Dimensions of constants when the argument of an exponential, log or sine must be dimensionless

1. A.
   $\left\lbrack M^{0}{LT}^{0} \right\rbrack$
2. B.
   $\left\lbrack M^{2}{LT}^{2} \right\rbrack$
3. C.
   $\left\lbrack {MLT}^{- 2} \right\rbrack$
4. D.
   $\left\lbrack {ML}^{2}{\text{ }T}^{- 2} \right\rbrack$

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1. A.
   $\left\lbrack M^{0}L^{0}T^{0} \right\rbrack,\left\lbrack M^{1}L^{2}T^{- 2}K^{- 1} \right\rbrack$
2. B.
   $\left\lbrack M^{1}L^{2}T^{- 2} \right\rbrack,\left\lbrack M^{1}L^{2}T^{- 2}K^{- 1} \right\rbrack$
3. C.
   $\left\lbrack M^{1}L^{2}T^{- 2}K^{- 1} \right\rbrack,\left\lbrack M^{0}L^{0}T^{0} \right\rbrack$
4. D.
   None of these

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1. A.
   $\left\lbrack M^{0}LT^{0} \right\rbrack$
2. B.
   $\left\lbrack M^{2}L{\text{ }T}^{- 2} \right\rbrack$
3. C.
   $\left\lbrack MLT\ ^{- 2} \right\rbrack$
4. D.
   $\left\lbrack MLTT^{- 1} \right\rbrack$

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1. A.
   $\left\lbrack M^{0}{\text{ }L}^{- 1}{\text{ }T}^{0} \right\rbrack$
2. B.
   $\left\lbrack {ML}^{0}{\text{ }T}^{- 2} \right\rbrack$
3. C.
   $\left\lbrack {MLT}^{- 2} \right\rbrack$
4. D.
   $\left\lbrack {ML}^{2}{\text{ }T}^{- 2} \right\rbrack$

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1. A.
   $\left\lbrack {ML}^{2}{\text{ }T}^{- 2}\theta^{- 1} \right\rbrack$
2. B.
   $\left\lbrack M^{0}{\text{ }L}^{2}{\text{ }T}^{- 2} \right\rbrack$
3. C.
   $\left\lbrack M^{0}{\text{ }L}^{0}{\text{ }T}^{0} \right\rbrack$
4. D.
   $\left\lbrack M^{0}{\text{ }L}^{2}{\text{ }T}^{0} \right\rbrack$

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1. A.
   Dimensions of $\beta$ is same as that of force.
2. B.
   Dimensions of $\alpha^{- 1}x$ is same as that of energy.
3. C.
   Dimensions of $\eta^{- 1}\sin\theta$ is same as that of $\alpha\beta$
4. D.
   Dimensions of $\alpha$ is same as that of $\beta$

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1. A.
   The dimensions of nt is [L]
2. B.
   The dimensions of $n$ is $\left\lbrack {LT}^{- 1} \right\rbrack$
3. C.
   The dimensions of $n/\lambda$ is $\lbrack T\rbrack$
4. D.
   The dimensions of $x$ is [L]

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