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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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