Units, Dimensions & Errors · JEE Advanced previous year questions

2024 4 questions

1. Q182024 · 26 May 2024 · Paper 1

   A dimensionless quantity is constructed in terms of electronic charge $e$, permittivity of free space ${\epsilon }_0$, Planck's constant $h$, and speed of light $c$. If the dimensionless quantity is written as $e^{\alpha }{\epsilon }_0^{\beta }{h}^{\gamma }{c}^{\delta }$ and $n$ is a non-zero integer, then $(\alpha ,\beta ,\gamma ,\delta )$ is given by

   1. A.$(2n,-n,-n,-n)$
   2. B.$(n,-n,-2n,-n)$
   3. C.$(n,-n,-n,-2n)$
   4. D.$(2n,-n,-2n,-2n)$
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   Answer: A

2. Q252024 · 26 May 2024 · Paper 1· Numerical answer

   The specific heat capacity of a substance is temperature dependent and is given by the formula $C=kT$, where $k$ is a constant of suitable dimensions in SI units, and $T$ is the absolute temperature. If the heat required to raise the temperature of $1\text{ kg}$ of the substance from $-73{}^{\circ }\mathrm{C}$ to $27{}^{\circ }\mathrm{C}$ is $nk$, the value of $n$ is _____. [Given: $0\text{ K}=-273{}^{\circ }\mathrm{C}$.]

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   Answer: 25000

3. Q192024 · 26 May 2024 · Paper 2

   A particle of mass $m$ is under the influence of the gravitational field of a body of mass $M(\gg m)$. The particle is moving in a circular orbit of radius $r_0$ with time period $T_0$ around the mass $M$. Then, the particle is subjected to an additional central force, corresponding to the potential energy $V_c(r)=m\alpha /r^3$, where $\alpha$ is a positive constant of suitable dimensions and $r$ is the distance from the center of the orbit. If the particle moves in the same circular orbit of radius $r_0$ in the combined gravitational potential due to $M$ and $V_c(r)$, but with a new time period $T_1$, then $(T_1^2-T_0^2)/T_1^2$ is given by [$G$ is the gravitational constant.]

   1. A.$\frac{3\alpha }{GM{r}_0^2}$
   2. B.$\frac{\alpha }{2GM{r}_0^2}$
   3. C.$\frac{\alpha }{GM{r}_0^2}$
   4. D.$\frac{2\alpha }{GM{r}_0^2}$
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   Answer: A

4. Q252024 · 26 May 2024 · Paper 2· Numerical answer

   The dimensions of a cone are measured using a scale with a least count of 2 mm. The diameter of the base and the height are both measured to be 20.0 cm. The maximum percentage error in the determination of the volume is ____.

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   Answer: 3