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A physical quantity X is expressed as
v (velocity) = $\sqrt{\frac{\mathrm{X}}{\mathrm{Density}}}$
The dimensions of X are
1. ML^–1T^–2 
2. MLT^–2
3. MLT^–1 
4. ML^–1T^–3

For the expression, \(10^{(at+3)}\), the dimensions of \(a\) will be:
1. \(\left[M^0L^0T^{0}\right]\)
2. \(\left[M^0L^0T^{1}\right]\)
3. \(\left[M^0L^0T^{-1}\right]\)
4. None of these

If force (F), velocity (v) and time (T) are taken as fundamental units, then the dimensions of mass are:
(a) [FvT^-1]
(b) [FvT^-2]
(c) [Fv^-1T^-1]
(d) [Fv^-1T]

The Martians use force (F), acceleration (A) and time (T) as their fundamental physical quantities. The dimensions of length on Martians system are 
1. [FT²]
2. [${\mathrm{F}}^{-1}{\mathrm{T}}^2$]
3. [${\mathrm{F}}^{-1}{\mathrm{A}}^2{\mathrm{T}}^{-1}$]
4. [AT²]

Which of the following quantities has the same dimensions as that of energy?
1. Power
2. Force
3. Momentum
4. Work

The position of a body with acceleration \(a\) is given by \(x= Ka^{m}t^{n}\) (assume \(t\) to be time). The values of \(m\) and \(n\) will be:
1. \(m=1,~n=1\)
2. \(m=1,~n=2\)
3. \(m=2,~n=1\)
4. \(m=2,~n=2\)

Unit of power is:
1. Kilowatt
2. Kilowatt-hour
3. Dyne
4. Joule

Which of the following measurements is the most precise?
1. 5.00 mm
2. 5.00 cm
3. 5.00 m
4. 5.00 km

What is the number of significant figures in \(0.310\times 10^{3}? \)
1. \(2\)
2. \(3\)
3. \(4\)
4. \(6\)

One nanometre is equal to:
1. \(10^9~\text{mm}\)
2. \(10^{-6}~\text{cm}\)
3. \(10^{-7}~\text{cm}\)
4. \(10^{-9}~\text{cm}\)

If \(97.52\) is divided by \(2.54\), the correct result in terms of significant figures is:

The measurements are made as \(18.425\) cm, \(7.21\) cm, and \(5.0\) cm. The addition of these measurements should be written as:
1. \(30.635\) cm
2. \(30.64\) cm
3. \(30.63\) cm
4. \(30.6\) cm

Choose any one of the following four responses :
(1) If both assertion and reason are true and the reason is the correct explanation of the assertion.
(2) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(3) If assertion is true but reason is false.
(4) If the assertion and reason both are false.
Assertion: Dimensional constants are the quantities whose values are constant.
Reason : Dimensional constants are dimensionless.

How many significant figures are present in the following numbers?

Select the correct answer set from the following:

The sum of the numbers \(436.32,227.2,\) and \(0.301\) in the appropriate significant figures is:

The length, breadth, and thickness of a block are given by l = 12 cm, b = 6 cm and t = 2.45 cm The volume of the block according to the idea of significant figures should be:
1. 1 × 10² cm³
2. 2 × 10² cm³
3. 1.764 × 10² cm³
4. None of these

The numbers \(2.745\) and \(2.735\) on rounding off to \(3\) significant figures will give respectively, 

The mass and volume of a body are \(4.237~\text{g }\) and \(2.5~\text{cm}^3,\) respectively. The density of the material of the body in correct significant figures will be:
1. \(1.6048~\text{g cm}^{-3}\)
2. \(1.69~\text{g cm}^{-3}\)
3. \(1.7~\text{g cm}^{-3}\)
4. \(1.695~\text{g cm}^{-3}\)