Units, Dimensions & Errors · JEE Main previous year questions

2026 19 questions

1. Q262026 · 6 Apr 2026 · Shift 1

   The density $\rho$ of a uniform cylinder is determined by measuring its mass $m$, length $l$ and diameter $d$. The measured values of $m$, $l$ and $d$ are $97.42\pm 0.02\mathrm{g}$, $8.35\pm 0.05\mathrm{mm}$ and $20.20\pm 0.02\mathrm{mm}$, respectively. Calculated percentage fractional error in $\rho$ is ____.

   1. A.0.63%
   2. B.0.82%
   3. C.0.72%
   4. D.0.25%
   Show answer

   Answer: B

2. Q272026 · 6 Apr 2026 · Shift 1

   The potential energy of a particle changes with distance $x$ from a fixed origin as $V=\frac{A\sqrt{x}}{x+B}$, where $A$ and $B$ are constant with appropriate dimensions. The dimensions of $AB$ are ____.

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

   Answer: D

3. Q262026 · 6 Apr 2026 · Shift 2

   The percentage error in the calculated volume of a sphere, if there is $2\%$ error in its diameter measurement, is ____ .

   1. A.$1$
   2. B.$2$
   3. C.$6$
   4. D.$8$
   Show answer

   Answer: C

4. Q262026 · 5 Apr 2026 · Shift 1

   In a Vernier calipers, when both jaws touch each other, zero of the Vernier scale is shifted to the right of zero of the main scale and $7^{\mathrm{th}}$ Vernier division coincides with a main scale reading. If the value of 1 main scale division is $1\mathrm{mm}$ and there are 10 Vernier scale divisions, then the Vernier caliper has

   1. A.0.07 cm negative zero error
   2. B.0.7 cm negative zero error
   3. C.0.07 cm positive zero error
   4. D.0.7 cm positive zero error
   Show answer

   Answer: C

5. Q272026 · 5 Apr 2026 · Shift 1

   $L$, $C$ and $R$ represents physical quantities inductance, capacitance and resistance respectively. The dimensional formula $\mathrm{M}{\mathrm{L}}^2{\mathrm{T}}^{-4}{\mathrm{A}}^{-2}$ corresponds to ____.

   1. A.$\frac{R}{\sqrt{LC}}$
   2. B.$\frac{R}{LC}$
   3. C.$\frac{C}{\sqrt{LR}}$
   4. D.$\frac{1}{R}\sqrt{\frac{L}{C}}$
   Show answer

   Answer: A

6. Q262026 · 4 Apr 2026 · Shift 1

   In a screw gauge when the circular scale is given five complete rotations it moves linearly by $2.5\text{ mm}$. If the circular scale has 100 divisions, the least count of screw gauge is _________ $\text{mm}$.

   1. A.$1\times 10^{-2}$
   2. B.$1\times 10^{-3}$
   3. C.$5\times 10^{-2}$
   4. D.$5\times 10^{-3}$
   Show answer

   Answer: D

7. Q262026 · 2 Apr 2026 · Shift 1

   The dimensional formula of $\frac{1}{2}{ϵ}_0{\mathrm{E}}^2$ (${ϵ}_0=$ permittivity of vacuum and $\mathrm{E}=$ electric field) is ${\mathrm{M}}^{\mathrm{a}}{\mathrm{L}}^{\mathrm{b}}{\mathrm{T}}^{\mathrm{c}}$. The value of $2\mathrm{a}-\mathrm{b}+\mathrm{c}=$ ____.

   1. A.0
   2. B.1
   3. C.-1
   4. D.2
   Show answer

   Answer: B

8. Q272026 · 2 Apr 2026 · Shift 1

   The diameter of a wire measured by a screw gauge of least count $0.001\mathrm{cm}$ is $0.08\mathrm{cm}$. The length measured by a scale of least count $0.1\mathrm{cm}$ is $150\mathrm{cm}$. When a weight of $100\mathrm{N}$ is applied to the wire, the extension in length is $0.5\mathrm{cm}$, measured by a micrometer of least count $0.001\mathrm{cm}$. The error in the measured Young's modulus is $\alpha \times 10^{9}N/{\mathrm{m}}^2$. The value of $\alpha$ is ____. (Ignore the contribution of the load to Young's modulus error calculation)

   1. A.1.3
   2. B.1.65
   3. C.0.13
   4. D.0.25
   Show answer

   Answer: B

9. Q262026 · 2 Apr 2026 · Shift 2

   Dimensions of universal gravitational constant (G) in terms of Planck's constant ($h$), distance ($L$), mass ($M$) and time ($T$) are ____.

   1. A.$[\mathrm{hTL}{\mathrm{M}}^{-2}]$
   2. B.$[\mathrm{h}{\mathrm{T}}^{-1}\mathrm{L}{\mathrm{M}}^{-2}]$
   3. C.$[\mathrm{hT}{\mathrm{L}}^2{\mathrm{M}}^{-2}]$
   4. D.$[{\mathrm{h}}^{-1}{\mathrm{T}}^{-1}\mathrm{L}{\mathrm{M}}^{-2}]$
   Show answer

   Answer: B

10. Q322026 · 2 Apr 2026 · Shift 2

    In a screw gauge the zero of main scale reference line coincides with the fifth division of the circular scale when two studs are in contact. There are 100 divisions in circular scale and pitch of screw gauge is $0.1\mathrm{mm}$. When diameter of a sphere is measured, the reading of main scale is $5\mathrm{mm}$ and $50^{\mathrm{th}}$ division of circular scale coincides with the reference line of main scale. The diameter of sphere is ____ $\mathrm{mm}$.

    1. A.5.045
    2. B.5.055
    3. C.5.450
    4. D.5.550
    Show answer

    Answer: A

11. Q332026 · 28 Jan 2026 · Shift 1

    When both jaws of vernier callipers touch each other, zero mark of the vernier scale is right to zero mark of main scale, $4^{\text{th}}$ mark on vernier scale coincides with certain mark on the main scale. While measuring the length of a cylinder, observer observes $15$ divisions on main scale and $5^{\text{th}}$ division of vernier scale coincides with a main scale division. Measured length of cylinder is ____ $\mathrm{mm}$. (Least count of Vernier calliper = $0.1\mathrm{mm}$ )

    1. A.15.5
    2. B.15.4
    3. C.15.9
    4. D.15.1
    Show answer

    Answer: D

12. Q432026 · 28 Jan 2026 · Shift 2

    In an experiment, a set of readings are obtained as follows: 1.24 mm, 1.25 mm, 1.23 mm, 1.21 mm. The expected least count of the instrument used in recording these readings is _______ mm.

    1. A.0.01
    2. B.0.05
    3. C.0.001
    4. D.0.1
    Show answer

    Answer: A

13. Q432026 · 23 Jan 2026 · Shift 1

    In a screw gauge, the zero of the circular scale lies 3 divisions above the horizontal pitch line when their metallic studs are brought in contact. Using this instrument thickness of a sheet is measured. If pitch scale reading is 1 mm and the circular scale reading is 51 then the correct thickness of the sheet is ____ mm. [Assume least count is 0.01 mm ]

    1. A.1.54
    2. B.1.50
    3. C.1.51
    4. D.1.48
    Show answer

    Answer: A

14. Q452026 · 23 Jan 2026 · Shift 1

    Four persons measure the length of a rod as 20.00 cm, 19.75 cm, 17.01 cm and 18.25 cm . The relative error in the measurement of average length of the rod is :

    1. A.0.18
    2. B.0.24
    3. C.0.06
    4. D.0.08
    Show answer

    Answer: C

15. Q382026 · 23 Jan 2026 · Shift 2

    To compare EMF of two cells using potentiometer the balancing lengths obtained are 200 cm and 150 cm . The least count of scale is 1 cm . The percentage error in the ratio of EMFs is _____

    1. A.1.75
    2. B.1.55
    3. C.1.17
    4. D.1.65
    Show answer

    Answer: C

16. Q312026 · 22 Jan 2026 · Shift 1
    
    1. A.$60^{\circ }\mathrm{C}$ and $45^{\circ }\mathrm{C}$ respectively
    2. B.$80^{\circ }\mathrm{C}$ and $70^{\circ }\mathrm{C}$ respectively
    3. C.$89^{\circ }\mathrm{C}$ and $73^{\circ }\mathrm{C}$ respectively
    4. D.$80^{\circ }\mathrm{C}$ and $60^{\circ }\mathrm{C}$ respectively
    Show answer

    Answer: C

17. Q282026 · 21 Jan 2026 · Shift 1

    In an experiment the values of two spring constants were measured as $k_1=(10\pm 0.2)N/m$ and $k_2=(20\pm 0.3)N/m$. If these springs are connected in parallel, then the percentage error in equivalent spring constant is :

    1. A.$1.33\%$
    2. B.$2.67\%$
    3. C.$1.67\%$
    4. D.$2.33\%$
    Show answer

    Answer: C

18. Q292026 · 21 Jan 2026 · Shift 1

    Consider a modified Bernoulli equation. $$\left(\mathrm{P}+\frac{A}{B{t}^2}\right)+\rho g(h+Bt)+\frac{1}{2}\rho V^2=\text{constant}$$ If $t$ has the dimension of time then the dimensions of $A$ and $B$ are ____ , ____ respectively.

    1. A.$\left[{\mathrm{ML}}^0{\mathrm{T}}^{-1}\right]$ and $\left[{\mathrm{M}}^0\mathrm{LT}\right]$
    2. B.$\left[{\mathrm{ML}}^0{\mathrm{T}}^{-2}\right]$ and $\left[{\mathrm{M}}^0{\mathrm{LT}}^{-1}\right]$
    3. C.$\left[{\mathrm{ML}}^0{\mathrm{T}}^{-2}\right]$ and $\left[{\mathrm{M}}^0{\mathrm{LT}}^{-2}\right]$
    4. D.$\left[{\mathrm{ML}}^0{\mathrm{T}}^{-1}\right]$ and $\left[{\mathrm{M}}^0{\mathrm{LT}}^{-1}\right]$
    Show answer

    Answer: D

19. Q272026 · 21 Jan 2026 · Shift 2

    Keeping the significant figures in view, the sum of the physical quantities 52.01 m, 153.2 m and 0.123 m is :

    1. A.205.3 m
    2. B.205 m
    3. C.205.333 m
    4. D.205.33 m
    Show answer

    Answer: A