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# Two resistors of resistances  ohm and  ohm are connected in series, the equivalent resistance of the series combination is: 1.  (300 ± 7) ohm 2.  (300 ± 1) ohm 3.  (300 ± 0) ohm 4.  (100 ± 1) ohm

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Two resistors of resistances  ohm and  ohm are connected in parallel. The equivalent resistance of the parallel combination is:

1.  (300 ± 7) ohm

2.  (66.7 ± 7) ohm

3.  (66.7 ± 1.8) ohm

4.  (100 ± 1) ohm

Subtopic:  Errors |
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The relative error in $$Z,$$ if $$Z=\frac{A^{4}B^{1/3}}{CD^{3/2}}$$ is:
1. $$\frac{\Delta A}{A}+\frac{\Delta B}{B}+\frac{\Delta C}{C}+\frac{\Delta D}{D}$$

2. $$4\frac{\Delta A}{A}+\frac{1}{3}\frac{\Delta B}{B}-\frac{\Delta C}{C}- \frac{3}{2}\frac{\Delta D}{D}$$

3. $$4\frac{\Delta A}{A}+\frac{1}{3}\frac{\Delta B}{B}+\frac{\Delta C}{C}+\frac{2}{3}\frac{\Delta D}{D}$$

4. $$4\frac{\Delta A}{A}+\frac{1}{3}\frac{\Delta B}{B}+\frac{\Delta C}{C}+\frac{3}{2}\frac{\Delta D}{D}$$

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The period of oscillation of a simple pendulum is . Measured value of L is 20.0 cm known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wrist watch of 1 s resolution. The percentage error in is:

1.  $2%$

2.  $3%$

3.  $5%$

4.  $0%$

Subtopic:  Errors |
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Each side of a cube is measured to be $$7.203~\text{m}$$. What are the total surface area and the volume respectively of the cube to appropriate significant figures?

 1 $$373.7~\text{m}^2$$ and $$311.3~\text{m}^3$$ 2 $$311.3~\text{m}^2$$ and $$373.7~\text{m}^3$$ 3 $$311.2992~\text{m}^2$$ and $$373.7147~\text{m}^3$$ 4 $$373.7147~\mathrm{m^2}$$ and $$311.2992~\text{m}^3$$
Subtopic:  Significant Figures |
78%
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$$5.74$$ g of a substance occupies $$1.2~\text{cm}^3$$. Its density by keeping the significant figures in view is:
1. $$4.7333~\text{g/cm}^3$$
2. $$3.8~\text{g/cm}^3$$
3. $$4.8~\text{g/cm}^3$$
4. $$3.7833~\text{g/cm}^3$$

Subtopic:  Dimensions |
83%
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The SI unit of energy is $$\mathrm{J = \text{kg}\left(m\right)^{2} s^{- 2}}$$; that of speed $$v$$ is $$\text{ms}^{- 1}$$ and of acceleration $$a$$ is $$\text{ms}^{- 2}$$. Which of the formula for kinetic energy ($$K$$) given below can you rule out on the basis of dimensional arguments (m stands for the mass of the body)?

 (a) $$K={m^{2} v^{3}}$$ (b) $$K=\dfrac{1}{2}mv^{2}$$ (c) $$K= ma$$ (d) $$K =\dfrac{3}{16}mv^{2}$$ (e) $$K = \dfrac{1}{2}mv^2+ ma$$

Choose the correct option:

 1 (a), (c) & (d) 2 (b) & (d) 3 (a), (c), (d) & (e) 4 (a), (c) & (e)

Subtopic:  Dimensions |
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Let us consider an equation $$\dfrac{1}{2}mv^2=mgh$$ where $$m$$ is the mass of the body, $$v$$ its velocity, $$g$$ is the acceleration due to gravity and $$h$$ is the height. The equation is:

 1 dimensionally correct. 2 dimensionally incorrect. 3 can not be checked by dimensional analysis. 4 can't say anything.

Subtopic:  Dimensions |
81%
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Consider a simple pendulum, having a bob attached to a string, that oscillates under the action of the force of gravity. Suppose that the period of oscillation of the simple pendulum depends on its length $$(l)$$, the mass of the bob $$(m)$$ and acceleration due to gravity $$(g)$$. Expression for its time period is:

1.  $$T = \dfrac{1}{2 \pi} \sqrt{\dfrac{l}{g}}$$

2.  $$T = 2 \pi \left(\dfrac{l}{g}\right)$$

3.  $$T = 2 \pi \sqrt{\dfrac{l}{g}}$$

4.  $$T = 2 \pi \sqrt{\dfrac{g}{l}}$$

Subtopic:  Dimensions |
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The resistance $$R=\frac{V}{I}$$ where $$V=(100 \pm 5) ~V$$ and $$I=(10 \pm 0.2)~ A$$. The percentage error in $$R$$ is:
1. $$5\%$$
2. $$2\%$$
3. $$7\%$$
4.
$$3\%$$

Subtopic:  Errors |
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