1
JEE Advanced 2022 Paper 2 Online
MCQ (Single Correct Answer)
+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.
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?
2
JEE Advanced 2021 Paper 1 Online
MCQ (Single Correct Answer)
+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


3
JEE Advanced 2018 Paper 1 Offline
MCQ (Single Correct Answer)
+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
The relation between $$\left[ {{\varepsilon _0}} \right]$$ and $$\left[ {{\mu _0}} \right]$$ is
4
JEE Advanced 2018 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1
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
$$$z \pm \Delta z = {{x \pm \Delta x} \over {y \pm \Delta y}} = {x \over y}\left( {1 \pm {{\Delta x} \over x}} \right){\left( {1 \pm {{\Delta y} \over y}} \right)^{ - 1}}.$$$
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
Questions Asked from Units & Measurements (MCQ (Single Correct Answer))
Number in Brackets after Paper Indicates No. of Questions
JEE Advanced 2023 Paper 2 Online (1)
JEE Advanced 2022 Paper 2 Online (1)
JEE Advanced 2021 Paper 1 Online (1)
JEE Advanced 2018 Paper 1 Offline (4)
JEE Advanced 2017 Paper 2 Offline (1)
JEE Advanced 2016 Paper 2 Offline (1)
JEE Advanced 2013 Paper 2 Offline (1)
JEE Advanced 2013 Paper 1 Offline (1)
IIT-JEE 2012 Paper 1 Offline (1)
IIT-JEE 2011 Paper 1 Offline (1)
IIT-JEE 2011 Paper 2 Offline (1)
IIT-JEE 2010 Paper 2 Offline (1)
IIT-JEE 2008 Paper 1 Offline (1)
IIT-JEE 2007 (1)
IIT-JEE 2007 Paper 2 Offline (1)
IIT-JEE 2006 (2)
IIT-JEE 2005 Screening (1)
IIT-JEE 2004 Screening (2)
IIT-JEE 2003 Screening (1)
IIT-JEE 2001 Screening (1)
IIT-JEE 2000 Screening (1)
JEE Advanced Subjects
Physics
Mechanics
Units & Measurements
Motion
Laws of Motion
Work Power & Energy
Impulse & Momentum
Rotational Motion
Properties of Matter
Heat and Thermodynamics
Simple Harmonic Motion
Waves
Gravitation
Electricity
Optics
Modern Physics
Chemistry
Physical Chemistry
Some Basic Concepts of Chemistry
Structure of Atom
Redox Reactions
Gaseous State
Equilibrium
Solutions
States of Matter
Thermodynamics
Chemical Kinetics and Nuclear Chemistry
Electrochemistry
Solid State & Surface Chemistry
Inorganic Chemistry
Periodic Table & Periodicity
Chemical Bonding & Molecular Structure
Isolation of Elements
Hydrogen
s-Block Elements
p-Block Elements
d and f Block Elements
Coordination Compounds
Salt Analysis
Organic Chemistry
Mathematics
Algebra
Quadratic Equation and Inequalities
Sequences and Series
Mathematical Induction and Binomial Theorem
Matrices and Determinants
Permutations and Combinations
Probability
Vector Algebra and 3D Geometry
Statistics
Complex Numbers
Trigonometry
Coordinate Geometry
Calculus