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A tiny metallic rectangular sheet has length and breadth of $5\text{ mm}$ and $2.5\text{ mm}$, respectively. Using a specially designed screw gauge which has pitch of $0.75\text{ mm}$ and $15$ divisions in the circular scale, you are asked to find the area of the sheet. In this measurement, the maximum fractional error will be $\frac{x}{100}$ where $x$ is _________.

The maximum percentage error in the measurement of density of a wire is
[Given, mass of wire \(= (0.60 \pm 0.003)\,\text{g}\)
radius of wire \(= (0.50 \pm 0.01)\,\text{cm}\)
length of wire \(= (10.00 \pm 0.05)\,\text{cm}\))

A quantity \( Q \) is formulated as \( x^{-2} y^{+3/2} z^{-2/5} \). \( X \), \( Y \) and \( Z \) are independent parameters which have 275 fractional errors of \( 0.1 \), \( 0.2 \) and \( 0.5 \), respectively in measurement. The maximum fractional error of \( Q \) is:

A bar magnet has total length \( 2l = 20 \) units and the field point \( P \) is at a distance \( d = 10 \) units from the centre of the magnet. If the relative uncertainty of length measurement is \( 1\% \), then uncertainty of the magnetic field at point \( P \) is:

A physical quantity \( C \) is related to four other quantities \( p, q, r \) and \( s \) as follows
\( C = \dfrac{p q^{2}}{r^{3}\sqrt{s}} \).
The percentage errors in the measurement of \( p, q, r \) and \( s \) are \( 1\% \), \( 2\% \), \( 3\% \) and \( 2\% \) respectively.
The percentage error in the measurement of \( C \) will be __________ \( \% \).

For an experimental expression \( y = \dfrac{32.3 \times 1125}{27.4} \), where all the digits are significant. Then to report the value of \( y \) we should write:

Given below are two statements:
Statement-I : In a vernier callipers, one vernier scale division is always smaller than one main scale division.
Statement-II : The vernier constant is given by one main scale division multiplied by the number of vernier scale divisions.
In the light of the above statements, choose the correct answer from the options given below.

The least count of a screw guage is \( 0.01 \, \text{mm} \). If the pitch is increased by \( 75\% \) and number of divisions on the circular scale is reduced by \( 50\% \), the new least count will be ________ \( \times 10^{-3} \, \text{mm} \).

A physical quantity \(Q\) is related to four observables \(a, b, c, d\) as follows:
\( Q = \dfrac{ab^{4}}{cd} \)
Where, \( a = (60 \pm 3)\, \text{Pa} \); \( b = (20 \pm 0.1)\, \text{m} \); \( c = (40 \pm 0.2)\, \text{N s m}^{-2} \) and \( d = (50 \pm 0.1)\, \text{m} \), then the percentage error in \(Q\) is \( \dfrac{x}{1000} \), where \( x = \) ___________.

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JEE Main 2025 22nd Jan Evening Shift

The maximum percentage error in the measurement of density of a wire is
[Given, mass of wire \(= (0.60 \pm 0.003)\,\text{g}\)
radius of wire \(= (0.50 \pm 0.01)\,\text{cm}\)
length of wire \(= (10.00 \pm 0.05)\,\text{cm}\))