If the units of force and length, are increased by four times, then the unit of energy increases by:
1. \(16\) times
2. \(8\) times
3. \(2\) times
4. \(4\) times

The velocity \(v\) of a particle at time \(t\) is given by \({v}={at}+\frac{{b}}{{t}+{c}}.\) The dimensions of \({a}\), \({b}\), and \({c}\) are respectively:
1. \( {\left[{LT}^{-2}\right],[{L}],[{T}]} \)
2. \( {\left[{L}^2\right],[{T}] \text { and }\left[{LT}^2\right]} \)
3. \( {\left[{LT}^2\right],[{LT}] \text { and }[{L}]} \)
4. \( {[{L}],[{LT}], \text { and }\left[{T}^2\right]}\)

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

A wire has a mass of \((0.3\pm0.003)\) grams, a radius of \((0.5\pm 0.005)\) mm, and a length of \((0.6\pm0.006)\) cm. The maximum percentage error in the measurement of its density will be:
1. \(1\)%
2. \(2\)%
3. \(3\)%
4. \(4\)%

The number of particles crossing a unit area perpendicular to the \(x\)-axis in unit time is given by $$\(n= -D\frac{n_2-n_1}{x_2-x_1}\), where \(n_1\) and \(n_2\) are the number of particles per unit volume for the value of \(x\) equal to \(x_1\) and \(x_2\) respectively. The dimensions of \(D,\) known as the diffusion constant, will be:
1. \(\left[M^0LT^{2}\right]\)
2. \(\left[M^0L^2T^{-4}\right]\)
3. \(\left[M^0LT^{-3}\right]\)
4. \(\left[M^0L^2T^{-1}\right]\)

A physical quantity \(A\) is related to four observable quantities \(a\), \(b\), \(c\) and \(d\) as follows, \(A= \frac{a^2b^3}{c\sqrt{d}},\) the percentage errors of measurement in \(a\), \(b\), \(c\) and \(d\) are \(1\%\), \(3\%\), \(2\%\) and \(2\%\) respectively. The percentage error in quantity \(A\) will be: 
1. \(12\%\)
2. \(7\%\)
3. \(5\%\)
4. \(14\%\)

How many significant figures are present in the following numbers?

Select the correct answer set from the following:

A physical quantity \(P\) is given by \(P=\dfrac{A^3 B^{1/2}}{C^{-4}D^{3/2}}.\) The quantity which contributes the maximum percentage error in \(P\) is:

In an experiment, the following observations were recorded: initial length \(L =2.820~\text{m}\), mass \(M = 3.00~\text{kg}\), change in length \(l = 0.087~\text{cm}\), diameter \(D = 0.041~\text{cm}\). Taking \(g = 9.81~\text{m/s}^2\) and using the formula, \(Y = \dfrac{4MgL}{\pi D^2l},\) the maximum permissible error in \(Y \) will be:
1. \(7.96\%\)
2. \(4.56\%\)
3. \(6.50\%\)
4. \(8.42\%\)