A screw gauge has the least count of \(0.01~\text{mm}\) and there are \(50\) divisions in its circular scale. The pitch of the screw gauge is:

1.	\(0.25~\text{mm}\)	2.	\(0.5~\text{mm}\)
3.	\(1.0~\text{mm}\)	4.	\(0.01~\text{mm}\)

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

A thin wire has a length of \(21.7~\text{cm}\) and a radius of \(0.46~\text{mm}\). 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?

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 \(4.237~\text{g }\) 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. \(1.695~\text{g cm}^{-3}\)

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