Question 1: Palette 1/41

JEE Advanced 2025 MCQ

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, σ the electrical conductivity and κ 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 :

A

[M⁰L⁰T⁰I⁰K⁰]

B

[M⁰L⁰T⁰I⁰K⁻¹]

C

[M¹L²T⁻²I⁻¹K⁻¹]

D

[M¹L²T⁻⁴I⁻¹K⁻¹]

Question 2: Palette 2/41

JEE Advanced 2025 MCQ

Figure 1 shows the configuration of main scale and Vernier scale before measurement. Fig. 2 shows the configuration corresponding to the measurement of diameter D of a tube. The measured value of D is:

A

0.12 cm

B

0.11 cm

C

0.13 cm

D

0.14 cm

Question 3: Palette 3/41

JEE Advanced 2025 MCQ

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 μm, respectively. Which of the following option(s) give(s) the volume of the strip in cm³ with correct significant figures:

A

$3.2 \times 10^{-5}$

B

$32.0 \times 10^{-6}$

C

$3.0 \times 10^{-5}$

D

$3 \times 10^{-5}$

Question 4: Palette 4/41

JEE Advanced 2024 MCQ

A dimensionless quantity is constructed in terms of electronic charge $e$, permittivity of free space $\varepsilon_0$, Planck's constant $h$, and speed of light $c$. If the dimensionless quantity is written as $e^\alpha \varepsilon_0{ }^\beta h^\gamma c^\delta$ and $n$ is a non-zero integer, then $(\alpha, \beta, \gamma, \delta)$ is given by :

A

$(2 n,-n,-n,-n)$

B

$(n,-n,-2 n,-n)$

C

$(n,-n,-n,-2 n)$

D

$(2 n,-n,-2 n,-2 n)$

Question 5: Palette 5/41

JEE Advanced 2023 MCQ

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

$\alpha=-7, \beta=1, \gamma=-2$

Question 6: Palette 6/41

JEE Advanced 2022 MCQ

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.

Measurement condition	Main scale reading	Circular scale reading
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

$2.14 \pm 0.01 \mathrm{~mm}, \pi(1.14 \pm 0.01) \mathrm{mm}^{2}$

Question 7: Palette 7/41

JEE Advanced 2021 MCQ

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

Question 8: Palette 8/41

JEE Advanced 2021 MSQ

A physical quantity $\overrightarrow S $ is defined as $\overrightarrow S = (\overrightarrow E \times \overrightarrow B )/{\mu _0}$, where $\overrightarrow E $ is electric field, $\overrightarrow B $ is magnetic field and $\mu$₀ is the permeability of free space. The dimensions of $\overrightarrow S $ are the same as the dimensions of which of the following quantity(ies)?

A

${{Energy} \over {Ch\arg e \times Current}}$

B

${{Force} \over {Length \times Time}}$

C

${{Energy} \over {Volume}}$

D

${{Power} \over {Area}}$

Question 9: Palette 9/41

JEE Advanced 2020 MSQ

Sometimes it is convenient to construct a system of units so that all quantities can be expressed in terms of only one physical quantity. In one such system, dimensions of different quantities are given in terms of a quantity X as follows: [position] = [X^{$\alpha $}]; [speed] = [X^{$\beta $} ]; [acceleration] = [X^p]; [linear momentum] = [X^q]; [force] = [X^r]. Then

A

$\alpha $ + p = 2$\beta $

B

p + q - r = $\beta $

C

p - q + r = $\alpha $

D

p + q + r = $\beta $

Question 10: Palette 10/41

JEE Advanced 2019 MSQ

Let us consider a system of units in which mass and angular momentum are dimensionless. If length has dimension of L, which of the following statement(s) is/are correct?

A

The dimension of force is [L]^-3

B

The dimension of power is [L]^-5

C

The dimension of energy is [L]^-2

D

The dimension of linear momentum is [L]^-1

Question 11: Palette 11/41

JEE Advanced 2018 MCQ

If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any dependent quantity. This is done by the use of series expansion and truncating the expansion at the first power of the error. For example, consider the relation $z = x/y.$ If the errors in $x,y$ and $z$ are $\Delta x,\Delta y$ and $\Delta z,$ respectively, then
$$z \pm \Delta z = {{x \pm \Delta x} \over {y \pm \Delta y}} = {x \over y}\left( {1 \pm {{\Delta x} \over x}} \right){\left( {1 \pm {{\Delta y} \over y}} \right)^{ - 1}}.$$

The series expansion for ${\left( {1 \pm {{\Delta y} \over y}} \right)^{ - 1}},$ to first power in $\Delta y/y.$ is $1 \pm \left( {\Delta y/y} \right).$ The relative errors in independent variables are always added. So the error in $z$ will be
$$\Delta z = z\left( {{{\Delta x} \over x} + {{\Delta y} \over y}} \right).$$

The above derivation makes the assumption that $\Delta x/x < < 1,$ $\Delta y/y < < 1.$ Therefore, the higher powers of these quantities are neglected.

Consider the ratio $r = {{\left( {1 - a} \right)} \over {1 + a}}$ to be determined by measuring a dimensionless quantity $a.$ If the error in the measurement of $a$ is $\Delta a\left( {\Delta a/a < < 1.} \right.$ then what is the error $\Delta r$ in determining $r$?

A

${{\Delta a} \over {{{\left( {1 + a} \right)}^2}}}$

B

${{2\Delta a} \over {{{\left( {1 + a} \right)}^2}}}$

C

${{2\Delta a} \over {\left( {1 - {a^2}} \right)}}$

D

${{2a\Delta a} \over {\left( {1 - {a^2}} \right)}}$

Question 12: Palette 12/41

JEE Advanced 2018 MCQ

If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any dependent quantity. This is done by the use of series expansion and truncating the expansion at the first power of the error. For example, consider the relation $z = x/y.$ If the errors in $x,y$ and $z$ are $\Delta x,\Delta y$ and $\Delta z,$ respectively, then
$$z \pm \Delta z = {{x \pm \Delta x} \over {y \pm \Delta y}} = {x \over y}\left( {1 \pm {{\Delta x} \over x}} \right){\left( {1 \pm {{\Delta y} \over y}} \right)^{ - 1}}.$$

The series expansion for ${\left( {1 \pm {{\Delta y} \over y}} \right)^{ - 1}},$ to first power in $\Delta y/y.$ is $1 \pm \left( {\Delta y/y} \right).$ The relative errors in independent variables are always added. So the error in $z$ will be
$$\Delta z = z\left( {{{\Delta x} \over x} + {{\Delta y} \over y}} \right).$$

The above derivation makes the assumption that $\Delta x/x < < 1,$ $\Delta y/y < < 1.$ Therefore, the higher powers of these quantities are neglected.

In an experiment the initial number of radioactive nuclei is $3000.$ It is found that $1000 \pm 40$ nuclei decayed in the first $1.0s.$ For $\left| x \right| < < 1.$ $\ln \left( {1 + x} \right) = x$ up to first power in $x.$ The error $\Delta \lambda ,$ in the determination of the decay constant $\lambda ,$ in ${s^{ - 1}},$ is

A

$0.04$

B

$0.03$

C

$0.02$

D

$0.01$

Question 13: Palette 13/41

JEE Advanced 2017 MCQ

A person measures the depth of a well by measuring the time interval between dropping a stone and receiving the sound of impact with the bottom of the well. The error in his measurement of time is $\delta T = 0.01$ seconds and he measures the depth of the well to be $L=20$ meters. Take the acceleration due to gravity $g = 10m{s^{ - 2}}$ and the velocity of sound is $300$ $m{s^{ - 1}}$. Then the fractional error in the measurement, $\delta L/L,$ is closest to

A

$0.2\% $

B

$1\% $

C

3%

D

5%

Question 14: Palette 14/41

JEE Advanced 2016 MCQ

There are two Vernier calipers both of which have 1 cm divided into 10 equal divisions on the main scale. The Vernier scale of one of the calipers (C₁) has 10 equal divisions that correspond to 9 main scale divisions. The Vernier scale of the other caliper (C₂) has 10 equal divisions that correspond to 11 main scale divisions. The readings of the two calipers are shown in the figure. The measured values (in cm) by calipers C₁ and C₂ respectively, are

A

2.85 and 2.82

B

2.87 and 2.83

C

2.87 and 2.86

D

2.87 and 2.87

Question 15: Palette 15/41

JEE Advanced 2016 MSQ

In an experiment to determine the acceleration due to gravity g, the formula used for the time period of a periodic motion is $T = 2\pi \sqrt {{{7\left( {R - r} \right)} \over {5g}}} $. The values of R and r are measured to be (60 $ \pm $ 1) mm and (10 $ \pm $ 1) mm, respectively. In five successive measurements, the time period is found to be 0.52 s, 0.56 s, 0.57 s, 0.54 s and 0.59 s. The least count of the watch used for the measurement of time period is 0.01 s. Which of the following statement(s) is(are) true?

A

The error in the measurement of r is 10 %

B

The error in the measurement of T is 3.57 %

C

The error in the measurement of T is 2 %

D

The error in the determined value of g is 11 %

Question 16: Palette 16/41

JEE Advanced 2016 MSQ

A length-scale (l) depends on the permittivity ($\varepsilon $) of a dielectric material, Boltzmann constant (k_B), the absolute temperature (T), the number per unit volume (n) of certain charged particles, and the charge (q) carried by each of the particles. Which of the following expression(s) for I is(are) dimensionally correct?

A

$l = \sqrt {\left( {{{n{q^2}} \over {\varepsilon {k_b}T}}} \right)} $

B

$l = \sqrt {\left( {{{\varepsilon {k_b}T} \over {n{q^2}}}} \right)} $

C

$l = \sqrt {\left( {{{{q^2}} \over {\varepsilon {n^{2/3}}{k_B}T}}} \right)} $

D

$l = \sqrt {\left( {{{{q^2}} \over {\varepsilon {n^{1/3}}{k_B}T}}} \right)} $

Question 17: Palette 17/41

JEE Advanced 2015 MSQ

Planck's constant h, speed of light c and gravitational constant G are used to form a unit of length L and a unit of mass M. Then the correct option(s) is(are)

A

$M \propto \sqrt c $

B

$M \propto \sqrt G $

C

$L \propto \sqrt h $

D

$L \propto \sqrt G $

Question 18: Palette 18/41

JEE Advanced 2015 MSQ

Consider a Vernier callipers in which each 1 cm on the main scale is divided into 8 equal divisions and a screw gauge with 100 divisions on its circular scale. In the Vernier callipers, 5 divisions of the Vernier scale coincide with 4 divisions on the main scale and in the screw gauge, one complete rotation of the circular scale moves it by two divisions on the linear scale. Then:

A

If the pitch of the screw gauge is twice the least count of the Vernier callipers, the least count of the screw gauge is 0.01 mm.

B

If the pitch of the screw gauge is twice the least count of the Vernier callipers, the least count of the screw gauge is 0.005 mm.

C

If the least count of the linear scale of the screw gauge is twice the least count of the Vernier callipers, the least count of the screw gauge is 0.01 mm.

D

If the least count of the linear scale of the screw gauge is twice the least count of the Vernier callipers, the least count of the screw gauge is 0.005 mm.

Question 19: Palette 19/41

JEE Advanced 2013 MCQ

Match List I with List II and select the correct answer using the codes given below the lists:

List I

P. Boltzmann Constant
Q. Coefficient of viscosity
R. Plank Constant
S. Thermal conductivity

List II

1. [ML²T^-1]
2. [ML^-1T^-1]
3. [MLT^-3K^-1]
4. [ML²T^-2K^-1]

A

$\eqalign{ & P\,\,\,\,Q\,\,\,\,R\,\,\,\,S \cr & 3\,\,\,\,\,\,1\,\,\,\,\,2\,\,\,\,\,4 \cr} $

B

$\eqalign{ & P\,\,\,\,Q\,\,\,\,R\,\,\,\,S \cr & 3\,\,\,\,\,\,2\,\,\,\,\,1\,\,\,\,\,4 \cr} $

C

$\eqalign{ & P\,\,\,\,Q\,\,\,\,R\,\,\,\,S \cr & 4\,\,\,\,\,\,2\,\,\,\,\,1\,\,\,\,\,3 \cr} $

D

$\eqalign{ & P\,\,\,\,Q\,\,\,\,R\,\,\,\,S \cr & 4\,\,\,\,\,\,1\,\,\,\,\,2\,\,\,\,\,3 \cr} $

Question 20: Palette 20/41

JEE Advanced 2013 MCQ

The diameter of a cylinder is measured using a Vernier callipers with no zero error. It is found that the zero of the Vernier scale lies between 5.10 cm and 5.15 cm of the main scale. The Vernier scale has 50 divisions equivalent to 2.45 cm. The 24^th division of the Vernier scale exactly coincides with one of the main scale divisions. The diameter of the cylinder is

A

5.112 cm

B

5.124 cm

C

5.136 cm

D

5.148 cm

Question 21: Palette 21/41

JEE Advanced 2012 MCQ

In the determination of Young's modulus $\left( {Y = {{4MLg} \over {\pi l{d^2}}}} \right)$ by using Searle's method, a wire of length L = 2 m and diameter d = 0.5 mm is used. For a load M = 2.5 kg, an extension l = 0.25 mm in the length of the wire is observed. Quantities d and l are measured using a screw gauge and a micrometer, respectively. They have the same pitch of 0.5 mm. The number of divisions on their circular scale is 100. The contributions to the maximum probable error of the Y measurement

A

due to the errors in the measurements of d and l are the same.

B

due to the error in the measurement of d is twice that due to the error in the measurement of l.

C

due to the error in the measurement of l is twice that due to the error in the measurement of d.

D

due to the error in the measurement of d is four times that due to the error in the measurement of l.

Question 22: Palette 22/41

JEE Advanced 2011 MCQ

A dense collection of equal number of electrons and positive ions is called neutral plasma. Certain solids containing fixed positive ions surrounded by free electrons can be treated as neutral plasma. Let 'N' be the number density of free electrons, each of mass 'm'. When the electrons are subjected to an electric field, they are displaced relatively away from the heavy positive ions. If the electric field becomes zero, the electrons begin to oscillate about the positive ions with a natural angular frequency '${\omega _p}$' which is called the plasma frequency. To sustain the oscillations, a time varying electric field needs to be applied that has an angular frequency $\omega $, where a part of the energy is absorbed and a part of it is reflected. As $\omega $ approaches ${\omega _p}$ all the free electrons are set to resonance together and all the energy is reflected. This is the explanation of high reflectivity of metals.

Taking the electronic charge as 'e' and the permittivity as $'{\varepsilon _0}'$. Use dimensional analysis to determine the correct expression for ${\omega _p}$.

A

$\sqrt {{{Ne} \over {m{\varepsilon _0}}}} $

B

$\sqrt {{{m{\varepsilon _0}} \over {Ne}}} $

C

$\sqrt {{{N{e^2}} \over {m{\varepsilon _0}}}} $

D

$\sqrt {{{m{\varepsilon _0}} \over {N{e^2}}}} $

Question 23: Palette 23/41

JEE Advanced 2011 MCQ

The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with a screw gauge, whose pitch is 0.5 mm and there are 50 divisions on the circular scale. The reading on the main scale is 2.5 mm and that on the circular scale is 20 divisions. If the measured mass of the ball has a relative error of 2 %, the relative percentage error in the density is

A

0.9 %

B

2.4 %

C

3.1 %

D

4.2 %

Question 24: Palette 24/41

JEE Advanced 2010 MCQ

A vernier calipers has 1 mm marks on the main scale. It has 20 equal divisions on the Vernier scale which match with 16 main scale divisions. For this Vernier calipers, the least count is

A

0.02 mm

B

0.05 mm

C

0.1 mm

D

0.2 mm

Question 25: Palette 25/41

JEE Advanced 2010 MSQ

A student uses a simple pendulum of exactly 1m length to determine g, the acceleration due to gravity. He uses a stop watch with the least count of 1 sec for this and records 40 seconds for 20 oscillations. For this observation, which of the following statement(s) is (are) true?

A

Error ΔT in measuring T, the time period, is 0.05 seconds

B

Error ΔT in measuring T, the time period, is 1 second

C

Percentage error in the determination of g is 5%

D

Percentage error in the determination of g is 2.5%

Question 26: Palette 26/41

JEE Advanced 2008 MCQ

Student I, II and III perform an experiment for measuring the acceleration due to gravity (g) using a simple pendulum. They use different length of the pendulum and/or record time for different number of oscillations. The observations area shown in the table.

Least count for length = 0.1 cm

Least count for time = 0.1 s

Student	Length of the pendulum (cm)	No. of oscillations (n)	Total time for(n) oscillations (s)	Time periods (s)
I	64.0	8	128.0	16.0
II	64.0	4	64.0	16.0
III	20.0	4	36.0	9.0

If E_I, E_II and E_III are the percentage errors in g, i.e., $\left(\frac{\triangle g}g\times100\right)$ for students I, II and III, respectively,then

A

E_I = 0

B

E_I is minimum

C

E_I = E_II

D

E_II is maximum

Question 27: Palette 27/41

JEE Advanced 2007 MCQ

Some physical quantities are given in Column I and some possible SI units in which these quantities may be expressed are given in Column II. Match the physical quantities in Column I with the units in Column II.

Column I

(A) GM_eM_s ,
G $ \to $ universal gravitational constant, M_e $ \to $ mass of the earth, M_s $ \to $ mass of the Sun

(B) ${{3RT} \over M}$,
R $ \to $ universal gas constant, T $ \to $ absolute temperature, M $ \to $ molar mass

(C) ${{{F^2}} \over {{q^2}{B^2}}}$ ,
F $ \to $ force, q $ \to $ charge, B $ \to $ magnetic field

(D) ${{G{M_e}} \over {{R_e}}}$,
G $ \to $ universal gravitational constant, M_e $ \to $ mass of the earth, R_e $ \to $ radius of the earth

Column II

(p) (volt) (coulomb) (metre)

(q) (kilogram) (metre)³ (second)⁻²

(r) (meter)²(second)⁻²

(s) (farad) (volt)² (kg)⁻¹

A

A $ \to $ (p) & (q), B $ \to $ (r) & (s), C $ \to $ (r) & (s), D $ \to $ (r) & (s)

B

A $ \to $ (p), B $ \to $ (r) & (s), C $ \to $ (r) & (s), D $ \to $ (r) & (s)

C

A $ \to $ (p) & (q), B $ \to $ (r) & (s), C $ \to $ (r) & (s), D $ \to $ (r)

D

A $ \to $ (p) & (q), B $ \to $ (r), C $ \to $ (r) & (s), D $ \to $ (r) & (s)

Question 28: Palette 28/41

JEE Advanced 2007 MCQ

A student performs an experiment to determine the Young's modulus of a wire, exactly 2 m long, by Searle's method. In a particular reading, the student measures the extension in the length of the wire to be 0.8 mm with an uncertainty of $\pm0.05\;\mathrm{mm}$ at a load of exactly 1.0 kg. The student also measures the diameter of the wire to be 0.4 mm with an uncertainty of $\pm0.01\;\mathrm{mm}$. Take g = 9.8 m/s² (exact). The Young's modulus obtained from the reading is

A

$\left(2.0\;\pm\;0.3\right)\times10^{11}\;\mathrm N/\mathrm m^2$

B

$\left(2.0\;\pm\;0.2\right)\times10^{11}\;\mathrm N/\mathrm m^2$

C

$\left(2.0\;\pm\;0.1\right)\times10^{11}\;\mathrm N/\mathrm m^2$

D

$\left(2.0\;\pm\;0.05\right)\times10^{11}\;\mathrm N/\mathrm m^2$

Question 29: Palette 29/41

JEE Advanced 2006 MCQ

A student performs an experiment for determination of $g\left(=\frac{4 \pi^2 l}{\mathrm{~T}^2}\right), l=1 m$, and he commits an error of $\Delta l$. For T , he takes the time of $n$ oscillations with the stop watch of least count $\Delta \mathrm{T}$ and he commits a human error of 0.1 s . For which of the following data, the measurement of $g$ will be most accurate?

A

$\begin{array}{l}\triangle\mathcal l\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\triangle\mathrm T\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\mathrm n\\5\;\mathrm{mm}\;\;\;\;\;\;\;\;\;\;\;\;0.2\;\sec\;\;\;\;\;\;\;\;\;\;\;\;10\end{array}$

B

$\begin{array}{l}\triangle\mathcal l\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\triangle\mathrm T\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\mathrm n\\5\;\mathrm{mm}\;\;\;\;\;\;\;\;\;\;\;\;0.2\;\sec\;\;\;\;\;\;\;\;\;\;\;\;20\end{array}$

C

$\begin{array}{l}\triangle\mathcal l\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\triangle\mathrm T\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\mathrm n\\5\;\mathrm{mm}\;\;\;\;\;\;\;\;\;\;\;\;0.1\;\sec\;\;\;\;\;\;\;\;\;\;\;\;10\end{array}$

D

$\begin{array}{l}\triangle\mathcal l\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\triangle\mathrm T\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\mathrm n\\1\;\mathrm{mm}\;\;\;\;\;\;\;\;\;\;\;\;0.1\;\sec\;\;\;\;\;\;\;\;\;\;\;\;50\end{array}$

Question 30: Palette 30/41

JEE Advanced 2006 MCQ

In a screw gauge, the zero of main scale coincides with the fifth division of circular scale in figure (i).The circular division of screw gauge is 50. It moves 0.5 mm on main scale in one rotation.The diameter of the ball in figure (ii) is

A

2.25 mm

B

2.20 mm

C

1.20 mm

D

1.25 mm

Question 31: Palette 31/41

JEE Advanced 2005 MCQ

Which of the following set have different dimensions?

A

Pressure, Young's modulus, Stress

B

EMF, Potential difference, Electric potential

C

Heat, Work done, Energy

D

Dipole moment, Electric flux, Electric field

Question 32: Palette 32/41

JEE Advanced 2005 MCQ

The side of a cube is measured by vernier callipers (10 divisions of a vernier scale coincide with 9 divisions of main scale, where 1 division of main scale is 1 mm). The main scale reads 10 mm and first division of vernier scale coincides with the main scale; Mass of the cube is 2.736 g. Find the density of the cube in appropriate significant figures.

A

$5\times10^3$

B

$7\times10^4$

C

$2.66\times10^3$

D

$3.45\times10^3$

Question 33: Palette 33/41

JEE Advanced 2004 MCQ

A wire of length $l = 6 \pm 0.06$ cm and $r = 0.5 \pm 0.005$ cm and mass $m = 0.3 \pm 0.003$ gm. Maximum percentage error in density is

A

4

B

2

C

1

D

6.8

Question 34: Palette 34/41

JEE Advanced 2004 MCQ

Pressure depends on distance as, $P = {\alpha \over \beta }\exp \left( { - {{\alpha z} \over {k\theta }}} \right)$, where $\alpha $, $\beta $ are constants, z in distance, k is Boltzman's constant and $\theta $ is temperature. The dimention of $\beta $ are

A

[M⁰L⁰T⁰]

B

[M^-1L^-1T^-1]

C

[M⁰L²T⁰]

D

[M^-1L¹T²]

Question 35: Palette 35/41

JEE Advanced 2003 MCQ

A cube has a side of length 1.2 ✕ 10^-2 m. Calculate its volume.

A

1.7 ✕ 10^-6 m³

B

1.73 ✕ 10^-6 m³

C

1.70 ✕ 10^-6 m³

D

1.732 ✕ 10^-6 m³

Question 36: Palette 36/41

JEE Advanced 2001 MCQ

A quantity X is given by ${\varepsilon _0}L{{\Delta V} \over {\Delta t}}$ where ${\varepsilon _0}$ is the permittivity of the free space, L is a length, ${\Delta V}$ is a potential difference and ${\Delta t}$ is a time interval. The dimentional formula for X is the same as that of

A

resistance

B

charge

C

voltage

D

current

Question 37: Palette 37/41

JEE Advanced 2000 MCQ

The dimension of $\left( {{1 \over 2}} \right){\varepsilon _0}{E^2}$
( ${\varepsilon _0}$ : permittivity of free space, E electric field )

A

MLT^-1

B

ML²T^-2

C

ML^-1T^-2

D

ML²T^-1

Question 38: Palette 38/41

JEE Advanced 1998 MSQ

Let [${\mathrm\varepsilon}_\mathrm o$] denote the dimentional formula of the permittivity of the vacuum, and [$\mu_o$] that of the permeability of the vacuum.If M = mass, L = length, T = time and I = electric current,

A

$\left[{\mathrm\varepsilon}_\mathrm o\right]\;=\;\mathrm M^{-1}\mathrm L^{-3}\mathrm T^2\;\mathrm I$

B

$\left[{\mathrm\varepsilon}_\mathrm o\right]\;=\;\mathrm M^{-1}\mathrm L^{-3}\mathrm T^4\mathrm I^2$

C

$\left[{\mathrm\mu}_\mathrm o\right]\;=\;\mathrm{MLT}^{-2}\mathrm I^{-2}$

D

$\left[{\mathrm\mu}_\mathrm o\right]\;=\;\mathrm{ML}^2\mathrm T^{-1}\;\mathrm I$

Question 39: Palette 39/41

JEE Advanced 1998 MSQ

The SI unit of inductance, the henry can be written as

A

weber/ampere

B

volt-sec/amp

C

Joule/(ampere)²

D

ohm-second

Question 40: Palette 40/41

JEE Advanced 1995 MSQ

The pairs of physical quantities that have the same dimensions is (are):

A

Reynolds number and coefficient of friction

B

Curie and frequency of a light wave

C

Latent heat and gravitational potential

D

Planck's constant and torque

Question 41: Palette 41/41

JEE Advanced 1986 MSQ

The dimensions of the quantities in one ( or more ) of the following pairs are the same. Identify the pair(s)

A

Torque and Work

B

Angular momentum and Work

C

Energy and Young's modulus

D

Light year and Wavelength