In which of the following, the number of significant figures is different from that in the others?
1. | \(2.303~\text{kg}\) | 2. | \(12.23~\text{m}\) |
3. | \(0.002\times10^{5}~\text{m}\) | 4. | \(2.001\times10^{-3}~\text{kg}\) |
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 \(0.01~\text{cm}\) is found to be \(5.72~\text{cm}\). 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 \(0.3~\text{mm}\). The correct height of the object is:
1. \( 5.72 ~\text{cm} \)
2. \( 5.59~\text{cm} \)
3. \( 5.85~\text{cm} \)
4. \( 5.69~\text{cm} \)
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 \({x}=\frac{{a} \sin \theta+{b} \cos \theta}{{a}+{b}},\) then:
1. | the dimensions of \(x\) and \(a\) must be the same |
2. | the dimensions of \(a\) and \(b\) are not the same |
3. | \(x\) is dimensionless |
4. | none of the above |
Two resistors \(R_1 = (3.0\pm0.3)~\Omega\) and \(R_2 = (5.0 \pm0.1)~\Omega\) 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. | \(1.9\pm0.07~\Omega\) | 2. | \(1.9\pm0.1~\Omega\) |
3. | \(2.9\pm0.2~\Omega\) | 4. | \(2.9\pm0.3~\Omega\) |
Find the thickness of the wire. The least count is \(0.01\) mm. The main scale reads: (in mm)
1. \(7.62\)
2. \(7.63\)
3. \(7.64\)
4. \(7.65\)
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