DPP - Daily Practice Problems
Chapter-wise Sheets
Date : Start Time : End Time :
PHYSICS CP01
SYLLABUS : Physical World, Units & Measurements
Max. Marks : 180 Marking Scheme : (+4) for correct & (–1) for incorrect answer Time : 60 min.
INSTRUCTIONS : This Daily Practice Problem Sheet contains 45 MCQs. For each question only one option is correct.
Darken the correct circle/ bubble in the Response Grid provided on each page.
1. The density of material in CGS system of units is 4g/cm3. In 4. Young’s modulus of a material has the same unit as that of
a system of units in which unit of length is 10 cm and unit of (a) pressure (b) strain
mass is 100 g, the value of density of material will be (c) compressibility (d) force
(a) 0.4 unit (b) 40 unit 5. Of the following quantities, which one has dimensions
(c) 400 unit (d) 0.04 unit different from the remaining three?
2. The time period of a body under S.H.M. is represented by: (a) Energy per unit volume
T = Pa Db Sc where P is pressure, D is density and S is (b) Force per unit area
surface tension, then values of a, b and c are (c) Product of voltage and charge per unit volume
3 1 (d) Angular momentum
(a) - , , 1 (b) -1, - 2, 3 6. The pressure on a square plate is measured by measuring
2 2
the force on the plate and length of the sides of the plate by
1 3 1 1
(c) ,- ,- (d) 1, 2, F
2 2 2 3 using the formula P = . If the maximum errors in the
3. The respective number of significant figures for the numbers l2
23.023, 0.0003 and 2.1 × 10–3 are measurement of force and length are 4% and 2%
(a) 5, 1, 2 (b) 5, 1, 5 (c) 5, 5, 2 (d) 4, 4, 2 respectively, then the maximum error in the measurement of
pressure is
(a) 1% (b) 2% (c) 8% (d) 10%
RESPONSE 1. 2. 3. 4. 5.
GRID 6.
Space for Rough Work
, P-2 DPP/ CP01
7. The siemen is the SI unit of measurement of mass and length are 4% and 3%
(a) resistivity (b) resistance respectively, the maximum error in the measurement of
(c) conductivity (d) conductance density will be
8. An object is moving through the liquid. The viscous (a) 7% (b) 9% (c) 12% (d) 13%
damping force acting on it is proportional to the velocity. 16. Which is different from others by units ?
Then dimensions of constant of proportionality are (a) Phase difference (b) Mechanical equivalent
(a) [ML–1T–1] (b) [MLT–1] (c) Loudness of sound (d) Poisson’s ratio
0
(c) [M LT ] –1 (d) [ML0T–1] DV
9. The least count of a stop watch is 0.2 second. The time of 20 17. A quantity X is given by e 0 L where Î0 is the
Dt
oscillations of a pendulum is measured to be 25 second. permittivity of the free space, L is a length, DV is a potential
The percentage error in the measurement of time will be difference and Dt is a time interval. The dimensional formula
(a) 8% (b) 1.8% (c) 0.8% (d) 0.1% for X is the same as that of
10. Weber is the unit of
(a) resistance (b) charge
(a) magnetic susceptibility
(b) intensity of magnetisation (c) voltage (d) current
(c) magnetic flux 18. If the error in the measurement of the volume of sphere is
(d) magnetic permeability 6%, then the error in the measurement of its surface area will
11. The physical quantity which has the dimensional formula be
[M1T–3] is (a) 2% (b) 3% (c) 4% (d) 7.5%
(a) surface tension (b) solar constant 19. If velocity (V), force (F) and energy (E) are taken as fundamental
(c) density (d) compressibility units, then dimensional formula for mass will be
12. The dimensions of Wien’s constant are –2 0 0 2 –2 0 –2 0
(a) V F E (b) V FE (c) VF E (d) V F E
(a) [ML0 T K] (b) [M0 LT0 K]
0 0
(c) [M L T K] (d) [MLTK] 20. Multiply 107.88 by 0.610 and express the result with correct
13. If the capacitance of a nanocapacitor is measured in terms number of significant figures.
of a unit ‘u’ made by combining the electric charge ‘e’, (a) 65.8068 (b) 65.807 (c) 65.81 (d) 65.8
Bohr radius ‘a0’, Planck’s constant ‘h’ and speed of light ‘c’ 21. Which of the following is a dimensional constant?
then (a) Refractive index (b) Poissons ratio
(c) Strain (d) Gravitational constant
e2 h hc
(a) u = (b) u = 2 22. If E, m, J and G represent energy, mass, angular momentum
a0 e a0 and gravitational constant respectively, then the
e2 c e2 a 0 dimensional formula of EJ2/m5G2 is same as that of the
(c) u= (d) u= (a) angle (b) length (c) mass (d) time
ha 0 hc
23. The refractive index of water measured by the relation
1 e2 real depth
14. The dimensions of are m= is found to have values of 1.34, 1.38,
Îo hc apparent depth
1.32 and 1.36; the mean value of refractive index with
(a) M–1 L–3 T4 A2 (b) ML3 T–4 A–2
percentage error is
(c) M0 L0 T0 A0 (d) M–1 L–3 T2 A
(a) 1.35 ± 1.48 % (b) 1.35 ± 0 %
15. The density of a cube is measured by measuring its mass (c) 1.36 ± 6 % (d) 1.36 ± 0 %
and length of its sides. If the maximum error in the
7. 8. 9. 10. 11.
RESPONSE 12. 13. 14. 15. 16.
GRID 17. 18. 19. 20. 21.
22. 23.
Space for Rough Work
,DPP/ CP01 P-3
24. If e is the charge, V the potential difference, T the temperature, 32. The mass of the liquid flowing per second per unit area of
eV cross-section of the tube is proportional to (pressure
then the units of are the same as that of
T difference across the ends)n and (average velocity of the
(a) Planck’s constant (b) Stefan’s constant liquid)m. Which of the following relations between m and n
(c) Boltzmann's constant (d) gravitational constant is correct?
25. The dimensions of mobility are
(a) m = n (b) m = – n (c) m2 = n (d) m = – n2
(a) M–2T 2A (b) M–1T 2A
(c) M T A –2 3 (d) M–1T 3A 33. The Richardson equation is given by I = AT2e–B/kT. The
26. Two quantities A and B have different dimensions which dimensional formula for AB2 is same as that for
mathematical operation given below is physically (a) I T2 (b) kT (c) I k2 (d) I k2/T
meaningful? 34. Turpentine oil is flowing through a capillary tube of length
(a) A/B (b) A + B (c) A – B (d) A = B l and radius r. The pressure difference between the two
27. The velocity of water waves (v) may depend on their
wavelength l, the density of water r and the acceleration ends of the tube is p. The viscosity of oil is given by :
due to gravity, g. The method of dimensions gives the
p(r 2 - x 2 )
relation between these quantities is h= . Here v is velocity of oil at a distance x from
(a) v (b) v2 µ gl 4vl
(c) v µ gl
2 2 (d) v2 µ g–1l2 the axis of the tube. From this relation, the dimensional
28. The physical quantities not having same dimensions are formula of h is
(a) torque and work
(b) momentum and Planck’s constant (a) [ML-1T -1 ] (b) [MLT -1 ]
(c) stress and Young’s modulus
(d) speed and (m0e0)–1/2 (c) [ML2 T -2 ] (d) [M 0 L0 T 0 ]
29. A physical quantity of the dimensions of length that can be
e2 éæ 2 p öù
formed out of c, G and is [c is velocity of light, G is 35. Given that y = A sin êç (ct - x) ÷ú , where y and x are
ë è l øû
4pe0
universal constant of gravitation and e is charge] measured in metre. Which of the following statements is
1/ 2 1/ 2 true?
é e2 ù 1 é e2 ù
(a) c2 ê G ú (b) ê ú (a) The unit of l is same as that of x and A
ëê 4pe 0 ûú c 2 ëê G4 pe0 ûú (b) The unit of l is same as that of x but not of A
1/ 2 2p
1 e2 1 é e2 ù (c) The unit of c is same as that of
(c) G (d) ê G ú l
c 4pe0 c 2 êë 4pe 0 úû
2p
30. The unit of impulse is the same as that of (d) The unit of (ct – x) is same as that of
(a) energy (b) power l
(c) momentum (d) velocity 36. If L = 2.331 cm, B = 2.1 cm, then L + B =
31. If Q denote the charge on the plate of a capacitor of (a) 4.431 cm (b) 4.43 cm (c) 4.4 cm (d) 4 cm
Q2 37. In the relation x = cos (wt + kx), the dimension(s) of w is/are
capacitance C then the dimensional formula for is (a) [M0 LT] (b) [M0L–1T0]
C
(c) [M0L0T –1] (d) [M0LT–1]
(a) [L2M2T] (b) [LMT2]
(c) [L2MT–2] (d) [L2M2T2]
24. 25. 26. 27. 28.
RESPONSE 29. 30. 31. 32. 33.
GRID
34. 35. 36. 37.
Space for Rough Work
, P-4 DPP/ CP01
38. In a vernier callipers, ten smallest divisions of the vernier 42. Which of the following do not have the same dimensional
scale are equal to nine smallest division on the main scale. If formula as the velocity?
the smallest division on the main scale is half millimeter, Given that m0 = permeability of free space, e0 = permittivity
then the vernier constant is of free space, n = frequency, l = wavelength, P = pressure, r
(a) 0.5 mm (b) 0.1 mm (c) 0.05 mm (d) 0.005 mm = density, w = angular frequency, k = wave number,
39. Which two of the following five physical parameters have
(a) 1 m 0 eo (b) n l (c) P/r (d) wk
the same dimensions?
(A) Energy density (B) Refractive index 43. Unit of magnetic moment is
(C) Dielectric constant (D) Young’s modulus (a) ampere–metre2 (b) ampere–metre
(c) weber–metre 2 (d) weber/metre
(E) Magnetic field
(a) (B) and (D) (b) (C) and (E) 44. An experiment is performed to obtain the value of
(c) (A) and (D) (d) (A) and (E) acceleration due to gravity g by using a simple pendulum of
length L. In this experiment time for 100 oscillations is
æ a ö measured by using a watch of 1 second least count and the
40. In the eqn. ç P + 2 ÷ (V - b) = constant, the unit of a is
è V ø value is 90.0 seconds. The length L is measured by using a
meter scale of least count 1 mm and the value is 20.0 cm. The
(a) dyne cm5 (b) dyne cm4
3
error in the determination of g would be:
(c) dyne/cm (d) dyne cm2
(a) 1.7% (b) 2.7% (c) 4.4% (d) 2.27%
41. The dimensions of Reynold’s constant are
45. The dimensional formula for magnetic flux is
(a) [M0L0T0] (b) [ML–1T–1] (a) [ML2T–2A–1] (b) [ML3T–2A–2]
–1
(c) [ML T ]–2 (d) [ML–2T–2] 0 –2 2 –2
(c) [M L T A ] (d) [ML2T–1A2]
RESPONSE 38. 39. 40. 41. 42.
GRID 43. 44. 45.
DAILY PRACTICE PROBLEM DPP CHAPTERWISE CP01 - PHYSICS
Total Questions 45
Total Marks 180
Attempted Correct
Incorrect Net Score
Cut-off Score 50 Qualifying Score 70
Success Gap = Net Score – Qualifying Score
Net Score = (Correct × 4) – (Incorrect × 1)
Space for Rough Work
Chapter-wise Sheets
Date : Start Time : End Time :
PHYSICS CP01
SYLLABUS : Physical World, Units & Measurements
Max. Marks : 180 Marking Scheme : (+4) for correct & (–1) for incorrect answer Time : 60 min.
INSTRUCTIONS : This Daily Practice Problem Sheet contains 45 MCQs. For each question only one option is correct.
Darken the correct circle/ bubble in the Response Grid provided on each page.
1. The density of material in CGS system of units is 4g/cm3. In 4. Young’s modulus of a material has the same unit as that of
a system of units in which unit of length is 10 cm and unit of (a) pressure (b) strain
mass is 100 g, the value of density of material will be (c) compressibility (d) force
(a) 0.4 unit (b) 40 unit 5. Of the following quantities, which one has dimensions
(c) 400 unit (d) 0.04 unit different from the remaining three?
2. The time period of a body under S.H.M. is represented by: (a) Energy per unit volume
T = Pa Db Sc where P is pressure, D is density and S is (b) Force per unit area
surface tension, then values of a, b and c are (c) Product of voltage and charge per unit volume
3 1 (d) Angular momentum
(a) - , , 1 (b) -1, - 2, 3 6. The pressure on a square plate is measured by measuring
2 2
the force on the plate and length of the sides of the plate by
1 3 1 1
(c) ,- ,- (d) 1, 2, F
2 2 2 3 using the formula P = . If the maximum errors in the
3. The respective number of significant figures for the numbers l2
23.023, 0.0003 and 2.1 × 10–3 are measurement of force and length are 4% and 2%
(a) 5, 1, 2 (b) 5, 1, 5 (c) 5, 5, 2 (d) 4, 4, 2 respectively, then the maximum error in the measurement of
pressure is
(a) 1% (b) 2% (c) 8% (d) 10%
RESPONSE 1. 2. 3. 4. 5.
GRID 6.
Space for Rough Work
, P-2 DPP/ CP01
7. The siemen is the SI unit of measurement of mass and length are 4% and 3%
(a) resistivity (b) resistance respectively, the maximum error in the measurement of
(c) conductivity (d) conductance density will be
8. An object is moving through the liquid. The viscous (a) 7% (b) 9% (c) 12% (d) 13%
damping force acting on it is proportional to the velocity. 16. Which is different from others by units ?
Then dimensions of constant of proportionality are (a) Phase difference (b) Mechanical equivalent
(a) [ML–1T–1] (b) [MLT–1] (c) Loudness of sound (d) Poisson’s ratio
0
(c) [M LT ] –1 (d) [ML0T–1] DV
9. The least count of a stop watch is 0.2 second. The time of 20 17. A quantity X is given by e 0 L where Î0 is the
Dt
oscillations of a pendulum is measured to be 25 second. permittivity of the free space, L is a length, DV is a potential
The percentage error in the measurement of time will be difference and Dt is a time interval. The dimensional formula
(a) 8% (b) 1.8% (c) 0.8% (d) 0.1% for X is the same as that of
10. Weber is the unit of
(a) resistance (b) charge
(a) magnetic susceptibility
(b) intensity of magnetisation (c) voltage (d) current
(c) magnetic flux 18. If the error in the measurement of the volume of sphere is
(d) magnetic permeability 6%, then the error in the measurement of its surface area will
11. The physical quantity which has the dimensional formula be
[M1T–3] is (a) 2% (b) 3% (c) 4% (d) 7.5%
(a) surface tension (b) solar constant 19. If velocity (V), force (F) and energy (E) are taken as fundamental
(c) density (d) compressibility units, then dimensional formula for mass will be
12. The dimensions of Wien’s constant are –2 0 0 2 –2 0 –2 0
(a) V F E (b) V FE (c) VF E (d) V F E
(a) [ML0 T K] (b) [M0 LT0 K]
0 0
(c) [M L T K] (d) [MLTK] 20. Multiply 107.88 by 0.610 and express the result with correct
13. If the capacitance of a nanocapacitor is measured in terms number of significant figures.
of a unit ‘u’ made by combining the electric charge ‘e’, (a) 65.8068 (b) 65.807 (c) 65.81 (d) 65.8
Bohr radius ‘a0’, Planck’s constant ‘h’ and speed of light ‘c’ 21. Which of the following is a dimensional constant?
then (a) Refractive index (b) Poissons ratio
(c) Strain (d) Gravitational constant
e2 h hc
(a) u = (b) u = 2 22. If E, m, J and G represent energy, mass, angular momentum
a0 e a0 and gravitational constant respectively, then the
e2 c e2 a 0 dimensional formula of EJ2/m5G2 is same as that of the
(c) u= (d) u= (a) angle (b) length (c) mass (d) time
ha 0 hc
23. The refractive index of water measured by the relation
1 e2 real depth
14. The dimensions of are m= is found to have values of 1.34, 1.38,
Îo hc apparent depth
1.32 and 1.36; the mean value of refractive index with
(a) M–1 L–3 T4 A2 (b) ML3 T–4 A–2
percentage error is
(c) M0 L0 T0 A0 (d) M–1 L–3 T2 A
(a) 1.35 ± 1.48 % (b) 1.35 ± 0 %
15. The density of a cube is measured by measuring its mass (c) 1.36 ± 6 % (d) 1.36 ± 0 %
and length of its sides. If the maximum error in the
7. 8. 9. 10. 11.
RESPONSE 12. 13. 14. 15. 16.
GRID 17. 18. 19. 20. 21.
22. 23.
Space for Rough Work
,DPP/ CP01 P-3
24. If e is the charge, V the potential difference, T the temperature, 32. The mass of the liquid flowing per second per unit area of
eV cross-section of the tube is proportional to (pressure
then the units of are the same as that of
T difference across the ends)n and (average velocity of the
(a) Planck’s constant (b) Stefan’s constant liquid)m. Which of the following relations between m and n
(c) Boltzmann's constant (d) gravitational constant is correct?
25. The dimensions of mobility are
(a) m = n (b) m = – n (c) m2 = n (d) m = – n2
(a) M–2T 2A (b) M–1T 2A
(c) M T A –2 3 (d) M–1T 3A 33. The Richardson equation is given by I = AT2e–B/kT. The
26. Two quantities A and B have different dimensions which dimensional formula for AB2 is same as that for
mathematical operation given below is physically (a) I T2 (b) kT (c) I k2 (d) I k2/T
meaningful? 34. Turpentine oil is flowing through a capillary tube of length
(a) A/B (b) A + B (c) A – B (d) A = B l and radius r. The pressure difference between the two
27. The velocity of water waves (v) may depend on their
wavelength l, the density of water r and the acceleration ends of the tube is p. The viscosity of oil is given by :
due to gravity, g. The method of dimensions gives the
p(r 2 - x 2 )
relation between these quantities is h= . Here v is velocity of oil at a distance x from
(a) v (b) v2 µ gl 4vl
(c) v µ gl
2 2 (d) v2 µ g–1l2 the axis of the tube. From this relation, the dimensional
28. The physical quantities not having same dimensions are formula of h is
(a) torque and work
(b) momentum and Planck’s constant (a) [ML-1T -1 ] (b) [MLT -1 ]
(c) stress and Young’s modulus
(d) speed and (m0e0)–1/2 (c) [ML2 T -2 ] (d) [M 0 L0 T 0 ]
29. A physical quantity of the dimensions of length that can be
e2 éæ 2 p öù
formed out of c, G and is [c is velocity of light, G is 35. Given that y = A sin êç (ct - x) ÷ú , where y and x are
ë è l øû
4pe0
universal constant of gravitation and e is charge] measured in metre. Which of the following statements is
1/ 2 1/ 2 true?
é e2 ù 1 é e2 ù
(a) c2 ê G ú (b) ê ú (a) The unit of l is same as that of x and A
ëê 4pe 0 ûú c 2 ëê G4 pe0 ûú (b) The unit of l is same as that of x but not of A
1/ 2 2p
1 e2 1 é e2 ù (c) The unit of c is same as that of
(c) G (d) ê G ú l
c 4pe0 c 2 êë 4pe 0 úû
2p
30. The unit of impulse is the same as that of (d) The unit of (ct – x) is same as that of
(a) energy (b) power l
(c) momentum (d) velocity 36. If L = 2.331 cm, B = 2.1 cm, then L + B =
31. If Q denote the charge on the plate of a capacitor of (a) 4.431 cm (b) 4.43 cm (c) 4.4 cm (d) 4 cm
Q2 37. In the relation x = cos (wt + kx), the dimension(s) of w is/are
capacitance C then the dimensional formula for is (a) [M0 LT] (b) [M0L–1T0]
C
(c) [M0L0T –1] (d) [M0LT–1]
(a) [L2M2T] (b) [LMT2]
(c) [L2MT–2] (d) [L2M2T2]
24. 25. 26. 27. 28.
RESPONSE 29. 30. 31. 32. 33.
GRID
34. 35. 36. 37.
Space for Rough Work
, P-4 DPP/ CP01
38. In a vernier callipers, ten smallest divisions of the vernier 42. Which of the following do not have the same dimensional
scale are equal to nine smallest division on the main scale. If formula as the velocity?
the smallest division on the main scale is half millimeter, Given that m0 = permeability of free space, e0 = permittivity
then the vernier constant is of free space, n = frequency, l = wavelength, P = pressure, r
(a) 0.5 mm (b) 0.1 mm (c) 0.05 mm (d) 0.005 mm = density, w = angular frequency, k = wave number,
39. Which two of the following five physical parameters have
(a) 1 m 0 eo (b) n l (c) P/r (d) wk
the same dimensions?
(A) Energy density (B) Refractive index 43. Unit of magnetic moment is
(C) Dielectric constant (D) Young’s modulus (a) ampere–metre2 (b) ampere–metre
(c) weber–metre 2 (d) weber/metre
(E) Magnetic field
(a) (B) and (D) (b) (C) and (E) 44. An experiment is performed to obtain the value of
(c) (A) and (D) (d) (A) and (E) acceleration due to gravity g by using a simple pendulum of
length L. In this experiment time for 100 oscillations is
æ a ö measured by using a watch of 1 second least count and the
40. In the eqn. ç P + 2 ÷ (V - b) = constant, the unit of a is
è V ø value is 90.0 seconds. The length L is measured by using a
meter scale of least count 1 mm and the value is 20.0 cm. The
(a) dyne cm5 (b) dyne cm4
3
error in the determination of g would be:
(c) dyne/cm (d) dyne cm2
(a) 1.7% (b) 2.7% (c) 4.4% (d) 2.27%
41. The dimensions of Reynold’s constant are
45. The dimensional formula for magnetic flux is
(a) [M0L0T0] (b) [ML–1T–1] (a) [ML2T–2A–1] (b) [ML3T–2A–2]
–1
(c) [ML T ]–2 (d) [ML–2T–2] 0 –2 2 –2
(c) [M L T A ] (d) [ML2T–1A2]
RESPONSE 38. 39. 40. 41. 42.
GRID 43. 44. 45.
DAILY PRACTICE PROBLEM DPP CHAPTERWISE CP01 - PHYSICS
Total Questions 45
Total Marks 180
Attempted Correct
Incorrect Net Score
Cut-off Score 50 Qualifying Score 70
Success Gap = Net Score – Qualifying Score
Net Score = (Correct × 4) – (Incorrect × 1)
Space for Rough Work
