Which of the following sets cannot enter into the list of fundamental quantities in any system of units?

1. length, mass and velocity

2. length, time and velocity

3. mass, time and velocity

4. length, time and mass

From NCERT

Subtopic: Dimensions |

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A physical quantity is measured and the result is expressed as nu where u is the unit used and n is the numerical value. If the result is expressed in various units then

1. \(n\propto size~of~u\)

2. \(n\propto u^2\)

3. \(n\propto \sqrt u\)

4. \(n\propto \frac{1}{u}\)

Subtopic: Dimensions |

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Suppose a quantity x can be dimensionally represented in terms of M, L and T that is [x] = M^{a} L^{b} T^{c}. The quantity mass

1. can always be dimensionally represented in terms of L, T and x

2. can never be dimensionally represented in terms of L, T and x

3. may be represented in terms of L, T and x if a = 0

4. may be represented in terms of L, T and x if a ≠ 0

From NCERT

Subtopic: Dimensions |

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A dimensionless quantity

1. never has a unit

2. always has a unit

3. may have a unit

4. does not exist

Subtopic: Dimensions |

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A unitless quantity

1. never has a nonzero dimension

2. always has a nonzero dimension

3. may have a nonzero dimension

4. does not exist

From NCERT

Subtopic: Dimensions |

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\(\int \frac{\mathrm{dx}}{\sqrt{2 \mathrm{ax}-\mathrm{x}^{2}}}=\mathrm{a}^{\mathrm{n}} \sin ^{-1}\left[\frac{\mathrm{x}}{\mathrm{a}}-1\right]\)

The value of n is

You may use dimensional analysis to solve the problem.

1. 0

2. -1

3. 1

4. none of these

Subtopic: Dimensions |

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The dimensions of ML^{–1}T^{–2} may correspond to

(a) work done by a force

(b) linear momentum

(c) pressure

(d) energy per unit volume

Choose the correct option:

1. (a) and (b)

2. (b) and (c)

3. (c) and (d)

4. None of the above

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Choose the correct statement(s) :

(a) A dimensionally correct equation may be correct

(b) A dimensionally correct equation may be incorrect

(c) A dimensionally incorrect equation may be correct

(d) A dimensionally incorrect equation may be incorrect

Choose the correct option:

1. (a), (b) and (c)

2. (a), (b) and (d)

3. (b), (c) and (d)

4. None of these

Subtopic: Dimensions |

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Choose the correct statement(s) :

(a) All quantities may be represented dimensionally in terms of the base quantities

(b) A base quantity cannot be represented dimensionally in the terms of the rest of the base quantities

(c) The dimension of a base quantity in other base quantities is always zero

(d) The dimension of a derived quantify is never zero in any base quantity

Choose the correct option:

1. (a), (b) and (c)

2. (b), (c) and (d)

3. (a), (c) and (d)

4. None of the above

Subtopic: Dimensions |

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