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# 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. $$120$$

Subtopic: Â Dimensions |
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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

Subtopic: Â Dimensions |
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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. $$2.001\times10^{-3}~\text{kg}$$

Subtopic: Â Significant Figures |
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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. $$2$$

Subtopic: Â Dimensions |
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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. $$5.69~\text{cm}$$

Subtopic: Â Measurement & Measuring Devices |
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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 $$0.144 ~\text{cm}^3$$
Subtopic: Â Significant Figures |
Â 64%
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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

Subtopic: Â Dimensions |
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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. $$2.9\pm0.3~\Omega$$

Subtopic: Â Errors |
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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. $$7.65$$

Subtopic: Â Measurement & Measuring Devices |
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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

Subtopic: Â Measurement & Measuring Devices |
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