B
   -10
3. C
   10
4. D
   15

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