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1. The estimate of absolute error in the measurement of time using a clock is \(10^{-2}~\text{s}.\) The time difference, \(t=t_1-t_2,\) between two events is determined by using the clock. The error in \(t\) is:

1.	\(10^{-2}~\text{s}\)	2.	\(2\times10^{-2}~\text{s}\)
3.	\({\Large\frac12}\times10^{-2}~\text{s}\)	4.	zero

2. The percentage errors in the measurement of mass and momentum of an object are \(1\%\) and \(2\%\) respectively. The percentage error in the measurement of kinetic energy of the object will be:

1.	\(1\%\)	2.	\(3\%\)
3.	\(4\%\)	4.	\(5\%\)

3. The dimension of which group of quantities is the same? 
\(h\) : Planck's constant, \(K\) : kinetic energy, \(\omega\) : angular speed/frequency, \(F\): force, \(L\) : inductance, \(i\) : current, \(q\) : charge, \(t\) : time, \(x\): distance
1. \(h, ~Ftx,~ Liq\) 
2. \(K , h\omega , \omega Li\)
3. \(Fx, ~Li^2,~K \omega\)
4. \(\dfrac{Fx}{t} ,~ Kx, ~ ht\)

4. Among the following numerical values, which one has three significant figures?
1. \(0.300\)
2. \(30.30\)
3. \(0.030\)
4. \(3.033\)

5. A student measured the diameter of a small steel ball using a screw gauge of least count \(0.001\) cm. The main scale reading is \(5\) mm and zero of circular scale division coincides with \(25\) divisions above the reference level. If the screw gauge has a zero error of \(-0.004\) cm, the correct diameter of the ball is:

1.	\(0.521\) cm	2.	\(0.525\) cm
3.	\(0.053\) cm	4.	\(0.529\) cm

6. The quantities which have the same dimensions as those of solid angle are:
1. stress and angle
2. strain and arc
3. angular speed and stress
4. strain and angle

7. A vernier calipers has \(1~\text{mm}\) marks on the main scale. It has \(20\) equal divisions on the vernier scale which match with \(16\) main scale divisions. The least count of this vernier calipers is:
1. \(0.02~\text{mm}\)
2. \(0.05~\text{mm}\)
3. \(0.10~\text{mm}\)
4. \(0.20~\text{mm}\)

8.

A screw gauge gives the following readings when used to measure the diameter of a wire:
Main scale reading: \(0\) mm
Circular scale reading: \(52\) divisions 
Given that \(1\) mm on the main scale corresponds to \(100\) divisions on the circular scale, the diameter of the wire that can be inferred from the given data is:

1.	\(0.26\) cm	2.	\(0.052\) cm
3.	\(0.52\) cm	4.	\(0.026\) cm

9. Match the units mentioned in List-I with the units in List-II.

	List-I		List-II
(a)	H/s	(i)	s2
(b)	H×A	(ii)	Wb
(c)	H×F	(iii)	s
(d)	\(\Omega\)×F	(iv)	\(\Omega\)

 

1.	(a)–(ii), (b)–(iv), (c)–(i), (d)–(iii)
2.	(a)–(iv), (b)–(ii), (c)–(i), (d)–(iii)
3.	(a)–(iv), (b)–(ii), (c)–(iii), (d)–(i)
4.	(a)–(ii), (b)–(iii), (c)–(iv), (d)–(i)

10.

Using a screw gauge with pitch \(0.1 ~\text{cm}\) and \(50\) divisions on its circular scale, the thickness of an object is measured. It should be accurately recorded as:
1. \(2.124~\text{cm}\)
2. \(2.121~\text{cm}\)
3. \(2.125~\text{cm}\)
4. \(2.123~\text{cm}\)

11. The errors in the measurement which arise due to unpredictable fluctuations in temperature and voltage supply are:

1.	Random errors	2.	Instrumental errors
3.	Personal errors	4.	Least count errors

12. The least count of a stopwatch is \(0.1\) sec. The time of \(20\) oscillations of the pendulum is found to be \(20\) sec. The percentage error in the time period is:
1. \(0.25\%\)
2. \(0.5\%\)
3. \(0.75\%\)
4. \(1.0\%\)

13. Match List-I with List-II.

List-I		List-II
(a)	Gravitational constant (\(G\))	(i)	\([{L}^2 {~T}^{-2}] \)
(b)	Gravitational potential energy	(ii)	\([{M}^{-1} {~L}^3 {~T}^{-2}] \)
(c)	Gravitational potential	(iii)	\([{LT}^{-2}] \)
(d)	Gravitational intensity	(iv)	\([{ML}^2 {~T}^{-2}]\)

Choose the correct answer from the options given below:

	(a)	(b)	(c)	(d)
1.	(iv)	(ii)	(i)	(iii)
2.	(ii)	(i)	(iv)	(iii)
3.	(ii)	(iv)	(i)	(iii)
4.	(ii)	(iv)	(iii)	(i)

14. Taking into account the significant figures, what is the value of \((9.99~\text{m}-0.0099~\text{m})\)?
1. \(9.98~\text{m}\)
2. \(9.980~\text{m}\)
3. \(9.9~\text{m}\)
4. \(9.9801~\text{m}\)

15. Express the result of the calculation to \(3\) significant figures:
\(2\times0.536+0.0050+2.100\)

1.	\(3.177\)	2.	\(3.18\)
3.	\(3.19\)	4.	\(3.2\)

16. The dimensions \([MLT^{-2}A^{-2}]\) belong to the:
1. electric permittivity
2. magnetic flux
3. self-inductance
4. magnetic permeability

17. The diagram shows part of a vernier scale on a pair of calipers. Which reading is correct?
(least count is \(0.1~\text{mm}\))
      
1. \(3.7~\text{cm}\) 
2. \(3.72~\text{cm}\)
3. \(3.64~\text{cm}\)
4. \(3.76~\text{cm}\)

18. A metal wire has mass \((0.4\pm 0.002)~\text{g}\), radius \((0.3\pm 0.001)~\text{mm}\) and length \((5\pm 0.02)~\text{cm}\). The maximum possible percentage error in the measurement of density will nearly be:
1. \(1.4 \%\)
2. \(1.2 \%\)
3. \(1.3 \%\)
4. \(1.6 \%\)

19.

Time intervals measured by a clock give the following readings: 
\(1.25~\text{s},~1.24~\text{s}, ~1.27~\text{s},~1.21~\text{s},~1.28~\text{s}.\) 
What is the percentage relative error of the observations? 
1. \(2\)%
2. \(4\)%
3. \(16\)%
4. \(1.6\)%

20.

The main scale of a vernier calliper has \(n\) divisions/cm. \(n\) divisions of the vernier scale coincide with \((n-1)\) divisions of the main scale. The least count of the vernier calliper is:
1. \(\dfrac{1}{(n+1)(n-1)}\) cm
2. \(\dfrac{1}{n}\) cm
3. \(\dfrac{1}{n^{2}}\) cm
4. \(\dfrac{1}{(n)(n+1)}\) cm

21. Which, of the following, is dimensionless?
1. \(\text{impedance}\times\text{conductance} \)
2. \(\dfrac{\text{emissive power}}{\text{emissivity}}\)
3. \(\dfrac{\text{electric field}}{\text{magnetic field}}\)
4. \(\dfrac{\text{inductance}}{\text{capacitance}}\)

22. The quantity \(\eta\) is defined by:    \(\eta=\dfrac{1}{\mu_0\sigma}\)
where \(\mu_0\) is the permeability of free space and \(\sigma\) is the electrical conductivity (of a plasma). \(\eta\) is referred to as the magnetic diffusivity. Its SI unit is:
1. m²/s
2. m/s²
3. C-m²/s
4. T-m/s

23. The area of a rectangular field (in \(\text{m}^2\)) of length \(55.3\) m and breadth \(25\) m after rounding off the value, for correct significant digits is:
1. \(14\times10^{2}\)
2. \(138\times10^{1}\)
3. \(1382\)
4. \(1382.5\)

24. Rounding off the number \(978.02\) upto two significant figures will leave us with:
1. \(98\)
2. \(9.8\times10^1\)
3. \(9.8\times10^2\)
4. \(9.78\times10^2\)

25. The quantities \(K,c,\eta\) represent the thermal conductivity, the specific heat capacity and the viscosity of a liquid. Which of the following, is dimensionless?
1. \(Kc\eta\)
2. \(\Large\frac{Kc}{\eta}\)
3. \(\Large\frac{K\eta}{c}\)
4. \(\dfrac{\eta c}{K}\)