Units, Dimensions & Errors · JEE Main previous year questions

2023 15 questions

1. Q352023 · 13 Apr 2023 · Shift 2

   Given below are two statements: one is labelled as Assertion $\mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$ Assertion A : A spherical body of radius $(5\pm 0.1)\text{mm}$ having a particular density is falling through a liquid of constant density. The percentage error in the calculation of its terminal velocity is $4\%$. Reason R : The terminal velocity of the spherical body falling through the liquid is inversely proportional to its radius. In the light of the above statements, choose the correct answer from the options given below

   1. A.A is false but $\mathbf{R}$ is true
   2. B.A is true but $\mathbf{R}$ is false
   3. C.Both $\mathbf{A}$ and $\mathbf{R}$ are true but $\mathbf{R}$ is NOT the correct explanation of $\mathbf{A}$
   4. D.Both $\mathbf{A}$ and $\mathbf{R}$ are true and $\mathbf{R}$ is the correct explanation of $\mathbf{A}$
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   Answer: B

2. Q462023 · 11 Apr 2023 · Shift 2

   If force (F), velocity (V) and time (T) are considered as fundamental physical quantities, then dimensional formula of density will be :

   1. A.$\mathrm{F}{\mathrm{V}}^{-2}{\mathrm{T}}^2$
   2. B.$\mathrm{F}{\mathrm{V}}^4{\mathrm{T}}^{-6}$
   3. C.${\mathrm{F}}^2{\mathrm{V}}^{-2}{\mathrm{T}}^6$
   4. D.$\mathrm{F}{\mathrm{V}}^{-4}{\mathrm{T}}^{-2}$
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   Answer: D

3. Q322023 · 10 Apr 2023 · Shift 1

   A physical quantity P is given as $$P=\frac{a^2{b}^3}{c\sqrt{d}}$$ The percentage error in the measurement of a, b, c and d are 1%, 2%, 3% and 4% respectively. The percentage error in the measurement of quantity P will be

   1. A.12%
   2. B.13%
   3. C.16%
   4. D.14%
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   Answer: B

4. Q472023 · 10 Apr 2023 · Shift 2

   In an experiment with vernier callipers of least count $0.1\text{ mm}$, when two jaws are joined together the zero of vernier scale lies right to the zero of the main scale and 6th division of vernier scale coincides with the main scale division. While measuring the diameter of a spherical bob, the zero of vernier scale lies in between $3.2\text{ cm}$ and $3.3\text{ cm}$ marks, and 4th division of vernier scale coincides with the main scale division. The diameter of bob is measured as

   1. A.$3.18\text{ cm}$
   2. B.$3.22\text{ cm}$
   3. C.$3.26\text{ cm}$
   4. D.$3.25\text{ cm}$
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   Answer: A

5. Q352023 · 8 Apr 2023 · Shift 1

   Dimension of $\frac{1}{{\mu }_0{ϵ}_0}$ should be equal to

   1. A.${\mathrm{T}}^2/{\mathrm{L}}^2$
   2. B.$T/L$
   3. C.${\mathrm{L}}^2/{\mathrm{T}}^2$
   4. D.$L/T$
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   Answer: C

6. Q412023 · 8 Apr 2023 · Shift 1

   A cylindrical wire of mass $(0.4\pm 0.01)\text{g}$ has length $(8\pm 0.04)\text{cm}$ and radius $(6\pm 0.03)\text{mm}$. The maximum error in its density will be:

   1. A.$1\%$
   2. B.$5\%$
   3. C.$4\%$
   4. D.$3.5\%$
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   Answer: C

7. Q352023 · 6 Apr 2023 · Shift 2

   A $2\text{meter}$ long scale with least count of $0.2\mathrm{cm}$ is used to measure the locations of objects on an optical bench. While measuring the focal length of a convex lens, the object pin and the convex lens are placed at $80\mathrm{cm}$ mark and $1\mathrm{m}$ mark, respectively. The image of the object pin on the other side of lens coincides with image pin that is kept at $180\mathrm{cm}$ mark. The $\%$ error in the estimation of focal length is:

   1. A.$1.70$
   2. B.$0.51$
   3. C.$1.02$
   4. D.$0.85$
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   Answer: A

8. Q472023 · 1 Feb 2023 · Shift 1

   $(P+\frac{a}{V^2})(V-b)=RT$ represents the equation of state of some gases. Where $P$ is the pressure, $V$ is the volume, $T$ is the temperature and $a,b,R$ are the constants. The physical quantity, which has dimensional formula as that of $\frac{b^2}{a}$, will be:

   1. A.Energy density
   2. B.Bulk modulus
   3. C.Modulus of rigidity
   4. D.Compressibility
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   Answer: D

9. Q412023 · 31 Jan 2023 · Shift 1

   If $\mathrm{R},{\mathrm{X}}_L$, and ${\mathrm{X}}_C$ represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless :

   1. A.$\frac{\mathrm{R}}{{\mathrm{X}}_L{\mathrm{X}}_C}$
   2. B.$\mathrm{R}{\mathrm{X}}_L{\mathrm{X}}_C$
   3. C.$\frac{\mathrm{R}}{\sqrt{{\mathrm{X}}_L{\mathrm{X}}_C}}$
   4. D.$\mathrm{R}\frac{{\mathrm{X}}_L}{{\mathrm{X}}_C}$
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   Answer: C

10. Q492023 · 31 Jan 2023 · Shift 2

    Given below are two statements : Statement I : For transmitting a signal, size of antenna ( $l$ ) should be comparable to wavelength of signal (at least $l=\frac{\lambda }{4}$ in dimension) Statement II: In amplitude modulation, amplitude of carrier wave remains constant (unchanged). In the light of the above statements, choose the most appropriate answer from the options given below

    1. A.Statement I is incorrect but Statement II is correct
    2. B.Both Statement I and Statement II are correct
    3. C.Both Statement I and Statement II are incorrect
    4. D.Statement I is correct but Statement II is incorrect
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    Answer: D

11. Q582023 · 30 Jan 2023 · Shift 1· Numerical answer

    In a screw gauge, there are 100 divisions on the circular scale and the main scale moves by $0.5\text{ mm}$ on a complete rotation of the circular scale. The zero of circular scale lies 6 divisions below the line of graduation when two studs are brought in contact with each other. When a wire is placed between the studs, 4 linear scale divisions are clearly visible while $46^{\text{th}}$ division the circular scale coincide with the reference line. The diameter of the wire is _________ $\times 10^{-2}\text{ mm}$.

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    Answer: 220

12. Q332023 · 29 Jan 2023 · Shift 1

    In a cuboid of dimension $2\mathrm{L}\times 2\mathrm{L}\times \mathrm{L}$, a charge $q$ is placed at the center of the surface 'S' having area of $4{\mathrm{L}}^2$. The flux through the opposite surface to 'S' is given by

    1. A.$\frac{q}{2{ϵ}_0}$
    2. B.$\frac{q}{3{ϵ}_0}$
    3. C.$\frac{q}{12{ϵ}_0}$
    4. D.$\frac{q}{6{ϵ}_0}$
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    Answer: D

13. Q392023 · 29 Jan 2023 · Shift 1

    Match List I with List II : $$\begin{array}{llll}& \text{List I (Physical Quantity)}& & \text{List II (Dimensional Formula)}\\ \text{A.}& \text{Pressure gradient}& \text{I.}& [{\mathrm{M}}^0{\mathrm{L}}^2{\mathrm{T}}^{-2}]\\ \text{B.}& \text{Energy density}& \text{II.}& [{\mathrm{M}}^1{\mathrm{L}}^{-1}{\mathrm{T}}^{-2}]\\ \text{C.}& \text{Electric Field}& \text{III.}& [{\mathrm{M}}^1{\mathrm{L}}^{-2}{\mathrm{T}}^{-2}]\\ \text{D.}& \text{Latent heat}& \text{IV.}& [{\mathrm{M}}^1{\mathrm{L}}^1{\mathrm{T}}^{-3}{\mathrm{A}}^{-1}]\end{array}$$ Choose the correct answer from the options given below:

    1. A.A-III, B-II, C-IV, D-I
    2. B.A-III, B-II, C-I, D-IV
    3. C.A-II, B-III, C-IV, D-I
    4. D.A-II, B-III, C-I, D-IV
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    Answer: A

14. Q332023 · 29 Jan 2023 · Shift 2

    The equation of a circle is given by $x^2+y^2=a^2$, where a is the radius. If the equation is modified to change the origin other than (0, 0), then find out the correct dimensions of A and B in a new equation : $(x-At{)}^2+{\left(y-\frac{t}{B}\right)}^2=a^2$. The dimensions of t is given as $[{\mathrm{T}}^{-1}]$.

    1. A.$\mathrm{A}=[{\mathrm{L}}^{-1}{\mathrm{T}}^{-1}],\mathrm{B}=[\mathrm{L}{\mathrm{T}}^{-1}]$
    2. B.$\mathrm{A}=[{\mathrm{L}}^{-1}{\mathrm{T}}^{-1}],\mathrm{B}=[\mathrm{LT}]$
    3. C.$\mathrm{A}=[\mathrm{LT}],\mathrm{B}=[{\mathrm{L}}^{-1}{\mathrm{T}}^{-1}]$
    4. D.$\mathrm{A}=[{\mathrm{L}}^{-1}\mathrm{T}],\mathrm{B}=[\mathrm{L}{\mathrm{T}}^{-1}]$
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    Answer: C

15. Q522023 · 29 Jan 2023 · Shift 2· Numerical answer

    In an experiment of measuring the refractive index of a glass slab using travelling microscope in physics lab, a student measures real thickness of the glass slab as 5.25 mm and apparent thickness of the glass slab as 5.00 mm. Travelling microscope has 20 divisions in one cm on main scale and 50 divisions on vernier scale is equal to 49 divisions on main scale. The estimated uncertainty in the measurement of refractive index of the slab is $\frac{x}{10}\times 10^{-3}$, where $x$ is ____

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    Answer: 41