Units, Dimensions & Errors · JEE Advanced previous year questions

2025 4 questions

1. Q202025 · 18 May 2025 · Paper 1
   
   1. A.0.12 cm
   2. B.0.11 cm
   3. C.0.13 cm
   4. D.0.14 cm
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   Answer: C

2. Q222025 · 18 May 2025 · Paper 1· One or more correct

   Length, breadth and thickness of a strip having a uniform cross section are measured to be 10.5 cm, 0.05 mm, and 6.0 $\mu$m, respectively. Which of the following option(s) give(s) the volume of the strip in $\mathrm{c}{\mathrm{m}}^3$ with correct significant figures:

   1. A.$3.2\times 10^{-5}$
   2. B.$32.0\times 10^{-6}$
   3. C.$3.0\times 10^{-5}$
   4. D.$3\times 10^{-5}$
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   Answer: D

3. Q232025 · 18 May 2025 · Paper 1· One or more correct

   Consider a system of three connected strings, $S_1$, $S_2$ and $S_3$ with uniform linear mass densities $\mu$ kg/m, $4\mu$ kg/m and $16\mu$ kg/m, respectively, as shown in the figure. $S_1$ and $S_2$ are connected at the point $P$, whereas $S_2$ and $S_3$ are connected at the point $Q$, and the other end of $S_3$ is connected to a wall. A wave generator O is connected to the free end of $S_1$. The wave from the generator is represented by $y=y_0\cos (\omega t-kx)$ cm, where $y_0$, $\omega$ and $k$ are constants of appropriate dimensions. Which of the following statements is/are correct:

   1. A.When the wave reflects from $P$ for the first time, the reflected wave is represented by $y={\alpha }_1{y}_0\cos (\omega t+kx+\pi )$ cm, where ${\alpha }_1$ is a positive constant.
   2. B.When the wave transmits through $P$ for the first time, the transmitted wave is represented by $y={\alpha }_2{y}_0\cos (\omega t-kx)$ cm, where ${\alpha }_2$ is a positive constant.
   3. C.When the wave reflects from $Q$ for the first time, the reflected wave is represented by $y={\alpha }_3{y}_0\cos (\omega t-kx+\pi )$ cm, where ${\alpha }_3$ is a positive constant.
   4. D.When the wave transmits through $Q$ for the first time, the transmitted wave is represented by $y={\alpha }_4{y}_0\cos (\omega t-4kx)$ cm, where ${\alpha }_4$ is a positive constant.
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   Answer: A, D

4. Q172025 · 18 May 2025 · Paper 2

   A temperature difference can generate e.m.f. in some materials. Let $S$ be the e.m.f. produced per unit temperature difference between the ends of a wire, $\sigma$ the electrical conductivity and $\kappa$ the thermal conductivity of the material of the wire. Taking $M,L,T,I$ and $K$ as dimensions of mass, length, time, current and temperature, respectively, the dimensional formula of the quantity $Z=\frac{S^2\sigma }{\kappa }$ is:

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