A screw gauge has the least count of \(0.01~\mathrm{mm}\) and there are \(50\) divisions in its circular scale. The pitch of the screw gauge is:
1. \(0.25\) mm
2. \(0.5\) mm
3. \(1.0\) mm
4. \(0.01\) mm

Taking into account the significant figures, what is the value of \((9.99~\mathrm{m}-0.0099~\mathrm{m})\)?

If \({x}=\frac{{a} \sin \theta+{b} \cos \theta}{{a}+{b}}\), $\mathrm{then:}$

A thin wire has a length of \(21.7~\mathrm{cm}\) and a radius of \(0.46~\mathrm{mm}\). The volume of the wire to correct significant figures is:

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

In which of the following, the number of significant figures is different from that in the others?
1. \(2.303~\mathrm{kg}\)
2. \(12.23~\mathrm{m}\)
3. \(0.002\times10^{5}~\mathrm{m}\)
4. \(2.001\times10^{-3}~\mathrm{kg}\) 

Which of the following relations is dimensionally wrong? [The symbols have their usual meanings]
1. \(s= ut+\frac{1}{6}at^2\)
2. \(v^2= u^2+\frac{2as^2}{\pi}\)
3. \(v= u-2at\)
4. All of these

When units of mass, length, and time are taken as \(10~\text{kg}, 60~\text{m}~\text{and}~60~\text{s}\) respectively, the new unit of energy becomes \(x\) times the initial SI unit of energy. The value of \(x\) will be:
1. \(10\)
2. \(20\)
3. \(60\)
4. \(120\)

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

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