Units, Dimensions & Errors · JEE Main previous year questions

2019 12 questions

1. Q532019 · 12 Apr 2019 · Shift 1

   Which of the following combinations has the dimension of electrical resistance (${\in }_0$ is the permittivity of vacuum and ${\mu }_0$ is the permeability of vacuum)?

   1. A.$\sqrt{\frac{{\in }_0}{{\mu }_0}}$
   2. B.$\frac{{\in }_0}{{\mu }_0}$
   3. C.$\sqrt{\frac{{\mu }_0}{{\in }_0}}$
   4. D.$\frac{{\mu }_0}{{\in }_0}$
   Show answer

   Answer: C

2. Q312019 · 10 Apr 2019 · Shift 2

   In the formula $\mathrm{X}=5Y{\mathrm{Z}}^2$ , X and Z have dimensions of capacitance and magnetic field, respectively. What are the dimensions of Y in SI units?

   1. A.$[{\mathrm{M}}^{-3}{\mathrm{L}}^{-2}{\mathrm{T}}^8{\mathrm{A}}^4]$
   2. B.$[{\mathrm{M}}^{-2}{\mathrm{L}}^{-2}{\mathrm{T}}^6{\mathrm{A}}^3]$
   3. C.$[{\mathrm{M}}^{-1}{\mathrm{L}}^{-2}{\mathrm{T}}^4{\mathrm{A}}^2]$
   4. D.$[{\mathrm{M}}^{-2}{\mathrm{L}}^0{\mathrm{T}}^{-4}{\mathrm{A}}^{-2}]$
   Show answer

   Answer: A

3. Q312019 · 9 Apr 2019 · Shift 1

   In the density measurement of a cube, the mass and edge length are measured as $(10.00\pm 0.10)\mathrm{kg}$ and $(0.10\pm 0.01)\mathrm{m}$, respectively. The error in the measurement of density is :

   1. A.$0.01kg/{\mathrm{m}}^3$
   2. B.$0.10kg/{\mathrm{m}}^3$
   3. C.$0.31kg/{\mathrm{m}}^3$
   4. D.$0.07kg/{\mathrm{m}}^3$
   Show answer

   Answer: C

4. Q452019 · 9 Apr 2019 · Shift 2

   The area of a square is $5.29\mathrm{c}{\mathrm{m}}^2$. The area of 7 such squares taking into account the significant figures is :-

   1. A.$37.0\mathrm{c}{\mathrm{m}}^2$
   2. B.$37\mathrm{c}{\mathrm{m}}^2$
   3. C.$37.030\mathrm{c}{\mathrm{m}}^2$
   4. D.$37.03\mathrm{c}{\mathrm{m}}^2$
   Show answer

   Answer: A

5. Q452019 · 8 Apr 2019 · Shift 2

   In a simple pendulum experiment for determination of acceleration due to gravity (g), time taken for 20 oscillations is measured by using a watch of 1 second least count. The mean value of time taken comes out to be 30 s. The length of pendulum is measured by using a meter scale of least count 1 mm and the value obtained is 55.0 cm. The percentage error in the determination of g is close to :-

   1. A.0.2%
   2. B.3.5%
   3. C.0.7%
   4. D.6.8%
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   Answer: D

6. Q502019 · 8 Apr 2019 · Shift 2

   If surface tension (S), Moment of inertia (I) and Planck's constant (h), were to be taken as the fundamental units, the dimensional formula for linear momentum would be :-

   1. A.$S^{1/2}{I}^{1/2}{h}^0$
   2. B.$S^{3/2}{I}^{1/2}{h}^0$
   3. C.$S^{1/2}{I}^{1/2}{h}^{-1}$
   4. D.$S^{1/2}{I}^{3/2}{h}^{-1}$
   Show answer

   Answer: A

7. Q442019 · 12 Jan 2019 · Shift 1

   The least count of the main scale of a screw gauge is $1\mathrm{mm}$. The minimum number of divisions on its circular scale required to measure $5\mu \mathrm{m}$ diameter of a wire is :

   1. A.500
   2. B.100
   3. C.200
   4. D.50
   Show answer

   Answer: C

8. Q352019 · 12 Jan 2019 · Shift 2

   Let $\ell$, r, C and V represent inductance, resistance, capacitance and voltage, respectively. The dimension of $\frac{\ell }{rCV}$ in SI units will be :

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

   Answer: A

9. Q462019 · 12 Jan 2019 · Shift 2

   An alpha-particle of mass m suffers 1-dimensional elastic collision with a nucleus at rest of unknown mass. It is scattered directly backwards losing, 64% of its initial kinetic energy. The mass of the nucleus is

   1. A.2m
   2. B.4m
   3. C.1.5m
   4. D.3.5m
   Show answer

   Answer: B

10. Q342019 · 11 Jan 2019 · Shift 2

    Two rods A and B of identical dimensions are at temperature $30^{\circ }\mathrm{C}$. If A is heated upto $180^{\circ }\mathrm{C}$ and B upto $T^{\circ }\mathrm{C}$, then the new lengths are the same. If the ratio of the coefficients of linear expansion of A and B is $4:3$, then the value of T is

    1. A.$200^{\circ }\mathrm{C}$
    2. B.$270^{\circ }\mathrm{C}$
    3. C.$230^{\circ }\mathrm{C}$
    4. D.$250^{\circ }\mathrm{C}$
    Show answer

    Answer: C

11. Q492019 · 11 Jan 2019 · Shift 2

    If speed (V), acceleration (A) and force (F) are considered as fundamental units, the dimension of Young's modulus will be:

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

12. Q502019 · 11 Jan 2019 · Shift 2

    A copper wire is wound on a wooden frame, whose shape is that of an equilateral triangle. If the linear dimension of each side of the frame is increased by a factor of 3, keeping the number of turns of the coil per unit length of the frame the same, then the self inductance of the coil:

    1. A.decreases by a factor of $9\sqrt{3}$
    2. B.increases by a factor of 27
    3. C.decreases by a factor of 9
    4. D.increases by a factor of 3
    Show answer

    Answer: D