Which of the following pairs represent units of the same physical quantity ?

1.  kelvin and joule

2.  kelvin and calorie

3.  newton and calorie

4.  joule and calorie.

The radius of a circle is stated as 2.12 cm. Its area should be written as:
1. 14 cm²
2. 14.1 cm²
3. 14.11 cm²
4. 14.1124 cm²

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

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

The dimensions of ML^–1T^–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

\(\int \frac{\mathrm{dx}}{\sqrt{2 \mathrm{ax}-\mathrm{x}^{2}}}=\mathrm{a}^{\mathrm{n}} \sin ^{-1}\left[\frac{\mathrm{x}}{\mathrm{a}}-1\right]\)
The value of n is
You may use dimensional analysis to solve the problem.

1. 0

2. -1

3. 1

4. none of these

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

A dimensionless quantity

1. never has a unit

2. always has a unit

3. may have a unit

4. does not exist

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

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