Units, Dimensions & Errors · JEE Main previous year questions

2024 25 questions

1. Q332024 · 9 Apr 2024 · Shift 1

   The dimensional formula of latent heat is :

   1. A.$[{\mathrm{M}}^0\mathrm{L}{\mathrm{T}}^{-2}]$
   2. B.$[\mathrm{ML}{\mathrm{T}}^{-2}]$
   3. C.$[{\mathrm{M}}^0{\mathrm{L}}^2{\mathrm{T}}^{-2}]$
   4. D.$[\mathrm{M}{\mathrm{L}}^2{\mathrm{T}}^{-2}]$
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   Answer: C

2. Q432024 · 9 Apr 2024 · Shift 1

   One main scale division of a vernier caliper is equal to $\mathrm{m}$ units. If ${\mathrm{n}}^{\text{th}}$ division of main scale coincides with $(n+1{)}^{\text{th}}$ division of vernier scale, the least count of the vernier caliper is :

   1. A.$\frac{1}{(n+1)}$
   2. B.$\frac{m}{(n+1)}$
   3. C.$\frac{n}{(n+1)}$
   4. D.$\frac{m}{n(n+1)}$
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   Answer: B

3. Q472024 · 9 Apr 2024 · Shift 2

   The de-Broglie wavelength associated with a particle of mass $m$ and energy $E$ is $h/\sqrt{2mE}$. The dimensional formula for Planck's constant is :

   1. A.$\left[{\mathrm{M}}^2{\mathrm{L}}^2{\mathrm{T}}^{-2}\right]$
   2. B.$\left[\mathrm{M}{\mathrm{L}}^{-1}{\mathrm{T}}^{-2}\right]$
   3. C.$\left[\mathrm{M}{\mathrm{L}}^2{\mathrm{T}}^{-1}\right]$
   4. D.$\left[{\mathrm{MLT}}^{-2}\right]$
   Show answer

   Answer: C

4. Q402024 · 8 Apr 2024 · Shift 1

   Young's modulus is determined by the equation given by $Y=49000\frac{m}{l}\frac{\text{dyne}}{{\text{cm}}^2}$ where $M$ is the mass and $l$ is the extension of wire used in the experiment. Now error in Young modules ($Y$) is estimated by taking data from $M-l$ plot in graph paper. The smallest scale divisions are $5\text{ g}$ and $0.02\text{ cm}$ along load axis and extension axis respectively. If the value of $M$ and $l$ are $500\text{ g}$ and $2\text{ cm}$ respectively then percentage error of $Y$ is :

   1. A.$2\%$
   2. B.$0.02\%$
   3. C.$0.5\%$
   4. D.$0.2\%$
   Show answer

   Answer: A

5. Q442024 · 8 Apr 2024 · Shift 1

   The diameter of a sphere is measured using a vernier caliper whose 9 divisions of main scale are equal to 10 divisions of vernier scale. The shortest division on the main scale is equal to $1\text{ mm}$. The main scale reading is $2\text{ cm}$ and second division of vernier scale coincides with a division on main scale. If mass of the sphere is $8.635\text{ g}$, the density of the sphere is:

   1. A.$2.2{\text{ g/cm}}^3$
   2. B.$2.0{\text{ g/cm}}^3$
   3. C.$1.7{\text{ g/cm}}^3$
   4. D.$2.5{\text{ g/cm}}^3$
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   Answer: B

6. Q562024 · 8 Apr 2024 · Shift 1· Numerical answer
   
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   Answer: 15

7. Q402024 · 8 Apr 2024 · Shift 2

   There are $100$ divisions on the circular scale of a screw gauge of pitch $1\mathrm{mm}$. With no measuring quantity in between the jaws, the zero of the circular scale lies $5$ divisions below the reference line. The diameter of a wire is then measured using this screw gauge. It is found that $4$ linear scale divisions are clearly visible while $60$ divisions on circular scale coincide with the reference line. The diameter of the wire is :

   1. A.$4.65\mathrm{mm}$
   2. B.$4.60\mathrm{mm}$
   3. C.$4.55\mathrm{mm}$
   4. D.$3.35\mathrm{mm}$
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   Answer: C

8. Q422024 · 8 Apr 2024 · Shift 2

   Least count of a vernier caliper is $\frac{1}{20N}\mathrm{cm}$. The value of one division on the main scale is $1\mathrm{mm}$. Then the number of divisions of main scale that coincide with $N$ divisions of vernier scale is :

   1. A.$\left(\frac{2N-1}{2N}\right)$
   2. B.$\left(\frac{2N-1}{20N}\right)$
   3. C.$(2N-1)$
   4. D.$\left(\frac{2N-1}{2}\right)$
   Show answer

   Answer: D

9. Q332024 · 6 Apr 2024 · Shift 2

   Given below are two statements: Statement (I) : Dimensions of specific heat is $[{\mathrm{L}}^2{\mathrm{T}}^{-2}{\mathrm{K}}^{-1}]$. Statement (II) : Dimensions of gas constant is $[{\mathrm{ML}}^2{\mathrm{T}}^{-1}{\mathrm{K}}^{-1}]$. 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 incorrect
   3. C.Both statement (I) and statement (II) are correct
   4. D.Statement (I) is correct but statement (II) is incorrect
   Show answer

   Answer: D

10. Q372024 · 6 Apr 2024 · Shift 2

    In a vernier calliper, when both jaws touch each other, zero of the vernier scale shifts towards left and its $4^{\mathrm{th}}$ division coincides exactly with a certain division on main scale. If $50$ vernier scale divisions equal to $49$ main scale divisions and zero error in the instrument is $0.04\mathrm{mm}$ then how many main scale divisions are there in $1\mathrm{cm}$ ?

    1. A.5
    2. B.40
    3. C.10
    4. D.20
    Show answer

    Answer: D

11. Q492024 · 6 Apr 2024 · Shift 2

    In finding out refractive index of glass slab the following observations were made through travelling microscope $50\text{ vernier scale division}=49\mathrm{MSD}$; $20\text{ divisions on main scale in each }\mathrm{cm}$ For mark on paper $\mathrm{MSR}=8.45\mathrm{cm},\mathrm{VC}=26$ For mark on paper seen through slab $\mathrm{MSR}=7.12\mathrm{cm},\mathrm{VC}=41$ For powder particle on the top surface of the glass slab $\mathrm{MSR}=4.05\mathrm{cm},\mathrm{VC}=1$ ($\mathrm{MSR}=$ Main Scale Reading, $\mathrm{VC}=$ Vernier Coincidence) Refractive index of the glass slab is :

    1. A.1.52
    2. B.1.35
    3. C.1.24
    4. D.1.42
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    Answer: D

12. Q322024 · 5 Apr 2024 · Shift 2

    What is the dimensional formula of $a{b}^{-1}$ in the equation $(\mathrm{P}+\frac{\mathrm{a}}{{\mathrm{V}}^2})(\mathrm{V}-\mathrm{b})=\mathrm{RT}$, where letters have their usual meaning.

    1. A.$[{\mathrm{M}}^0{\mathrm{L}}^7{\mathrm{T}}^4]$
    2. B.$[{\mathrm{M}}^{-1}{\mathrm{L}}^5{\mathrm{T}}^3]$
    3. C.$[{\mathrm{M}}^0{\mathrm{L}}^3{\mathrm{T}}^{-2}]$
    4. D.$[{\mathrm{ML}}^2{\mathrm{T}}^{-2}]$
    Show answer

    Answer: D

13. Q432024 · 5 Apr 2024 · Shift 2

    A vernier callipers has 20 divisions on the vernier scale, which coincides with $19^{\text{th}}$ division on the main scale. The least count of the instrument is $0.1\mathrm{mm}$. One main scale division is equal to ____ $\mathrm{mm}$.

    1. A.5
    2. B.2
    3. C.1
    4. D.0.5
    Show answer

    Answer: B

14. Q402024 · 4 Apr 2024 · Shift 1

    In an experiment to measure focal length ($f$) of convex lens, the least counts of the measuring scales for the position of object (u) and for the position of image (v) are $\Delta u$ and $\Delta v$, respectively. The error in the measurement of the focal length of the convex lens will be:

    1. A.$2f\left[\frac{\Delta u}{u}+\frac{\Delta v}{v}\right]$
    2. B.$f\left[\frac{\Delta u}{u}+\frac{\Delta v}{v}\right]$
    3. C.$f^2\left[\frac{\Delta u}{u^2}+\frac{\Delta v}{v^2}\right]$
    4. D.$\frac{\Delta u}{u}+\frac{\Delta v}{v}$
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    Answer: C

15. Q312024 · 4 Apr 2024 · Shift 2

    Applying the principle of homogeneity of dimensions, determine which one is correct, where $T$ is time period, $G$ is gravitational constant, $M$ is mass, $r$ is radius of orbit.

    1. A.$T^2=\frac{4{\pi }^{2}r}{G{M}^2}$
    2. B.$T^2=4{\pi }^2{r}^3$
    3. C.$T^2=\frac{4{\pi }^2{r}^3}{GM}$
    4. D.$T^2=\frac{4{\pi }^2{r}^2}{GM}$
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    Answer: C

16. Q332024 · 1 Feb 2024 · Shift 1

    10 divisions on the main scale of a Vernier calliper coincide with 11 divisions on the Vernier scale. If each division on the main scale is of 5 units, the least count of the instrument is :

    1. A.$\frac{5}{11}$
    2. B.$\frac{10}{11}$
    3. C.$\frac{50}{11}$
    4. D.$\frac{1}{2}$
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    Answer: A

17. Q352024 · 1 Feb 2024 · Shift 1

    The dimensional formula of angular impulse is :

    1. A.$\left[\mathrm{M}{\mathrm{L}}^2{\mathrm{T}}^{-2}\right]$
    2. B.$\left[\mathrm{M}{\mathrm{L}}^{-2}{\mathrm{T}}^{-1}\right]$
    3. C.$\left[\mathrm{M}{\mathrm{L}}^2{\mathrm{T}}^{-1}\right]$
    4. D.$\left[\mathrm{ML}{\mathrm{T}}^{-1}\right]$
    Show answer

    Answer: C

18. Q542024 · 1 Feb 2024 · Shift 1· Numerical answer

    A particle is moving in one dimension (along $x$ axis) under the action of a variable force. Its initial position was $16\mathrm{m}$ right of origin. The variation of its position $(x)$ with time $(t)$ is given as $x=-3t^3+18t^2+16t$, where $x$ is in $\mathrm{m}$ and t is in $\mathrm{s}$. The velocity of the particle when its acceleration becomes zero is ____ $m/s$.

    Show answer

    Answer: 52

19. Q362024 · 1 Feb 2024 · Shift 2

    Match List - I with List - II. | List I (Number) | List II (Significant figure) | | :--- | :--- | | (A) 1001 | (I) 3 | | (B) 010.1 | (II) 4 | | (C) 100.100 | (III) 5 | | (D) 0.0010010 | (IV) 6 | Choose the correct answer from the options given below :

    1. A.(A)-(II), (B)-(I), (C)-(IV), (D)-(III)
    2. B.(A)-(IV), (B)-(III), (C)-(I), (D)-(II)
    3. C.(A)-(I), (B)-(II), (C)-(III), (D)-(IV)
    4. D.(A)-(III), (B)-(IV), (C)-(II), (D)-(I)
    Show answer

    Answer: A

20. Q482024 · 31 Jan 2024 · Shift 1

    A force is represented by $F=a{x}^2+b{t}^{\frac{1}{2}}$ where $x=$ distance and $t=$ time. The dimensions of $b^2/a$ are:

    1. A.$\left[\mathrm{M}{\mathrm{L}}^2{\mathrm{T}}^{-3}\right]$
    2. B.$\left[\mathrm{M}{\mathrm{L}}^3{\mathrm{T}}^{-3}\right]$
    3. C.$\left[ML{T}^{-2}\right]$
    4. D.$\left[M{L}^{-1}{T}^{-1}\right]$
    Show answer

    Answer: B

21. Q322024 · 31 Jan 2024 · Shift 2

    Consider two physical quantities $A$ and $B$ related to each other as $E=\frac{B-x^2}{At}$ where $E,x$ and $t$ have dimensions of energy, length and time respectively. The dimension of $AB$ is

    1. A.$L^{-2}{M}^1{T}^0$
    2. B.$L^2{M}^{-1}{T}^1$
    3. C.$L^0{M}^{-1}{T}^1$
    4. D.$L^{-2}{M}^{-1}{T}^1$
    Show answer

    Answer: B

22. Q332024 · 29 Jan 2024 · Shift 2

    A physical quantity $Q$ is found to depend on quantities $a,b,c$ by the relation $Q=\frac{a^4{b}^3}{c^2}$. The percentage error in $a,b$ and $c$ are $3\%,4\%$ and $5\%$ respectively. Then, the percentage error in $Q$ is :

    1. A.$43\%$
    2. B.$34\%$
    3. C.$66\%$
    4. D.$14\%$
    Show answer

    Answer: B

23. Q472024 · 27 Jan 2024 · Shift 1

    Given below are two statements : Statement (I) : Planck's constant and angular momentum have same dimensions. Statement (II) : Linear momentum and moment of force have same dimensions. In the light of the above statements, choose the correct answer from the options given below :

    1. A.Statement I is true but Statement II is false
    2. B.Both Statement I and Statement II are false
    3. C.Both Statement I and Statement II are true
    4. D.Statement I is false but Statement II is true
    Show answer

    Answer: A

24. Q312024 · 27 Jan 2024 · Shift 2

    Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : In Vernier calliper if positive zero error exists, then while taking measurements, the reading taken will be more than the actual reading. Reason (R) : The zero error in Vernier Calliper might have happened due to manufacturing defect or due to rough handling. In the light of the above statements, choose the correct answer from the options given below :

    1. A.Both (A) and (R) are correct and (R) is the correct explanation of (A)
    2. B.Both (A) and (R) are correct but (R) is not the correct explanation of (A)
    3. C.(A) is true but (R) is false
    4. D.(A) is false but (R) is true
    Show answer

    Answer: B

25. Q432024 · 27 Jan 2024 · Shift 2

    The equation of state of a real gas is given by $(\text{P}+\frac{\text{a}}{{\text{V}}^2})(\text{V}-\text{b})=\text{RT}$, where P, V and T are pressure, volume and temperature respectively and R is the universal gas constant. The dimensions of $\frac{\text{a}}{{\text{b}}^2}$ is similar to that of :

    1. A.$\text{P}$
    2. B.$\text{RT}$
    3. C.$\text{PV}$
    4. D.$\text{R}$
    Show answer

    Answer: A