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 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

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. \(2.001\times10^{-3}~\mathrm{kg}\) 

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:

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

The pitch of a screw gauge is 1mm 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:
1. \(4\%\)
2. \(6\%\)
3. \(8\%\)                                                  
4. \(2\%\)

If the dimensions of a physical quantity are given by ${\mathrm{}}^{}$\(M^aL^bT^c\), then the physical quantity will be:

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 \((9.99~\mathrm{m}-0.0099~\mathrm{m})\)?