1
JEE Advanced 2023 Paper 2 Online
+3
-1
Young's modulus of elasticity $Y$ is expressed in terms of three derived quantities, namely, the gravitational constant $G$, Planck's constant $h$ and the speed of light $c$, as $Y=c^\alpha h^\beta G^\gamma$. Which of the following is the correct option?
A
$\alpha=7, \beta=-1, \gamma=-2$
B
$\alpha=-7, \beta=-1, \gamma=-2$
C
$\alpha=7, \beta=-1, \gamma=2$
D
$\alpha=-7, \beta=1, \gamma=-2$
2
JEE Advanced 2022 Paper 2 Online
+3
-1 Area of the cross-section of a wire is measured using a screw gauge. The pitch of the main scale is $0.5 \mathrm{~mm}$. The circular scale has 100 divisions and for one full rotation of the circular scale, the main scale shifts by two divisions. The measured readings are listed below.

Two arms of gauge touching
each other without wire
0 division 4 divisions
Attempt-1: With wire 4 divisions 20 divisions
Attempt-2: With wire 4 divisions 16 divisions

What are the diameter and cross-sectional area of the wire measured using the screw gauge?

A
$2.22 \pm 0.02 \mathrm{~mm}, \pi(1.23 \pm 0.02) \mathrm{mm}^{2}$
B
$2.22 \pm 0.01 \mathrm{~mm}, \pi(1.23 \pm 0.01) \mathrm{mm}^{2}$
C
$2.14 \pm 0.02 \mathrm{~mm}$, $\pi(1.14 \pm 0.02) \mathrm{mm}^{2}$
D
$2.14 \pm 0.01 \mathrm{~mm}, \pi(1.14 \pm 0.01) \mathrm{mm}^{2}$
3
JEE Advanced 2021 Paper 1 Online
+3
-1 The smallest division on the main scale of a Vernier calipers is 0.1 cm. Ten divisions of the Vernier scale correspond to nine divisions of the main scale. The figure below on the left shows the reading of this calipers with no gap between its two jaws. The figure on the right shows the reading with a solid sphere held between the jaws. The correct diameter of the sphere is A
3.07 cm
B
3.11 cm
C
3.15 cm
D
3.17 cm
4
JEE Advanced 2018 Paper 1 Offline
+3
-1
In electromagnetic theory, the electric and magnetic phenomena are related to each other. Therefore, the dimensions of electric and magnetic quantities must also be related to each other. In the questions below, $$[E]$$ and $$[B]$$ stand for dimensions of electric and magnetic fields respectively, while $$\left[ {{\varepsilon _0}} \right]$$ and $$\left[ {{\mu _0}} \right]$$ stand for dimensions of the permittivity and permeability of free space respectively. $$\left[ L \right]$$ and $$\left[ T \right]$$ are dimensions of length and time respectively. All the quantities are given in $$SI$$ units.

The relation between $$\left[ {{\varepsilon _0}} \right]$$ and $$\left[ {{\mu _0}} \right]$$ is
A
$$\left[ {{\mu _0}} \right] = \left[ {{\varepsilon _0}} \right]{\left[ L \right]^2}{\left[ T \right]^{ - 2}}$$
B
$$\left[ {{\mu _0}} \right] = \left[ {{\varepsilon _0}} \right]{\left[ L \right]^{ - 2}}{\left[ T \right]^2}$$
C
$$\left[ {{\mu _0}} \right] = {\left[ {{\varepsilon _0}} \right]^{ - 1}}{\left[ L \right]^2}{\left[ T \right]^{ - 2}}$$
D
$$\left[ {{\mu _0}} \right] = {\left[ {{\varepsilon _0}} \right]^{ - 1}}{\left[ L \right]^{ - 2}}{\left[ T \right]^2}$$
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