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This mock test of Integration, Differentiation, Errors And Significant Figures Practice Level -1 for Class 11 helps you for every Class 11 entrance exam.
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QUESTION: 1

The density of a solid ball is to be determined in anexperiment. The diameter of the ball is measuredwith a screw gauge, whose pitch is 0.5 mm and thereare 50 divisions on the circular scale. The readingon the main scale is 2.5 mm and that on the circularscale is 20 divisions. If the measured mass of theball has a relative error of 2%, the relative percentageerror in the density is

Solution:

QUESTION: 2

A screw gauge gives the following reading when used to measure the diameter of a wire. Main scale reading : 0 mm

Circular scale reading: 52 division

Given that 1 mm on the main scale corresponds to 100 divisions of the circular scale. The diameter of wire from the above data is

Solution:

Least count of screw gauge =1/100 mm = 0.01 mn

Diameter - Divisions on cirular scale × least count + main scale reading = 52 × 1/100 + 0

100 = 0.52 mm

diameter = 0.052 cm

QUESTION: 3

The mass and volume of a body are found to be 5.00 ± 0.05 kg and 1.00 ± 0.05 m3 respectively. Then themaximum possible percentage error in its density is

Solution:

*Multiple options can be correct

QUESTION: 4

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

Solution:

QUESTION: 5

A vernier callipers has 1 mm marks on the mainscale. It has 20 equal divisions on the vernier scalewhich match with 16 main scale divisions. For thisvernier callipers, the least count is

Solution:

QUESTION: 6

The respective number of significant figures for thenumbers 23.02310.0003 and 2.1 x 10^{-3} are ‘

Solution:

*Multiple options can be correct

QUESTION: 7

A student performed the experiment of determinationof focal length of a concave mirror by u-v methodusing an optical bench of length 1.5 m. The focallength of the mirror used is 24 cm. The maximumerror in the location of the image can be 0.2 cm.The 5 sets of (u, v) values recorded by the student(in cm) are : (42, 56), (48, 48),(60, 40), (66, 33),(78, 39). The data set(s) that cannot come fromexperiment and is (are) incorrectly recorded, is (are)

Solution:

QUESTION: 8

In an experiment the angles are required to bemeasured using an instrument. 29 divisions of the main scale exactly coincide with the 30 divisions ofthe vernier scale. If the smallest division of the mainscale is half-a-degree (=05°), then the least count of the instrument is

Solution:

QUESTION: 9

The percentage errors in the measurement of lengthand’ time period of a simple pendulum are 1% and2% respectively. Then the maximum error in themeasurement of acceleration due to gravity is

Solution:

QUESTION: 10

If 3.8 x 10^{-6} is added to 4.2 x 10^{-5} giving due regard tosignificant figures, then the result will be

Solution:

QUESTION: 11

The number of significant figures in the numbers4.8000 xl0^{4} and 48000.50 are respectively

Solution:

QUESTION: 12

A student has measured the length of a wire equalto 0.04580 m. This value of length has the number ofsignificant figure is equal to :

Solution:

QUESTION: 13

Students I, II and III perform an experiment for measuringthe acceleration due to gravity (g) using a simplependulum. They use different lengths of the pendulumand/or record time for different number of oscillations.The observations are shown in the table.Least count for length = 0.1 cm.Least count for time = 0.1 s.If E_{I}, E_{II} and E_{III} are the percentage errors in g, i e,g for students I, II and III respectively.

Solution:

QUESTION: 14

A body of mass m = 3.513 kg is moving along thex-axis with a speed of 5.00 ms^{-1}. The magnitude of itsmomentum is recorded as

Solution:

QUESTION: 15

Two full turns of the circular scale of a screw gaugecover a distance of 1 mm on its main scale. The totalnumber of divisions on the circular scale is 50. Further,it is found that the screw gauge has a zero error of -0.03 mm. While measuring the diameter of a thin wire,a student notes the main scale reading of 3 mm andthe number of circular scale divisions in line with themain scale as 35. The diameter of the wire is

Solution:

QUESTION: 16

If voltage V = (100 ± 5) volt and current I = (10 ± 0.2) A,the percentage error in resistance R is

Solution:

QUESTION: 17

A student performs an experiment to determine theYoung’s modulus of a wire, exactly 2 m long, bySearle’s method. In a particular reading, the studentmeasures the extension in the length of the wire to be0.8 mm with an uncertainty of ± 0.05 mm at a load ofexactly 1.0 kg. The student also measures thediameter of the wire to be 0.4 mm ‘with an uncertaintyof ± 0.01 mm. Take g = 9.8ms^{-2} (exact). The Young’smodulus obtained from the reading is

Solution:

QUESTION: 18

The values of two resistors are R_{1} = (6 ± 0.3) k Ω and R_{2} =(10 ± 0.2) kΩ .The percentage error in theequivalent resistance when they are connected inparallel is

Solution:

QUESTION: 19

A physical quantity A is related to four observablesa, b, c and d as follows

The percentage errors of measurement in a, b, c andd are 1%, 3%, 2% and 2% respectively. What is thepercentage error in the quantity A ?

Solution:

QUESTION: 20

A student performs an experiment for determination of

and he commits an error of Δi . ForT he takes the time of n oscillations with the stop watchof least count Δ T and he commits a human error of 0.1 s. For which of the following data, the measurementof g will be most accurate?

Solution:

QUESTION: 21

The circular scale of a screw gauge has 50 divisionsand pitch of 0.5 mm. Find the diameter of sphere. Mainscale reading is 2.

Solution:

QUESTION: 22

If error in radius is 3%, what is error in volume of sphere?

Solution:

QUESTION: 23

The length of a simple pendulum is about 100 cm knownto an accuracy of 1 mm. Its period of oscillation is 2sdetermined by measuring the time for 100 oscillationsusing a clock of 0.1 s resolution. What is theaccuracy in the determined value of g ?

Solution:

QUESTION: 24

A physical quantity is given by Thepercentage error in measurement of M, L and T are α, ß and γ respectively. Then, the maximum % error inthe quantity X is

Solution:

QUESTION: 25

If the length of a rectangle i = 10.5 cm, breadth b = 2.1 cm and minimum possible measurement byscale = 0.1 cm, then the area is

Solution:

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