DPP - Daily Practice Problems
Name : Date :
Start Time : End Time :
01
SYLLABUS : Physical World, Units & Dimensions
Max. Marks : 120 Time : 60 min.
GENERAL INSTRUCTIONS
• The Daily Practice Problem Sheet contains 30 MCQ's. For each question only one option is correct. Darken the correct
circle/ bubble in the Response Grid provided on each page.
• You have to evaluate your Response Grids yourself with the help of solution booklet.
• Each correct answer will get you 4 marks and 1 mark shall be deduced for each incorrect answer. No mark will be given/
deducted if no bubble is filled. Keep a timer in front of you and stop immediately at the end of 60 min.
• The sheet follows a particular syllabus. Do not attempt the sheet before you have completed your preparation for that
syllabus. Refer syllabus sheet in the starting of the book for the syllabus of all the DPP sheets.
• After completing the sheet check your answers with the solution booklet and complete the Result Grid. Finally spend time
to analyse your performance and revise the areas which emerge out as weak in your evaluation.
DIRECTIONS (Q.1-Q.21) : There are 21 multiple choice and n2 are number of particles per unit volume in the position
questions. Each question has 4 choices (a), (b), (c) and (d), out x1 and x2. Find dimensions of D called as diffusion constant.
of which ONLY ONE choice is correct. (a) [M 0 L T 2] (b) [M 0 L2 T –4]
0
(c) [M L T ] –3 (d) [M 0 L2 T –1]
Q.1 If L, C and R represent inductance, capacitance and
2
Q.3 X = 3YZ find dimensions of Y in (MKSA) system, if X and
resistance respectively, then which of the following does
not represent dimensions of frequency? Z are the dimensions of capacity and magnetic field
respectively
1 R
(a) (b) (a) [M –3L –2T – 4A –1] (b) [ML– 2]
RC L
(c) [M –3L–2T 4A 4] (d) [M –3L– 2T 8A 4]
1 C aZ
(c) (d) a - kq
LC L Q.4 In the relation P = , P is pressure, Z is the distance,
e
Q.2 Number of particles crossing unit area perpendicular to b
k is Boltzmann constant and q is the temperature. The
n2 - n1
X-axis in unit time is given by n = - D , where n1 dimensional formula of b will be
x2 - x1 (a) [M 0L 2T 0] (b) [M 1L 2T 1]
1 0
(c) [M L T ] –1 (d) [M 0L 2T –1]
RESPONSE GRID 1. 2. 3. 4.
Space for Rough Work
, 2 DPP/ P 01
1/ 2
Q.12 Wavelength of ray of light is 0.00006 m. It is equal to
P éF ù (a) 6 microns (b) 60 microns
Q.5 The frequency of vibration of string is given by n = ê ú .
2l ë m û (c) 600 microns (d) 0.6 microns
Here P is number of segments in the string and l is the Q.13 SI unit of permittivity is
length. The dimensional formula for m will be (a) C2 m2 N–2 (b) C–1 m 2N –2
(a) [M 0LT –1] (b) [ML 0T –1] 2
(c) C m N 2 2 (d) C2 m–2 N –1
(c) [ML –1T 0] (d) [M 0L 0T 0]
Q.6 What is the relationship between dyne and newton of force? 1
Q.14 The dimensions of e E2 (e0 = permittivity of free space
(a) 1 dyne = 10–5 newton (b) 1 dyne = 10–7 newton 2 0
(c) 1 dyne = 105 newton (d) 1 dyne = 107 newton and E = electric field) are
Q.7 The speed of light (c), gravitational constant (G) and (a) MLT–1 (b) ML2 T–2
(c) ML T –1 –2 (d) ML2 T–1
Planck's constant (h) are taken as the fundamental units in a
system. The dimensions of time in this new system should Q.15 Which of the following pairs is wrong?
be (a) Pressure-Baromter
(a) G1/2 h1/2 c –5/2 (b) G–1/2 h 1/2 c 1/2 (b) Relative density-Pyrometer
1/2
(c) G h c 1/2 –3/2 (d) G1/2 h 1/2 c 1/2 (c) Temperature-Thermometer
Q.8 If the constant of gravitation (G), Planck's constant (h) and (d) Earthquake-Seismograph
the velocity of light (c) be chosen as fundamental units. Q.16 A physical quantity x depends on quantities y and z as
The dimensions of the radius of gyration is follows: x = Ay + B tan Cz, where A, B and C are constants.
(a) h1/2 c –3/2G 1/2 (b) h1/2 c 3/2 G 1/2 Which of the following do not have the same dimensions?
(c) h1/2 c –3/2 G –1/2 (d) h–1/2 c –3/2 G 1/2 (a) x and B (b) C and z–1
Q.9 The magnitude of any physical quantity (c) y and B/A (d) x and A
(a) depends on the method of measurement Q.17 If the time period (T) of vibration of a liquid drop depends
(b) does not depend on the method of measurement on surface tension (S), radius (r) of the drop and density (r)
(c) is more in SI system than in CGS system of the liquid, then the expression of T is
(d) directly proportional to the fundamental units of mass,
length and time
(a) T = k rr 3 / S (b) T = k r1/ 2 r 3 / S
Q.10 The unit of Stefan's constant s is (c) T = k rr 3 / S1/ 2 (d) None of these
(a) Wm–2 K–1 (b) Wm2K–4
(c) Wm–2 K–4 (d) Wm–2K4 Q.18 The dimensional formula for Planck’s constant (h) is
2
Q.11 In S = a + bt + ct , S is measured in metres and t in seconds. (a) [ML–2T–3 ] (b) [M0L2T–2 ]
The unit of c is 0 2
(c) [M L T ]–1 (d) [ML–2T–2 ]
(a) ms–2 (b) m Q.19 What are the dimensions of permeability (m0) of vaccum?
(c) ms–1 (d) None (a) MLT–2I2 (b) MLT–2I–2
(c) ML–1T–2I2 (d) ML–1T –2I–2
5. 6. 7. 8. 9.
RESPONSE 10. 11. 12. 13. 14.
GRID
15. 16. 17. 18. 19.
Space for Rough Work
,DPP/ P 01 3
Q.20 A small steel ball of radius r is allowed to fall under gravity Q.23 P represents radiation pressure, c represents speed of light and
through a column of a viscous liquid of coefficient of S represents radiation energy striking unit area per sec. The non
viscosity h. After some time the velocity of the ball attains a zero integers x, y, z such that Px Sy cz is dimensionless are
constant value known as terminal velocity vT. The terminal (1) x = 1 (2) y = – 1
velocity depends on (i) the mass of the ball m, (ii) h, (iii) r (3) z = 1 (4) x = – 1
and (iv) acceleration due to gravity g. Which of the following Q.24 Which of the following pairs have same dimensions?
relations is dimensionally correct? (1) Angular momentum and work
mg hr (2) Torque and work
(a) vT µ (b) vT µ
hr mg (3) Energy and Young’s modulus
(4) Light year and wavelength
mgr
(c) vT µ hrmg (d) vT µ DIRECTION (Q.25-Q.27) : Read the passage given below and
h
answer the questions that follows :
Q.21 The equation of state of some gases can be expressed as
Three of the fundamental constants of physics are the universal
æ a ö gravitational constant, G = 6.7 × 10–11m3kg–1s–2, the speed
çP+ 2 ÷ (V - b) = RT . Here P is the pressure, V is the of light, c = 3.0 × 10 8 m/s, and Planck’s constant,
è V ø
h = 6.6 × 10–34 kg m2 s–1.
volume, T is the absolute temperature and a, b and R are
Q.25 Find a combination of these three constants that has the
constants. The dimensions of 'a' are
dimensions of time. This time is called the Planck time and
(a) ML5 T–2 (b) ML–1 T–2 represents the age of the universe before which the laws of
(c) M0L3T0 (d) M0L6T0 physics as presently understood cannot be applied.
DIRECTIONS (Q.22-Q.24) : In the following questions, more
hG hG
than one of the answers given are correct. Select the correct (a) (b)
answers and mark it according to the following codes: c 4
c3
Codes :
hG hG
(a) 1, 2 and 3 are correct (b) 1 and 2 are correct (c) (d)
c c5
(c) 2 and 4 are correct (d) 1 and 3 are correct
Q.26 Find the value of Planck time in seconds
Q.22 The frequency of vibration f of a mass m suspended from
a spring of spring constant k is given by a relation of the (a) 1.3 × 10– 33 s (b) 1.3 × 10– 43 s
type f = c mx ky, where c is a dimensionless constant. The (c) 2.3 × 10– 13 s (d) 0.3 × 10– 23 s
values of x and y are
Q.27 The energy of a photon is given by E = hc .
1 1 l
(1) x= (2) x=-
2 2
If l = 4 ´ 10 -7 m , the energy of photon is
1 1 (a) 3.0 eV (b) 4.5 eV
(3) y=- (4) y=
2 2 (c) 2.10 eV (d) 3.95 eV
RESPONSE 20. 21. 22. 23. 24.
GRID 25. 26. 27.
Space for Rough Work
, 4 DPP/ P 01
DIRECTIONS (Q. 28-Q.30) : Each of these questions contains two
æ 1 1 ö
statements: Statement-1 (Assertion) and Statement-2 (Reason). v = Rç - ÷ , where the symbols have their usual
ç n2 n 2 ÷
Each of these questions has four alternative choices, only one of è 1 2 ø
which is the correct answer. You have to select the correct choice.
meaning.
(a) Statement-1 is True, Statement-2 is True; Statement-2 is a Q.29 Statement -1: The time period of a pendulum is given by
correct explanation for Statement-1.
the formula, T = 2p g / l .
(b) Statement-1 is True, Statement-2 is True; Statement-2 is NOT
a correct explanation for Statement-1. Statement -2: According to the principle of homogeneity of
(c) Statement -1 is False, Statement-2 is True. dimensions, only that formula is correct in which the
(d) Statement -1 is True, Statement-2 is False. dimensions of L.H.S. is equal to dimensions of R.H.S.
Q.28 Statement -1 : Unit of Rydberg constant R is m–1 Q.30 Statement -1: L/R and CR both have same dimensions.
Statement -2 : It follows from Bohr’s formula Statement -2: L/R and CR both have dimension of time.
RESPONSE GRID 28. 29. 30.
DAILY PRACTICE PROBLEM SHEET 1 - PHYSICS
Total Questions 30 Total Marks 120
Attempted Correct
Incorrect N et Score
Cut-off Score 30 Qualifying Score 50
Success Gap = Net Score – Qualifying Score
Net Score = (Correct × 4) – (Incorrect × 1)
Space for Rough Work
Name : Date :
Start Time : End Time :
01
SYLLABUS : Physical World, Units & Dimensions
Max. Marks : 120 Time : 60 min.
GENERAL INSTRUCTIONS
• The Daily Practice Problem Sheet contains 30 MCQ's. For each question only one option is correct. Darken the correct
circle/ bubble in the Response Grid provided on each page.
• You have to evaluate your Response Grids yourself with the help of solution booklet.
• Each correct answer will get you 4 marks and 1 mark shall be deduced for each incorrect answer. No mark will be given/
deducted if no bubble is filled. Keep a timer in front of you and stop immediately at the end of 60 min.
• The sheet follows a particular syllabus. Do not attempt the sheet before you have completed your preparation for that
syllabus. Refer syllabus sheet in the starting of the book for the syllabus of all the DPP sheets.
• After completing the sheet check your answers with the solution booklet and complete the Result Grid. Finally spend time
to analyse your performance and revise the areas which emerge out as weak in your evaluation.
DIRECTIONS (Q.1-Q.21) : There are 21 multiple choice and n2 are number of particles per unit volume in the position
questions. Each question has 4 choices (a), (b), (c) and (d), out x1 and x2. Find dimensions of D called as diffusion constant.
of which ONLY ONE choice is correct. (a) [M 0 L T 2] (b) [M 0 L2 T –4]
0
(c) [M L T ] –3 (d) [M 0 L2 T –1]
Q.1 If L, C and R represent inductance, capacitance and
2
Q.3 X = 3YZ find dimensions of Y in (MKSA) system, if X and
resistance respectively, then which of the following does
not represent dimensions of frequency? Z are the dimensions of capacity and magnetic field
respectively
1 R
(a) (b) (a) [M –3L –2T – 4A –1] (b) [ML– 2]
RC L
(c) [M –3L–2T 4A 4] (d) [M –3L– 2T 8A 4]
1 C aZ
(c) (d) a - kq
LC L Q.4 In the relation P = , P is pressure, Z is the distance,
e
Q.2 Number of particles crossing unit area perpendicular to b
k is Boltzmann constant and q is the temperature. The
n2 - n1
X-axis in unit time is given by n = - D , where n1 dimensional formula of b will be
x2 - x1 (a) [M 0L 2T 0] (b) [M 1L 2T 1]
1 0
(c) [M L T ] –1 (d) [M 0L 2T –1]
RESPONSE GRID 1. 2. 3. 4.
Space for Rough Work
, 2 DPP/ P 01
1/ 2
Q.12 Wavelength of ray of light is 0.00006 m. It is equal to
P éF ù (a) 6 microns (b) 60 microns
Q.5 The frequency of vibration of string is given by n = ê ú .
2l ë m û (c) 600 microns (d) 0.6 microns
Here P is number of segments in the string and l is the Q.13 SI unit of permittivity is
length. The dimensional formula for m will be (a) C2 m2 N–2 (b) C–1 m 2N –2
(a) [M 0LT –1] (b) [ML 0T –1] 2
(c) C m N 2 2 (d) C2 m–2 N –1
(c) [ML –1T 0] (d) [M 0L 0T 0]
Q.6 What is the relationship between dyne and newton of force? 1
Q.14 The dimensions of e E2 (e0 = permittivity of free space
(a) 1 dyne = 10–5 newton (b) 1 dyne = 10–7 newton 2 0
(c) 1 dyne = 105 newton (d) 1 dyne = 107 newton and E = electric field) are
Q.7 The speed of light (c), gravitational constant (G) and (a) MLT–1 (b) ML2 T–2
(c) ML T –1 –2 (d) ML2 T–1
Planck's constant (h) are taken as the fundamental units in a
system. The dimensions of time in this new system should Q.15 Which of the following pairs is wrong?
be (a) Pressure-Baromter
(a) G1/2 h1/2 c –5/2 (b) G–1/2 h 1/2 c 1/2 (b) Relative density-Pyrometer
1/2
(c) G h c 1/2 –3/2 (d) G1/2 h 1/2 c 1/2 (c) Temperature-Thermometer
Q.8 If the constant of gravitation (G), Planck's constant (h) and (d) Earthquake-Seismograph
the velocity of light (c) be chosen as fundamental units. Q.16 A physical quantity x depends on quantities y and z as
The dimensions of the radius of gyration is follows: x = Ay + B tan Cz, where A, B and C are constants.
(a) h1/2 c –3/2G 1/2 (b) h1/2 c 3/2 G 1/2 Which of the following do not have the same dimensions?
(c) h1/2 c –3/2 G –1/2 (d) h–1/2 c –3/2 G 1/2 (a) x and B (b) C and z–1
Q.9 The magnitude of any physical quantity (c) y and B/A (d) x and A
(a) depends on the method of measurement Q.17 If the time period (T) of vibration of a liquid drop depends
(b) does not depend on the method of measurement on surface tension (S), radius (r) of the drop and density (r)
(c) is more in SI system than in CGS system of the liquid, then the expression of T is
(d) directly proportional to the fundamental units of mass,
length and time
(a) T = k rr 3 / S (b) T = k r1/ 2 r 3 / S
Q.10 The unit of Stefan's constant s is (c) T = k rr 3 / S1/ 2 (d) None of these
(a) Wm–2 K–1 (b) Wm2K–4
(c) Wm–2 K–4 (d) Wm–2K4 Q.18 The dimensional formula for Planck’s constant (h) is
2
Q.11 In S = a + bt + ct , S is measured in metres and t in seconds. (a) [ML–2T–3 ] (b) [M0L2T–2 ]
The unit of c is 0 2
(c) [M L T ]–1 (d) [ML–2T–2 ]
(a) ms–2 (b) m Q.19 What are the dimensions of permeability (m0) of vaccum?
(c) ms–1 (d) None (a) MLT–2I2 (b) MLT–2I–2
(c) ML–1T–2I2 (d) ML–1T –2I–2
5. 6. 7. 8. 9.
RESPONSE 10. 11. 12. 13. 14.
GRID
15. 16. 17. 18. 19.
Space for Rough Work
,DPP/ P 01 3
Q.20 A small steel ball of radius r is allowed to fall under gravity Q.23 P represents radiation pressure, c represents speed of light and
through a column of a viscous liquid of coefficient of S represents radiation energy striking unit area per sec. The non
viscosity h. After some time the velocity of the ball attains a zero integers x, y, z such that Px Sy cz is dimensionless are
constant value known as terminal velocity vT. The terminal (1) x = 1 (2) y = – 1
velocity depends on (i) the mass of the ball m, (ii) h, (iii) r (3) z = 1 (4) x = – 1
and (iv) acceleration due to gravity g. Which of the following Q.24 Which of the following pairs have same dimensions?
relations is dimensionally correct? (1) Angular momentum and work
mg hr (2) Torque and work
(a) vT µ (b) vT µ
hr mg (3) Energy and Young’s modulus
(4) Light year and wavelength
mgr
(c) vT µ hrmg (d) vT µ DIRECTION (Q.25-Q.27) : Read the passage given below and
h
answer the questions that follows :
Q.21 The equation of state of some gases can be expressed as
Three of the fundamental constants of physics are the universal
æ a ö gravitational constant, G = 6.7 × 10–11m3kg–1s–2, the speed
çP+ 2 ÷ (V - b) = RT . Here P is the pressure, V is the of light, c = 3.0 × 10 8 m/s, and Planck’s constant,
è V ø
h = 6.6 × 10–34 kg m2 s–1.
volume, T is the absolute temperature and a, b and R are
Q.25 Find a combination of these three constants that has the
constants. The dimensions of 'a' are
dimensions of time. This time is called the Planck time and
(a) ML5 T–2 (b) ML–1 T–2 represents the age of the universe before which the laws of
(c) M0L3T0 (d) M0L6T0 physics as presently understood cannot be applied.
DIRECTIONS (Q.22-Q.24) : In the following questions, more
hG hG
than one of the answers given are correct. Select the correct (a) (b)
answers and mark it according to the following codes: c 4
c3
Codes :
hG hG
(a) 1, 2 and 3 are correct (b) 1 and 2 are correct (c) (d)
c c5
(c) 2 and 4 are correct (d) 1 and 3 are correct
Q.26 Find the value of Planck time in seconds
Q.22 The frequency of vibration f of a mass m suspended from
a spring of spring constant k is given by a relation of the (a) 1.3 × 10– 33 s (b) 1.3 × 10– 43 s
type f = c mx ky, where c is a dimensionless constant. The (c) 2.3 × 10– 13 s (d) 0.3 × 10– 23 s
values of x and y are
Q.27 The energy of a photon is given by E = hc .
1 1 l
(1) x= (2) x=-
2 2
If l = 4 ´ 10 -7 m , the energy of photon is
1 1 (a) 3.0 eV (b) 4.5 eV
(3) y=- (4) y=
2 2 (c) 2.10 eV (d) 3.95 eV
RESPONSE 20. 21. 22. 23. 24.
GRID 25. 26. 27.
Space for Rough Work
, 4 DPP/ P 01
DIRECTIONS (Q. 28-Q.30) : Each of these questions contains two
æ 1 1 ö
statements: Statement-1 (Assertion) and Statement-2 (Reason). v = Rç - ÷ , where the symbols have their usual
ç n2 n 2 ÷
Each of these questions has four alternative choices, only one of è 1 2 ø
which is the correct answer. You have to select the correct choice.
meaning.
(a) Statement-1 is True, Statement-2 is True; Statement-2 is a Q.29 Statement -1: The time period of a pendulum is given by
correct explanation for Statement-1.
the formula, T = 2p g / l .
(b) Statement-1 is True, Statement-2 is True; Statement-2 is NOT
a correct explanation for Statement-1. Statement -2: According to the principle of homogeneity of
(c) Statement -1 is False, Statement-2 is True. dimensions, only that formula is correct in which the
(d) Statement -1 is True, Statement-2 is False. dimensions of L.H.S. is equal to dimensions of R.H.S.
Q.28 Statement -1 : Unit of Rydberg constant R is m–1 Q.30 Statement -1: L/R and CR both have same dimensions.
Statement -2 : It follows from Bohr’s formula Statement -2: L/R and CR both have dimension of time.
RESPONSE GRID 28. 29. 30.
DAILY PRACTICE PROBLEM SHEET 1 - PHYSICS
Total Questions 30 Total Marks 120
Attempted Correct
Incorrect N et Score
Cut-off Score 30 Qualifying Score 50
Success Gap = Net Score – Qualifying Score
Net Score = (Correct × 4) – (Incorrect × 1)
Space for Rough Work
