If the units of force and length, each is 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 ± 0.003 g, a radius of 0.5 ± 0.005 mm, and a length of 0.6 ± 0.006 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. \(14\%\)

The number of significant figures in the numbers \(25.12,\) \(2009,\) \(4.156\) and \(1.217\times 10^{-4}\) is:
1. \(1\)
2. \(2\)
3. \(3\)
4. \(4\)

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

In an experiment, the following observations were recorded: initial length L = 2.820 m, mass M = 3.00 kg, change in length l = 0.087 cm, diameter D = 0.041 cm. Taking g = 9.81 m/s² and using the formula, Y = $\frac{4MgL}{\pi D^{2}l}$, the maximum permissible error in Y will be:

1. 7.96%

2. 4.56%

3. 6.50%

4. 8.42%

The length of a cylinder is measured with a meter rod having the least count of 0.1 cm. Its diameter is measured with vernier callipers having the least count of 0.01 cm. Given that the length is 5.0 cm and the radius is 2.0 cm. The percentage error in the calculated value of the volume will be

1. 1%

2. 2%

3. 3%

4. 4%