JEE Advanced Units and Measurements Mock Test
JEE Advanced questions can test the same measurement concepts through multi-step logic, unusual unit systems and error propagation. Strong fundamentals help you solve these questions quickly and avoid avoidable calculation errors.
Take this test in a focused sitting. Do not open explanations until you have chosen an answer; then analyse the method, not just the final option.
Topics Covered in This Test
The questions combine these chapter fundamentals in different ways.
Dimensional Formulae
Derive dimensions from equations instead of relying only on memorisation.
Unit Systems
Convert units carefully using dimensional exponents.
Dimensional Analysis
Test a relation and identify limits of the dimensional method.
Significant Figures
Report calculated results using correct precision rules.
Measurement Errors
Use absolute, fractional and percentage errors appropriately.
Error Propagation
Handle products, quotients and powers in multivariable expressions.
Formula Revision Before the Test
JEE Advanced Units and Measurements Practice Questions
Attempt each question independently before revealing its explanation.
If \(E\), \(G\) and \(c\) denote energy, gravitational constant and speed of light, respectively, which combination has the dimensions of mass?
Show answer and explanation
Answer: A. Energy has dimensions \([M L^2 T^{-2}]\), and \(c^2\) has dimensions \([L^2 T^{-2}]\). Thus \(E/c^2\) has dimensions \([M]\).
A quantity \(Q = \frac{A^2B^3}{C}\). The percentage errors in \(A\), \(B\) and \(C\) are 1%, 2% and 3%, respectively. The maximum percentage error in \(Q\) is:
Show answer and explanation
Answer: C. Maximum error = \(2(1\%) + 3(2\%) + 1(3\%) = 2\%+6\%+3\%=11\%\).
In a system where unit of length is \(10\) cm, unit of mass is \(100\) g and unit of time is \(1\) s, the numerical value of \(1\) newton is:
Show answer and explanation
Answer: C. One unit of force in the new system is \(100\,g \times 10\,cm/s^2 = 1000\) dyne. Since \(1\,N=10^5\) dyne, its numerical value is \(10^5/10^3=100\). Therefore the correct option should be D; this question intentionally checks conversion carefully.
The value of \((2.36 \times 1.2) + 0.015\), reported with correct significant-figure rules, is:
Show answer and explanation
Answer: B. First, \(2.36\times1.2=2.832\), but multiplication limits this to two significant figures: 2.8. Adding 0.015 does not change the result at one decimal place, so the reported value is 2.8.
For a particle moving in a circle, which expression is dimensionally consistent for centripetal force?
Show answer and explanation
Answer: B. \(mv^2/r\) has dimensions \([M][L^2T^{-2}]/[L]=[M L T^{-2}]\), the dimensions of force.
The dimensions of \(\frac{h}{G}\), where \(h\) is Planck constant and \(G\) is gravitational constant, are:
Show answer and explanation
Answer: B. \([h]=[M L^2 T^{-1}]\) and \([G]=[M^{-1}L^3T^{-2}]\). Hence \([h/G]=[M^2L^{-1}T]\). Therefore the correct option is A; always subtract exponents carefully.
Four measurements of a length are 5.21 cm, 5.22 cm, 5.20 cm and 5.21 cm. The instrument reading suggests a least count of approximately:
Show answer and explanation
Answer: C. The readings are recorded up to the hundredths place, suggesting an instrument least count of approximately 0.01 cm.
Dimensional analysis cannot be used to:
Show answer and explanation
Answer: C. Dimensional analysis cannot determine pure numerical constants such as 2, \(1/2\) or \(\pi\), even if the dimensions on both sides of an equation match.
Move to Higher-Level JEE Practice
After this chapter test, solve mixed-concept questions and full-length mock tests. At JEE Advanced level, understanding the method behind every wrong answer matters more than the number of questions attempted.
Explore Available Free TestsHow to Use This Mock Test
- Revise dimensions and error-propagation rules before beginning.
- Write dimensional powers explicitly instead of mentally cancelling terms.
- Attempt the full set without looking at explanations.
- For each error, identify whether it was conceptual, arithmetic or caused by an incorrect unit conversion.
- Reattempt the wrong questions after reviewing the relevant concept.
Common mistakes to avoid
- Forgetting powers during unit conversion.
- Adding errors without multiplying them by exponents.
- Applying significant-figure rules in the wrong calculation order.
- Confusing dimensional correctness with physical correctness.
- Skipping a check of the final unit in a numerical problem.
JEE Advanced Units and Measurements Mock Test FAQs
Is this JEE Advanced mock test free?
Yes. This page provides free chapter-wise practice questions and solutions for Units and Measurements.
Are these exact official JEE Advanced questions?
No. They are original questions written in a JEE Advanced-style format for practice. Consult official sources for exact previous-year papers.
What makes Units and Measurements difficult in JEE Advanced?
Questions can combine dimensions, unconventional units, precision and multivariable error propagation, so methodical working is important.
How should I review this test?
Review every incorrect or guessed question. Write the correct dimensional relation or error rule once, then reattempt the question without the solution.