JEE Mains JEE Advance BITSAT
JEE Mains | PYQ

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In an experiment for estimating the value of focal length of converging mirror, image of an object placed at \(40 \, \text{cm}\) from the pole of the mirror is formed at distance \(120 \, \text{cm}\) from the pole of the mirror. These distances are measured with a modified scale in which there are \(20\) small divisions in \(1 \, \text{cm}\). The value of error in measurement of focal length of the mirror is \( \frac{1}{K} \, \text{cm} \). The value of \( K \) is _______.

The diameter of a wire measured by a screw gauge of least count \( 0.001 \,\text{cm} \) is \( 0.08 \,\text{cm} \). The length measured by a scale of least count \( 0.1 \,\text{cm} \) is \( 150 \,\text{cm} \). When a weight of \( 100 \,\text{N} \) is applied to the wire, the extension in length is \( 0.5 \,\text{cm} \), measured by a micrometer of least count \( 0.001 \,\text{cm} \). The error in the measured Young’s modulus is \( \alpha \times 10^{9} \,\text{N}/\text{m}^{2} \). The value of \( \alpha \) is ______. (Ignore the contribution of the load to Young’s modulus error calculation)

A physical quantity ‘\( y \)’ is represented by the formula \( y = m^{2} r^{-4} g^{x} l^{-\dfrac{3}{2}} \). If the percentage errors found in \( y, m, r, l \) and \( g \) are \( 18 \), \( 1 \), \( 0.5 \), \( 4 \) and \( p \) respectively, then find the value of \( x \) and \( p \).

As shown in the figure, in an experiment to determine young’s modulus of a wire, the extension-load curve is plotted. The curve is a straight line passing through the origin and makes an angle of \( 45^\circ \) with the load axis. The length of wire is \( 62.8 \, \text{cm} \) and its diameter is \( 4 \, \text{mm} \). The Young’s modulus is found to be \( x \times 10^{4} \, \text{N} \, \text{m}^{-2} \). The value of \( x \) is ___________.

Assertion \( A \): If in five complete rotations of the circular scale, the distance travelled on main scale of the screw gauge is \( 5 \, \text{mm} \) and there are \( 50 \) total divisions on circular scale, then least count is \( 0.001 \, \text{cm} \).
Reason \( R \): Least Count \( = \dfrac{\text{Pitch}}{\text{Total divisions on circular scale}} \).
In the light of the above statements, choose the most appropriate answer from the options given below:

Student A and Student B used two screw gauges of equal pitch and \( 100 \) equal circular divisions to measure the radius of a given wire. The actual value of the radius of the wire is \( 0.322 \, \text{cm} \). The absolute value of the difference between the final circular scale readings observed by the students A and B is __________________ . [Figure shows position of reference ‘\( O \)’ when jaws of screw gauge are closed]
Given pitch = \( 0.1 \, \text{cm} \).

In a vernier callipers, \( 50 \) vernier scale divisions are equal to \( 48 \) main scale divisions. If one main scale division \( = 0.05 \, \text{mm} \), then the least count of the vernier callipers is ____________ \( \text{mm} \).

If \( 50 \) Vernier divisions are equal to \( 49 \) main scale division of a traveling microscope and one smallest reading of main scale is \( 0.5 \, \text{mm} \), the Vernier constant of traveling microscope is:

In a screw gauge when the circular scale is given five complete rotations it moves linearly by \( 2.5 \, \text{mm} \). If the circular scale has \( 100 \) divisions, the least count of screw gauge is ______ \( \text{mm} \).

If the percentage errors in measuring the length and the diameter of a wire are \( 0.1\% \) each. The percentage error in measuring its resistance will be:

In a Screw Gauge, fifth division of the circular scale coincides with the reference line when the ratchet is closed. There are \( 50\) divisions on the circular scale, and the main scale moves by \( 0.5 \text{mm} \) on a complete rotation. For a particular observation the reading on the main scale is \( 5 \text{mm} \) and the \( 20^{\text{th}} \) division of the circular scale coincides with reference line. Calculate the true reading.

In an experiment the values of two spring constants were measured as \( k_1 = (10 \pm 0.2) \, \text{N/m} \) and \( k_2 = (20 \pm 0.3) \, \text{N/m} \). If these springs are connected in parallel, then the percentage error in equivalent spring constant is:

The maximum error in the measurement of resistance, current and time for which current flows in a n electrical circuit are \( 1\% \), \( 2\% \) and \( 3\% \) respectively. The maximum percentage error in the detection of the dissipated heat will be:

A \( 2 \, \text{meter} \) long scale with least count of \( 0.2 \, \text{cm} \) is used to measure the locations of objects on an optical bench. While measuring the focal length of a convex lens, the object pin and the convex lens are placed at \( 80 \, \text{cm} \) mark and \( 1 \, \text{m} \) mark, respectively. The image of the object pin on the other side of lens coincides with image pin that is kept at \( 180 \, \text{cm} \) mark. The \( \\% \) error in the estimation of focal length is:

The resistance \( R = \frac{V}{I} \) where \( V = (200 \pm 5) \, \text{V} \) and \( I = (20 \pm 0.2) \, \text{A} \), the percentage error in the measurement of \( R \) is:

When both jaws of vernier callipers touch each other, zero mark of the vernier scale is right to zero mark of main scale, \( 4^{\text{th}} \) mark on vernier scale coincides with certain mark on the main scale. While measuring the length of a cylinder, observer observes \( 15 \) divisions on main scale and \( 5^{\text{th}} \) division of vernier scale coincides with a main scale division. Measured length of cylinder is ________ \( \text{mm} \). (Least count of Vernier calliper = \( 0.1 \, \text{mm} \))

A torque meter is calibrated to reference standard of mass, length and time each with \( 5\% \) accuracy. After calibration, the measured torque with this torque meter will have net accuracy of:

Young's modulus is determined by the equation given by \( Y = 49000 \, \frac{m}{l} \, \text{dyne} / \text{cm}^2 \) where \( M \) is the mass and \( l \) is the extension of wire used in the experiment. Now error in young modules (\( Y \)) is estimated by taking data from \( M\text{–}l \) plot in graph paper. The smallest scale divisions are \( 5 \, \text{g} \) and \( 0.02 \, \text{cm} \) along load axis and extension axis respectively. If the value of \( M \) and \( l \) are \( 500 \, \text{g} \) and \( 2 \, \text{cm} \) respectively then percentage error of \( Y \) is:

A student determined Young’s Modules of elasticity using the formula \( Y=\dfrac{MgL^{3}}{4bd^{3}\,\delta} \). The value of \( g \) is taken to be \( 9.8 \, \text{m} / \text{s}^{2} \), without any significant error, his observation are as following.

Then the fractional error in the measurement of \( Y \) is:

The density \( \rho \) of a uniform cylinder is determined by measuring its mass \( m \), length \( l \) and diameter \( d \). The measured values of \( m \), \( l \) and \( d \) are \( 97.42\pm0.02 \, \text{g} \), \( 8.35\pm0.05 \, \text{mm} \) and \( 20.20\pm0.02 \, \text{mm} \), respectively. Calculated percentage fractional error in \( \rho \) is ______.

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 _________.

In a screw gauge the zero of main scale reference line coincides with the fifth division of the circular scale when two studs are in contact. There are \( 100 \) divisions in circular scale and pitch of screw gauge is \( 0.1 \, \text{mm} \). When diameter of a sphere is measured, the reading of main scale is \( 5 \, \text{mm} \) and \( 50^{\text{th}} \) division of circular scale coincides with the reference line of main scale. The diameter of sphere is ________ \( \text{mm} \).

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:

In a screw gauge, there are \(100\) divisions on the circular scale and the main scale moves by \(0.5 \, \text{mm}\) on a complete rotation of the circular scale. The zero of circular scale lies \(6\) divisions below the line of graduation when two studs are brought in contact with each other. When a wire is placed between the studs, \(4\) linear scale divisions are clearly visible while \(46^{\text{th}}\) division the circular scale coincide with the reference line. The diameter of the wire is _______ \( \times 10^{-2} \, \text{mm} \).

A travelling microscope has \( 20 \) divisions per \( \text{cm} \) on the main scale while its vernier scale has total \( 50 \) divisions and \( 25 \) vernier scale divisions are equal to \( 24 \) main scale divisions, what is the least count of the travelling microscope?

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:

In a vernier calliper, when both jaws touch each other, zero of the vernier scale shifts towards left and its \( 4^{\text{th}} \) division coincides exactly with a certain division on main scale. If \( 50 \) vernier scale divisions equal to \( 49 \) main scale divisions and zero error in the instrument is \( 0.04 \, \text{mm} \) then how many main scale divisions are there in \( 1 \, \text{cm} \)?

Time periods of oscillation of the same simple pendulum measured using four different measuring clocks were recorded as \( 4.62 \, \text{s} \), \( 4.632 \, \text{s} \), \( 4.6 \, \text{s} \) and \( 4.64 \, \text{s} \). The arithmetic mean of these readings in correct significant figure is:

One main scale division of a vernier caliper is equal to \( m \) units. If \( n^{\text{th}} \) division of main scale coincides with \( (n+1)^{\text{th}} \) division of vernier scale, the least count of the vernier caliper is:

Two resistor \( R_{1}=(4 \pm 0.8)\, \Omega \) and \( R_{2}=(4 \pm 0.4)\, \Omega \) are connected in parallel. The equivalent resistance of their parallel combination will be:

In a Vernier Calipers, \( 10 \) divisions of Vernier scale is equal to the \( 9 \) divisions of main scale. When both jaws of Vernier calipers touch each other, the zero of the Vernier scale is shifted to the left of zero of the main scale and \( 4{\text{th}} \) Vernier scale division exactly coincides with the main scale reading. One main scale division is equal to \( 1 \, \text{mm} \). While measuring diameter of a spherical body, the body is held between two jaws. It is now observed that zero of the Vernier scale lies between \( 30 \) and \( 31 \) divisions of main scale reading and \( 6{\text{th}} \) Vernier scale division exactly coincides with the main scale reading. The diameter of the spherical body will be:

A physical quantity \( Q \) is found to depend on quantities \( a, b, c \) by the relation \( Q = \dfrac{a^{4} b^{3}}{c^{2}} \). The percentage error in \( a, b \) and \( c \) are \( 3\% \), \( 4\% \) and \( 5\% \) respectively, Then, the percentage error in \( Q \) is:

In a vernier callipers, each \( \mathrm{cm} \) on the main scale is divided into \( 20 \) equal parts. If tenth vernier scale division coincides with ninth main scale division. Then the value of vernier constant will be __________ \( \times 10^{-2} \,\mathrm{mm} \).

The acceleration due to gravity is found upto an accuracy of \( 4\% \) on a planet. The energy supplied to a simple pendulum of known mass \( m \) to undertake oscillations of time period \( T \) is being estimated. If time period is measured to an accuracy of \( 3\% \), the accuracy to which \( E \) is known as __________ \( \% \).

The time period of a simple pendulum is given by \( T = 2\pi \sqrt{\frac{l}{g}} \). The measured value of the length of pendulum is \( 10 \, \text{cm} \) known to a \( 1 \, \text{mm} \) accuracy. The time for \( 200 \) oscillations of the pendulum is found to be \( 100 \, \text{second} \) using a clock of \( 1 \, \text{s} \) resolution. The percentage accuracy in the determination of \( g \) using this pendulum is \( x \). The value of \( x \) to the nearest integer is:

In van dar Wall equation \( \left[P + \dfrac{a}{V^{2}}\right]\left[V - b\right] = R T \); \( P \) is pressure, \( V \) is volume, \( R \) is universal gas constant and \( T \) is temperature. The ratio of constants \( \dfrac{a}{b} \) is dimensionally equal to:

If the length of the pendulum in pendulum clock increases by \( 0.1\% \), then the error in time per day is:

In the experiment of Ohm’s law, a potential difference of \( 5.0 \, \text{V} \) is applied across the end of a conductor of length \( 10.0 \, \text{cm} \) and diameter of \( 5.00 \, \text{mm} \). The measured current in the conductor is \( 2.00 \, \text{A} \). The maximum permissible percentage error in the resistivity of the conductor is:

In a Vernier calipers, when both jaws touch each other, zero of the Vernier scale is shifted to the right of zero of the main scale and \( 7^{\text{th}} \) Vernier division coincides with a main scale reading. If the value of \( 1 \) main scale division is \( 1 \, \text{mm} \) and there are \( 10 \) Vernier scale divisions, then the Vernier caliper has

The diameter of a sphere is measured using a vernier caliper whose \( 9 \) divisions of main scale are equal to \( 10 \) divisions of vernier scale. The shortest division on the main scale is equal to \( 1 \, \text{mm} \). The main scale reading is \( 2 \, \text{cm} \) and second division of vernier scale coincides with a division on main scale. If mass of the sphere is \( 8.635 \, \text{g} \), the density of the sphere is:

Match List I with List II

Choose the correct answer from the options given below:

In experiment to find out the diameter of wire using screw gauge, the following observations were noted:

(a) Screw moves \( 0.5 \, \text{mm} \) on main scale in one complete rotation
(b) Total divisions on circular scale \( = 50 \)
(c) Main scale reading is \( 2.5 \, \text{mm} \)
(d) \( 45^{\text{th}} \) division of circular scale is in the pitch line
(e) Instrument has \( 0.03 \, \text{mm} \) negative error
Then the diameter of wire is

In an experiment to measure focal length \( (f) \) of convex lens, the least counts of the measuring scales for the position of object \( (u) \) and for the position of image \( (v) \) are \( \Delta u \) and \( \Delta v \), respectively. The error in the measurement of the focal length of the convex lens will be:

A travelling microscope is used to determine the refractive index of a glass slab. If \( 40 \) divisions are there in \( 1 \, \text{cm} \) on main scale and \( 50 \) Vernier scale divisions are equal to \( 49 \) main scale divisions, then least count of the travelling microscope is _______ \( \times 10^{-6} \, \text{m} \).

The one division of main scale of Vernier calipers reads \( 1 \, \text{mm} \) and \( 10 \) divisions of Vernier scale is equal to the \( 9 \) divisions on main scale. When the two jaws of the instrument touch each other, the zero of the Vernier lies to the right of zero of the main scale and its fourth division coincides with a main scale division. When a spherical bob is tightly placed between the two jaws, the zero of the Vernier scale lies in between \( 4.1 \, \text{cm} \) and \( 4.2 \, \text{cm} \) and \( 6^{\text{th}} \) Vernier division coincides with a main scale division. The diameter of the bob will be ______ \( \times 10^{-2} \, \text{cm} \).

A cylindrical wire of mass \( (0.4 \pm 0.01) \, \text{g} \) has length \( (8 \pm 0.04) \, \text{cm} \) and radius \( (6 \pm 0.03) \, \text{mm} \). The maximum error in its density will be:

Four persons measure the length of a rod as \( 20.00 \, \text{cm} \), \( 19.75 \, \text{cm} \), \( 17.01 \, \text{cm} \) and \( 18.25 \, \text{cm} \). The relative error in the measurement of average length of the rod is:

While measuring diameter of wire using screw gauge the following readings were noted. Main scale reading is \( 1 \, \text{mm} \) and circular scale reading is equal to \( 42 \) divisions. Pitch of screw gauge is \( 1 \, \text{mm} \) and it has \( 100 \) divisions on circular scale. The diameter of the wire is \( \dfrac{x}{50} \, \text{mm} \). The value of \( x \) 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 __________ \( \% \).

Consider the efficiency of carnot’s engine is given by \( \eta = \displaystyle\frac{\alpha \beta}{\sin \theta} \log_e \frac{\beta x}{k T} \), where \( \alpha \) and \( \beta \) are constants If \( T \) is temperature, \( k \) is Boltzmann constant, \( \theta \) is angular displacement and \( x \) has the dimensions of length. Then, choose the incorrect option.

The radius of a sphere is measured to be \( (7.50 \pm 0.85)\, \text{cm} \). Suppose the percentage error in its volume is \( x \). The value of \( x \), to the nearest \( x \), is:

In a screw gauge, the zero of the circular scale lies \( 3 \) divisions above the horizontal pitch line when their metallic studs are brought in contact. Using this instrument thickness of a sheet is measured. If pitch scale reading is \( 1 \, \text{mm} \) and the circular scale reading is \( 51 \) then the correct thickness of the sheet is ______ \( \text{mm} \). [Assume least count is \( 0.01 \, \text{mm} \)]

A vernier callipers has \( 20 \) divisions on the vernier scale, which coincides with \( 19^{\text{th}} \) division on the main scale. The least count of the instrument is \( 0.1\,\text{mm} \). One main scale division is equal to _____ \( \text{mm} \).

Identify the physical quantity that cannot be measured using spherometer:

Two transparent media having refractive indices \( 1.0 \) and \( 1.5 \) are separated by a spherical refracting surface of radius of curvature \( 30 \, \text{cm} \). The centre of curvature of surface is towards denser medium and a point object is placed on the principle axis in rarer medium at a distance of \( 15 \, \text{cm} \) from the pole of the surface. The distance of image from the pole of the surface is ______ \( \text{cm} \).

The radius \( (r) \), length \( (l) \) and resistance \( (R) \) of a metal wire was measured in the laboratory as
\( r = (0.35 \pm 0.05) \, \text{cm} \)
\( R = (100 \pm 10) \, \text{ohm} \)
\( l = (15 \pm 0.2) \, \text{cm} \)
The percentage error in resistivity of the material of the wire is:

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:

A silver wire has a mass \( (0.6 \pm 0.006) \, \text{g} \), radius \( (0.5 \pm 0.005) \, \text{mm} \) and length \( (4 \pm 0.04) \, \text{cm} \). The maximum percentage error in the measurement of its density will be:

The Vernier constant of Vernier calipers is \( 0.1 \, \text{mm} \) and it has zero error of \( (-0.05) \, \text{cm} \). While measuring diameter of a sphere, the main scale reading is \( 1.7 \, \text{cm} \) and coinciding Vernier division is \( 5 \). The corrected diameter will be _______ \( \times 10^{-2} \, \text{cm} \).

In an experiment to find acceleration due to gravity \( (g) \) using simple pendulum, time period of \( 0.5 \, \text{s} \) is measured from time of \( 100 \) oscillation with a watch of \( 1 \, \text{s} \) resolution. If measured value of length is \( 10 \, \text{cm} \) known to \( 1 \, \text{mm} \) accuracy. The accuracy in the determination of \( g \) is found to be \( x\% \). the value of \( x \) is:

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.

To compare EMF of two cells using potentiometer the balancing lengths obtained are \( 200 \, \text{cm} \) and \( 150 \, \text{cm} \). The least count of scale is \( 1 \, \text{cm} \). The percentage error in the ratio of EMFs is ______.

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 ________ \( \times 10^{-3} \, \text{mm} \).

The momentum of a body is increased by \( 50\% \). The percentage increase in the kinetic energy of the body is ________ \( \% \).

A screw gauge of pitch \( 0.5 \, \text{mm} \) is used to measure the diameter of uniform wire of length \( 6.8 \, \text{cm} \), the main scale reading is \( 1.5 \, \text{mm} \) and circular scale reading is \( 7 \). The calculated curved surface area of wire to appropriate significant figures is:
[Screw gauge has \( 50 \) divisions on its circular scale]

To find the spring constant \((k) \) of a spring experimentally, a student commits \( 2\% \) positive error in the measurement of time and \( 1\% \) negative error in measurement of mass. The percentage error in determining value of \( k \) is:

The diameter of a spherical bob is measured using a vernier callipers. \( 9 \) divisions of the main scale, in the vernier callipers, are equal to \( 10 \) divisions of vernier scale. One main scale division is \( 1 \, \text{mm} \). The main scale reading is \( 10 \, \text{mm} \) and \( 8^{\text{th}} \) division of vernier scale was found to coincide exactly with one of the main scale division. If the given vernier calliper has positive zero error of \( 0.04 \, \text{cm} \), then the radius of the bob is ______ \( \times 10^{-2} \, \text{cm} \) .

In an experiment to determine the resistance of a given wire using Ohm's law, the voltmeter and ammeter readings are noted as \( 10\,\mathrm{V} \) and \( 5\,\mathrm{A} \), respectively. The least counts of voltmeter and ammeter are \( 500\,\mathrm{mV} \) and \( 200\,\mathrm{mA} \), respectively. The estimated error in the resistance measurement is __________ \( \Omega \) .

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 \( x = \) ___________.

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): In Vernier Calliper if positive zero error exists, then while taking measurements, the reading taken will be more than the actual reading.
Reason (R): The zero error in Vernier Calliper might have happened due to manufacturing defect or due to rough handling.
In the light of the above statements, choose the correct answer from the options give below:

In finding out refractive index of glass slab the following observations were made through travelling microscope \( 50 \) vernier scale division \( = 49 \) MSD; \( 20 \) divisions on main scale in each \( \text{cm} \)
For mark on paper
MSR \( = 8.45 \, \text{cm} \), VC \( = 26 \)
For mark on paper seen through slab
MSR \( = 7.12 \, \text{cm} \), VC \( = 41 \)
For powder particle on the top surface of the glass slab
MSR \( = 4.05 \, \text{cm} \), VC \( = 1 \)
(MSR \( = \) Main Scale Reading, VC \( = \) Vernier Coincidence)
Refractive index of the glass slab is:

If \( Z = \frac{A^2 B^3}{C^4} \), then the relative error in \( Z \) will be:

Two resistances are given as \( R_{1} = (10 \pm 0.5)\, \Omega \) and \( R_{2} = (15 \pm 0.5)\, \Omega \). The percentage error in the measurement of equivalent resistance when they are connected in parallel is:

The period of oscillation of a simple pendulum is \( T = 2\pi\sqrt{\frac{L}{g}} \). Measured value of ‘L’ is \( 1.0 \, \text{m} \) from meter scale having a minimum division of \( 1 \, \text{mm} \) and time of one complete oscillation is \( 1.95 \, \text{s} \) measured from stopwatch of \( 0.01 \, \text{s} \) resolution. The percentage error in the determination of ‘g’ will be:

\( 10 \) divisions on the main scale of a vernier calliper coincide with \( 11 \) divisions on the Vernier scale. If each division on the main scale is of \( 5 \) units, the least count of the instrument is:

The vernier scale used for measurement has a positive zero error of \( 0.2 \, \text{mm} \). If while taking a measurement it was noted that ‘\( 0 \)’ on the vernier scale lies between \( 8.5 \, \text{cm} \) and \( 8.6 \, \text{cm} \), vernier coincidence is \( 6 \), then the correct value of measurement is ______ \( \text{cm} \). (least count = \( 0.01 \, \text{cm} \))

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JEE Main 2023 6th April Morning Shift

Two resistances are given as \( R_{1} = (10 \pm 0.5)\, \Omega \) and \( R_{2} = (15 \pm 0.5)\, \Omega \). The percentage error in the measurement of equivalent resistance when they are connected in parallel is: