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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 |

Subtopic: Â Dimensions |

From NCERT

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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. \(n\propto \mathrm{size~of}~u\)

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

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

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

Subtopic: Â Dimensions |

Â 75%

From NCERT

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Suppose a quantity \(x\) can be dimensionally represented in terms of \(M,\) \(L\) and \(T\) that is \([x]\) =\(M^aL^bT^c.\) 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 \(a\neq0.\) |

Subtopic: Â Dimensions |

From NCERT

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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: Â Dimensions |

Â 77%

From NCERT

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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

Subtopic: Â Dimensions |

From NCERT

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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 \(\mathrm{n}\) is:

1. \(0\)

2. \(-1\)

3. \(1\)

4. none of these

Subtopic: Â Dimensions |

Â 52%

From NCERT

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The dimensions of \(\left [ML^{-1} T^{-2} \right ]\) 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 |

Subtopic: Â Dimensions |

Â 81%

From NCERT

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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: Â Dimensions |

Â 68%

From NCERT

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Consider the following statements:

(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: Â Dimensions |

Â 61%

From NCERT

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The radius of a circle is stated as \(2.12\) cm. Its area should be written as:

1. \(14\mathrm{~cm^2}\)

2. \(14.1\mathrm{~cm^2}\)

3. \(14.11\mathrm{~cm^2}\)

4. \(14.1124\mathrm{~cm^2}\)

Subtopic: Â Significant Figures |

Â 71%

From NCERT

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