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:

1.	\( 0.15~ \text{cm}^3 \)	2.	\( 0.1443~ \text{cm}^3 \)
3.	\( 0.14~ \text{cm}^3 \)	4.	\( 0.144 ~\text{cm}^3\)

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

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:

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. \(s= ut+\dfrac{1}{6}at^2\)
2. \(v^2= u^2+\dfrac{2as^2}{\pi}\)
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. \(120\)

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

The pitch of a screw gauge is \(1~\)mm and there are \(100\) divisions on the circular scale. While measuring the diameter of a wire, the linear scale reads \(1\) mm and \(47\)^th division on the circular scale coincides with the reference line. The length of the wire is \(5.6\) cm. Curved surface area (in cm²) of the wire in appropriate number of significant figures will be:

1. \(2.4\) cm²

2. \(2.56\) cm²

3. \(2.6\) cm²

4. \(2.8\) cm²

If the error in the measurement of the radius of a sphere is \(2\%\), then the error in the determination of the volume of the sphere will be: