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. \(120\)

If \(\int \frac{d x}{\sqrt{a^2-x^2}}=a^n \sin ^{-1} \frac{x}{a}\) is dimensionally correct, then the value of \(n\) will be:
1. \(1\)
2. \(\text{zero}\)
3. \(\text-1\)
4. \(2\)

In an experiment, the height of an object measured by a vernier callipers having least count of \(0.01~\mathrm{cm}\) is found to be \(5.72~\mathrm{cm}\). When no object is there between jaws of this vernier callipers, the reading of the main scale is \(0.1\) cm and the reading of the vernier scale is \(0.3~\mathrm{mm}\). The correct height of the object is:
1. \( 5.72 \mathrm{~cm} \)
2. \( 5.59 \mathrm{~cm} \)
3. \( 5.85 \mathrm{~cm} \)
4. \( 5.69 \mathrm{~cm}\)
 

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

Two resistors R₁ = (3.0 ± 0.3) Ω  and R₂ = (5.0 ± 0.1) Ω are connected in parallel. The equivalent resistance, R_eq, will be
Hint: \({1 \over R_{eq}} = {1 \over R_{1}} + {1 \over R_{2}} \)
1. 1.9 ± 0.07 Ω
2. 1.9 ± 0.1 Ω
3. 2.9 ± 0.2 Ω
4. 2.9 ± 0.3 Ω

Find the thickness of the wire. The least count is 0.01 mm. The main scale reads in mm.
            

1. 7.62 mm
2. 7.63 mm
3. 7.64 mm
4. 7.65 mm

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