1. A
   $\dfrac{1}{6}$
2. B
   $\dfrac{5}{108}$
3. C
   $\dfrac{4}{9}$
4. D
   $\dfrac{5}{18}$

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1. A
   $3$
2. B
   $5$
3. C
   $23$
4. D
   $25$

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1. A
   $6$
2. B
   $11$
3. C
   $17$
4. D
   $21$

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1. A
   $191$
2. B
   $161$
3. C
   $131$
4. D
   $121$

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1. A
   $\dfrac{810}{361}$
2. B
   $\dfrac{9}{19}$
3. C
   $\dfrac{21}{361}$
4. D
   $\dfrac{121}{361}$

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1. A
   $\dfrac{2}{b}$
2. B
   $\dfrac{1}{a}+\dfrac{1}{c}$
3. C
   $\dfrac{1}{2}\!\left(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}\right)$
4. D
   None of these

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1. A
   $210$
2. B
   $220$
3. C
   $230$
4. D
   $240$

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1. A
   $\dfrac{1}{2}$
2. B
   $\dfrac{1}{4}$
3. C
   $\dfrac{1}{7}$
4. D
   $\dfrac{1}{14}$

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

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1. A
   $\dfrac{1}{91}$
2. B
   $\dfrac{24}{455}$
3. C
   $\dfrac{1}{65}$
4. D
   $\dfrac{6}{455}$

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

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1. A
   $\dfrac{57}{32}$
2. B
   $\dfrac{53}{32}$
3. C
   $\dfrac{51}{32}$
4. D
   $1$

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

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

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

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

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1. A
   $625$
2. B
   $400$
3. C
   $196$
4. D
   $120$

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1. A
   $2^{100}\omega^{2}$
2. B
   $2^{100}\omega$
3. C
   $2^{100}$
4. D
   $-2^{100}$

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1. A
   Both A and B are null matrices
2. B
   Either A or B is a null matrix
3. C
   B is a null matrix if A is a non-singular matrix
4. D
   Both A and B are singular matrices

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