Target DPP Test

1. The energy of a damped oscillator is given by the expression: $E(t)=A^2e^{-\alpha t}, $ where $\alpha =0.1~ \text{s}^{-1}. $ The amplitude $A$ is measured with a relative error of $1 \text{%},$ and the time $t$ is measured with an error of $2 \text{%}.$ The maximum possible percentage error in the value of $E(t) $ at $t=2~\text{s} $ is:
1. $1.2 \text{%}$
2. $2 \text{%}$
3. $6 \text{%}$
4. $2.4 \text{%}$

2.

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$

3. The length of a cylinder is measured with a meter rod having the least count of $0.1~\text{cm}$. Its diameter is measured with vernier callipers having the least count of $0.01~\text{cm}$. Given that the length is $5.0~\text{cm}$ and the radius is $2.0~\text{cm}$. The percentage error in the calculated value of the volume will be:

1.	$1\%$	2.	$2\%$
3.	$3\%$	4.	$4\%$

4.

The determination of the value of acceleration due to gravity $(g)$ by simple pendulum method employs the formula,
$g=4\pi^2\frac{L}{T^2}$
The expression for the relative error in the value of $g$ is:
1. $\frac{\Delta g}{g}=\frac{\Delta L}{L}+2\Big(\frac{\Delta T}{T}\Big)$
2. $\frac{\Delta g}{g}=4\pi^2\Big[\frac{\Delta L}{L}-2\frac{\Delta T}{T}\Big]$
3. $\frac{\Delta g}{g}=4\pi^2\Big[\frac{\Delta L}{L}+2\frac{\Delta T}{T}\Big]$
4. $\frac{\Delta g}{g}=\frac{\Delta L}{L}-2\Big(\frac{\Delta T}{T}\Big)$

5.

A wire of length $l = 6 \pm 0.06$ cm and radius $r = 0.5 \pm 0.005$ cm and mass $m = 0.3 \pm 0.003$ gm. The maximum percentage error in density is :
(1) 4
(2) 2
(3) 1
(4) 6.8

6. Given that the side of a cube is $(30 \pm 0.2) $ cm, the percentage error in its volume comes out to be:
1. $1\text{%}$
2. $3\text{%}$
3. $1.5\text{%}$
4. $2\text{%}$

7.

38. A physical quantity X is related to four measurable quantities a, b, c, and d as follows $X = a^{2} b^{3} c^{5 / 2} d^{- 2}$ . The percentage error in measuring a, b, c, and d is 1%, 2%, 3%, and 4%, respectively. What is the percentage error in quantity X?
(1) 22.1 %
(2) 13.2 %
(3) 34.6 %
(4) 23.5 %

This objective question is based on NCERT Exemplar subjective Question.

8. An expression containing physical quantities is $(1273.43-51.7052+745) \times 21. $ After evaluation, the correct answer is:
1. $41301.2208$
2. $4.1 \times 10^4 $
3. $41307$
4. $41000$

9.

A wire has a mass of $(0.3\pm0.003)$ grams, a radius of $(0.5\pm 0.005)$ mm, and a length of $(0.6\pm0.006)$ cm. The maximum percentage error in the measurement of its density will be:
1. $1$
2. $2$
3. $3$
4. $4$

10. The mass of a box measured by the grocer’s balance is $2.300~\text{kg}$. Two gold pieces of masses $20.15~\text{g}$ and $20.17~\text{g}$ are added to the box. The total mass of the box and the difference in the masses of the gold piece, recorded to correct significant figures, will be, respectively:

1.	$2340.32~\text{g}$, $0.002~\text{g}$
2.	$2.340~\text{kg}$, $0.02~\text{g}$
3.	$2.3~\text{kg}$, $0~\text{g}$
4.	$2.334032~\text{kg}$, $0.02~\text{g}$

11.

A student performs an experiment for determination of $g = \frac{4 π^{2} l}{T^{2}}$ where l $\approx$ 1 m and he commits an error of $∆ l$ . For T, he takes the time of n oscillations with the stop watch of least count $∆ T$ . For which of the following data, the measurement of g will be most accurate:-
$∆ l$ $∆ T$ n
a. 5 mm 0.2 s 10
b. 5 mm 0.2 s 20
c. 5 mm 0.1 s 20
d. 5 mm 0.1 s 50
1. (a)
2. (b)
3. (c)
4. (d)

12.

The unit of percentage error is
1. Same as that of physical quantity
2. Different from that of physical quantity
3. Percentage error is unit less
4. Errors have got their own units which are different from that of physical quantity measured

13.

The sum of the numbers $436.32,227.2,$ and $0.301$ in the appropriate significant figures is:

1.	$ 663.821 $	2.	$ 664 $
3.	$ 663.8 $	4.	$663.82$

14.

The mean length of an object is 5 cm. which of the following measurements is most accurate?
(1) 4.9 cm
(2) 4.805 cm
(3) 5.25 cm
(4) 5.4 cm

15. The mass of a paper box is $2.3$ g. Two cork pieces, each of mass $0.035$ g, are placed in it. The total mass of the box and the cork pieces, with due regard to significant digits, will be:
1. $2.4$ g
2. $2.370$ g
3. $2.37$ g
4. $2.3$ g

16.

Two clocks are being tested against a standard clock located in a national laboratory. At 12:00:00 noon by the standard clock, the readings of the two clocks are:

Days	Clock 1	Clock 2
Monday	12:00:05	10:15:06
Tuesday	12:01:15	10:14:59
Wednesday	11:59:08	10:15:18
Thursday	12:01:50	10:15:07
Friday	11:59:15	10:14:53
Saturday	12:01:30	10:15:24
Sunday	12:01:19	10:15:11

If you are doing an experiment that requires precision time interval measurements, which of the two clocks will you prefer?

1.	clock 1
2.	clock 2
3.	neither clock 1 nor clock 2
4.	both clock 1 and clock 2

17. The addition of ($34.683$ +$58.930$ + $68.35112$) with correct significant figure is:
1. $161.964$
2. $161.9$
3. $161.95$
4. $161.96$

18.

The period of oscillation of a simple pendulum $T=2\pi\sqrt{\frac{L}{g}}$. Measured value of '$L$' is $1.0$ m from meter scale having a minimum division of $1$ mm and time of one complete oscillation is $1.95$ s measured from stopwatch of $0.01$ s resolution. The percentage error in the determination of '$g$' will be :
1. $1.13\%$
2. $1.03\%$
3. $1.33\%$
4. $1.30\%$

19.

The resistance R = $\frac{V}{i}$ where V= 100 ± 5 volts and i = 10 ± 0.2 amperes. What is the total error in R
1. 5%
2. 7%
3. 5.2%
4. $\frac{5}{2}$ %

20.

In the vernier calipers, 9 main scale divisions matched with 10 vernier scale divisions. Assume the edge of vernier scale as the '0' for Vernier Scale.The thickness of the object using the defected vernier capllipers will be:

(A) 13.3 mm
(B) 13.4 mm
(C) 13.5 mm
(D) 13.6 mm

21. Random errors can be reduced by:

1.	eliminating the error.
2.	taking more number of observations.
3.	improving least count of the instrument.
4.	none of these.

22.

35. Time for 20 oscillations of a pendulum is measured as $t_{1} = 39 .6 s$ ; $t_{2} = 39 .9 s$ and $t_{3} = 39 .5 s$ . What is the accuracy of the measurement?

$(1) \pm 0.2 \sec$
$(2) \pm 0.02 \sec$
$(3) \pm 2.0 \sec$
$(4) \pm 0.3 \sec$

This objective question is based on NCERT Exemplar subjective Question.

23. 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

24. A silver wire has a mass $(0.6 \pm 0.006) \mathrm{g}$ radius $(0.5 \pm 0.005) \mathrm{mm}$ and length $(4 \pm 0.04) \mathrm{cm}$. The maximum percentage error in the measurement of its density will be:
1. 4%
2. 3%
3. 6%
4. 7%

25.

What is the number of significant figures in $0.310\times 10^{3}?$

1.	$2$	2.	$3$
3.	$4$	4.	$6$

26. The value of Stefan's constant $(\sigma)$ is determined by experimentally measuring the remaining quantities in the equation: $E=A\sigma T^4.$
Both $E,A$ are measured to an accuracy of $1\%,$ while temperature $T$ is measured to $0.5\%.$ The error in the determination of $\sigma$ is:
1. $2\%$
2. $4\%$
3. $2.5\%$
4. $0.5\%$

27. The edge of a cube is measured by a scale of least count $1$ mm. The measured value is $l=1.2$ cm. The volume of the cube should be recorded as:
1. $\left ( 1.728\pm 0.003 \right )$ cm³
2. $\left ( 1.73\pm 0.004 \right )$ cm³
3. $\left ( 1.7\pm 0.4 \right )$ cm³
4. $\left ( 1.7\pm 0.3 \right )$ cm³

28.

The number of significant figures in 12500.40 is
1. 4
2. 5
3. 6
4. 7

29.

The period of oscillation of a simple pendulum is $T = 2 π \sqrt{\frac{L}{g}}$ . 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 g is:
1. $2 %$
2. $3 %$
3. $5 %$
4. $0 %$

30.

The decimal equivalent of 1/20 upto three significant figure is
(1) 0.0500
(2) 0.05000
(3) 0.0050
(4) $5.0 \times 10^{- 2}$

31.

A body of mass m = 3.513 kg is moving along the x-axis with a speed of 5.00 $m s^{- 1}$ . The magnitude of its momentum is recorded as
(1) 17.6 $k g m s^{- 1}$
(2) 17.565 $k g m s^{- 1}$
(3) 17.56 $k g m s^{- 1}$
(4) 17.57 $k g m s^{- 1}$

32.

Subtract $12.589-12.4$ and give the answer to the correct significant figure:

1.	$0.2$	2.	$0.189$
3.	$0.188$	4.	$0.199$

33. 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. $9.9801~\text{m}$

34.

Choose the correct statement.
1. Round off of 18.65 to 3 significant figures is 18.6.
2. Round off of 18.55 to 3 significant figures is 18.6.
3. Round off of 18.75 to 3 significant figures is 18.7.
4. Both (1) & (2)

35.

If P=2.348 cm and Q=2.1 cm, then P - Q equals=?
1. 0.248 cm
2. 0.25 cm
3. 0.2 cm
4. 0.3 cm

36.

The numbers $2.745$ and $2.735$ on rounding off to $3$ significant figures will give respectively,

1.	$2.75$ and $2.74$	2.	$2.74$ and $2.73$
3.	$2.75$ and $2.73$	4.	$2.74$ and $2.74$

37.

The number of significant digits in 1001, 100.1, 100.10, 0.001001 are, respectively,:
1. 4, 5, 4, 4
2. 4, 4, 5, 4
3. 4, 4, 4, 4
4. 5, 5, 4, 4

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

39.

The random error in the arithmetic mean of 100 observations is x; then random error in the arithmetic mean of 400 observations would be
1. 4x
2. $\frac{1}{4} x$
3. 2x
4. $\frac{1}{2} x$

40.

The length and breadth of a rectangular sheet are $16.2$ cm and $10.1$ cm, respectively. The area of the sheet in appropriate significant figures and error would be, respectively,

1.	$164\pm3~\text{cm}^2$	2.	$163.62\pm2.6~\text{cm}^2$
3.	$163.6\pm2.6~\text{cm}^2$	4.	$163.62\pm3~\text{cm}^2$

41.

The following observations were taken to determine the surface tension $T$ of water by the capillary method:
diameter of the capillary, $D=1.25 \times 10^{-2} ~\text{m}$
rise of water, $h=1.45\times 10^{-2}~\text{m}$
Using $g= 9.80~\text{m/s}^2$ and the simplified relation, the possible error in surface tension is closest to:
1. $0.15\%$
2. $1.5\%$
3. $2.4\%$
4. $10\%$

42. The figure shows a situation when the jaws of vernier are touching each other.
Each main scale division is of $1 \mathrm{~mm}$ and $5^{\text {th }}$division of vernier scale coincides with a main scale division.
The zero error of the instrument is:

1. $+0.5 \mathrm{~mm}$
2. $-0.5 \mathrm{~mm} $
3. $+0.9 \mathrm{~mm}$
4. $-0.1 \mathrm{~mm}$

Fill OMR Sheet*

*If above link doesn't work, please go to test link from where you got the pdf and fill OMR from there

CLICK HERE to get FREE ACCESS for 2 days of ANY NEETprep course

1.	\( 0.15~ \text{cm}^3 \)	2.	\( 0.1443~ \text{cm}^3 \)
3.	\( 0.14~ \text{cm}^3 \)	4.	\( 0.144 ~\text{cm}^3\)

1.	\(2340.32~\text{g}\), \(0.002~\text{g}\)
2.	\(2.340~\text{kg}\), \(0.02~\text{g}\)
3.	\(2.3~\text{kg}\), \(0~\text{g}\)
4.	\(2.334032~\text{kg}\), \(0.02~\text{g}\)

1.	\(2.75\) and \(2.74\)	2.	\(2.74\) and \(2.73\)
3.	\(2.75\) and \(2.73\)	4.	\(2.74\) and \(2.74\)

1.	\(164\pm3~\text{cm}^2\)	2.	\(163.62\pm2.6~\text{cm}^2\)
3.	\(163.6\pm2.6~\text{cm}^2\)	4.	\(163.62\pm3~\text{cm}^2\)

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

1.	\(2\)	2.	\(3\)
3.	\(4\)	4.	\(6\)

1.	\(0.2\)	2.	\(0.189\)
3.	\(0.188\)	4.	\(0.199\)

Please be patient as the PDF generation may take up to a minute.

Fill OMR Sheet*