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JEE Mathematics in Physics PYQs with Solutions

222 previous year questions from Mathematics in Physics (JEE Main & Advanced Physics) with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

222 questionsPhysics2002–2026Answers + solutions

About Mathematics in Physics PYQs

Mathematics in Physics has 222 previous year questions in the Quantrex Academy JEE Main & Advanced Physics bank. The 220 questions in this list come from JEE Main (147), 99 Percentile Qs Bank for JEE Main (30), Highly selective Backlog Qs for JEE Main (20) and 3 other sources, spanning 2002 to 2026. Each question opens on its own page with the options, the correct answer and the worked solution where available.

Questions by year (this list)

  • 2026: 3
  • 2025: 8
  • 2024: 20
  • 2023: 14
  • 2022: 14
  • 2021: 25
  • 2020: 8
  • 2019: 14
  • 2018: 6
  • 2017: 3
  • 2016: 3
  • 2015: 3

Mathematics in Physics questions with solutions

1

The density ρ 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 ± 0.02 g, 8.35 ± 0.05 mm and

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2

Four persons measure the length of a rod as 20.00 ~cm, 19.75 ~cm, 17.01 ~cm and 18.25 cm. The relative error in the measurement of average length of the rod is :

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3

In an experiment the values of two spring constants were measured as k_ 1 =(10 ± 0.2) N / m and k_ 2 =(20 ± 0.3) N / m . If these springs are connected in parallel, then the

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4

Length, breadth and thickness of a strip having a uniform cross section are measured to be 10.5 cm , 0.05 mm , and 6.0 μ ~m , respectively. Which of the following option(s)

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5

A quantity Q is formulated as X^ -2 Y^ +(3)/(2) Z^ -(2)/(5) · X, Y and Z are independent parameters which have fractional errors of 0.1,0.2 and 0.5 , respectively in measurement.

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6

A physical quantity C is related to four other quantities p, q, r and s as follows C= pq^2 r^3 ~s The percentage errors in the measurement of p, q, r and s are 1 \%, 2 \% 3 \% and

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7

A physical quantity Q is related to four observables a, b, c, d as follows : Q= ab ^4 ~cd where, a=(60 ± 3) Pa ; b=(20 ± 0.1) m ; c=(40 ± 0.2) Nsm^ -2 and d=(50 ± 0.1) m , then

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8

For an experimental expression y=(32.3 × 1125)/(27.4) , where all the digits are significant. Then to report the value of y we should write

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9

The energy of a system is given as E(t)=α^3 e^ -β t , where t is the time and β=0.3 ~s^ -1 . The errors in the measurement of α and t are 1.2 \% and 1.6 \% , respectively. At t=5

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10

Two particles are located at equal distance from origin. The position vectors of those are represented by A =2 i +3 n j +2 k and B =2 i -2 j +4 p k , respectively. If both the

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11

The maximum percentage error in the measurment of density of a wire is [Given, mass of wire =(0.60 ± 0.003) g radius of wire =(0.50 ± 0.01) cm length of wire =(10.00 ± 0.05) cm]

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12

The dimensions of a cone are measured using a scale with a least count of 2 ~mm . The diameter of the base and the height are both measured to be 20.0 ~cm . The maximum percentage

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13

The resultant of two vectors A and B is perpendicular to A and its magnitude is half that of B . The angle between vectors A and B is ______ ∘ .

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14

If a and b makes an angle ^ -1 ((5)/(9)) with each other, then | a + b |= 2 | a - b | for | a |=n| b | The integer value of n is ____

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15

In an expression a × 10^ b ;

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16

Young's modulus is determined by the equation given by Y=49000 m l dyn cm^2 where M is the mass and l is the extension of wire used in the experiment. Now error in Young modules

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17

Three vectors OP , OQ and OR each of magnitude A are acting as shown in figure. The resultant of the three vectors is A x . The value of x is ________ .

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18

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

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19

For three vectors A =(-x i -6 j -2 k ), B =(- i +4 j +3 k ) and C =(-8 i - j +3 k ) , if A ·( B × C )=0 , then value of x is _________

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20

A particle moves in x-y plane under the influence of a force F such that its linear momentum is p (t)= i (kt)- j (kt) . If k is constant, the angle between F and p will be :

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21

The angle between vector Q and the resultant of (2 Q +2 P ) and (2 Q -2 P ) is :

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22

Time periods of oscillation of the same simple pendulum measured using four different measuring clocks were recorded as 4.62 ~s, 4.632 ~s, 4.6 ~s and 4.64 ~s . The arithmetic mean

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23

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 Δ u and

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24

Two forces F _1 and F _2 are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to the force of larger

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25

Match List - I with List - II. List - I (Number) List - II (Signficant figure) (A) 1001 (I) 3 (B) 010 . 1 (II) 4 (C) 100 . 100 (III) 5 (D) 0 . 0010010 (IV) 6 Choose the correct

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26

The radius (r) , length (l) and resistance (R) of a metal wire was measured in the laboratory as r = (0 .35 ± 0 .05)cm , R = (100 ± 10)ohm , l = (15 ± 0 .2)cm The percentage error

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27

If two vectors → A and → B having equal magnitude R are inclined at an angle θ , then

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28

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:

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29

A vector has magnitude same as that of → A = 3 ^ j + 4 ^ j and is parallel to → B = 4 ^ i + 3 ^ j . The x and y components of this vector in first quadrant are x and 3

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30

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

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31

The resistance R = (V)/(I) , where V = ( 200 ± 5 ) V and I = ( 20 ± 0 . 2 ) A , the percentage error in the measurement of R is :

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32

In an experiment for determination of the focal length of a thin convex lens, the distance of the object from the lens is 10 ± 0 . 1cm and the distance of its real image from the

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33

A vector in x - y plane makes an angle of 30 ^ o with y -axis. The magnitude of y -component of vector is 2 3 . The magnitude of x -component of the vector will be :

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34

Three forces F _ 1 = 10N, F _ 2 = 8N, F _ 3 = 6N are acting on a particle of mass 5kg . The forces F _ 2 and F _ 3 are applied perpendicularly so that particle remains at rest. If

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35

When vector → A = 2 ^ i + 3 ^ j + 2 ^ k is subtracted from vector → B , it gives a vector equal to 2 ^ j . Then the magnitude of vector → B will be:

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36

A physical quantity P is given as P = a ^ 2 b ^ 3 c d . The percentage error in the measurement of a, b, c and d are 1 % , 2 % , 3 % and 4 % respectively. The percentage error in

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37

A cylindrical wire of mass ( 0 . 4 ± 0 . 01 ) g has length ( 8 ± 0 . 04 ) cm and radius ( 6 ± 0 . 03 ) mm . The maximum error in its density will be

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38

Two forces having magnitude A and (A)/(2) are perpendicular to each other. The magnitude of their resultant is:

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39

Two resistance are given as R _ 1 = ( 10 ± 0 . 5 ) Ω and R _ 2 = ( 15 ± 0 . 5 ) Ω . The percentage error in the measurement of equivalent resistance when they are connected in

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40

The length of a metallic wire is increased by 20 % and its area of cross-section is reduced by 4 % . The percentage change in resistance of the metallic wire is ________ .

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41

A body is moving with constant speed, in a circle of radius 10m . The body completes one revolution in 4s . At the end of 3rd second, the displacement of body (in m ) from its

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42

In an experiment of measuring the refractive index of a glass slab using travelling microscope in physics lab, a student measures real thickness of the glass slab as 5 . 25mm and

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43

If → P = 3 ^ i + 3 ^ j + 2 ^ k and → Q = 4 ^ i + 3 ^ j + 2 . 5 ^ k then, the unit vector in the direction of → P × → Q is (1)/(x) ( 3 ^ i + ^ j - 2 3 ^ k ) . The value of x is

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44

If two vectors → P = ^ i + 2m ^ j + m ^ k and → Q = 4 ^ i - 2 ^ j + m ^ k are perpendicular to each other. Then, the value of m will be

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45

Vectors a ^ i + b ^ j + ^ k and 2 ^ i - 3 ^ j + 4 ^ k are perpendicular to each other when 3a + 2b = 7 , the ratio of a to b is (x)/(2) . The value of x is _____.

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46

In an experiment to find acceleration due to gravity (g) using simple pendulum, time period of 0 . 5s is measured from time of 100 oscillation with a watch of 1s resolution. If

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47

If the projection of 2 ^ i + 4 ^ j - 2 ^ k on ^ i + 2 ^ j + α ^ k is zero. Then, the value of α will be

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48

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

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49

If → A = (2 ^ i + 3 ^ j - ^ k )m and → B = ( ^ i + 2 ^ j + 2 ^ k )m . The magnitude of component of vector → A along vector → B will be _____ m .

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50

In an experiment of determine the Young's modulus of wire of a length exactly 1m , the extension in the length of the wire is measured as 0 . 4mm with an uncertainty of ± 0 .

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51

The maximum error in the measurement of resistance, current and time for which current flows in an electrical circuit are 1 % , 2 % and 3 % respectively. The maximum percentage

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52

A person moved from A to B on a circular path as shown in figure. If the distance travelled by him is 60m , then the magnitude of displacement would be : (Given cos135 ° = - 0 . 7

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53

Two vectors → A and → B have equal magnitudes. If magnitude of → A + → B is equal to two times the magnitude of → A - → B , then the angle between → A and → B will be

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54

The distance of the Sun from earth is 1 . 5 × 10 ^ 11 m and its angular diameter is 2000 '' when observed from the earth. The diameter of the Sun will be

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55

A silver wire has a mass (0 . 6 ± 0 . 006)g , radius (0 . 5 ± 0 . 005)mm and length (4 ± 0 . 04)cm . The maximum percentage error in the measurement of its density will be

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56

For z = a ^ 2 x ^ 3 y(1)/(2) , where ' a ' is a constant. If percentage error in measurement of ' x ' and ' y ' are 4 % and 12 % , respectively, then the

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57

If Z = A ^ 2 B ^ 3 C ^ 4 , then the relative error in Z will be

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58

→ A is a vector quantity such that | → A | = non-zero constant. Which of the following expression is true for → A ?

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59

Which of the following relations is true for two unit vector ^ A and ^ B making an angle θ to each other?

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60

A student determined Young's Modulus of elasticity using the formula Y = Mg L ^ 3 4 bd ^ 3 δ . The value of g is taken to be 9 . 8m s ^ - 2 without any significant error, his

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61

Statement I: If three forces → F 1, → F 2 and → F 3 are represented by three sides of a triangle and → F _ 1 + → F _ 2 = - → F 3, then these three forces are concurrent forces and

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62

Statement-I : Two forces ( → P + → Q ) and ( → P - → Q ) where → P ⊥ → Q , when act at an angle θ _ 1 each other, the magnitude of their resultant is 3( P ^ 2 + Q ^ 2 ) , when

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63

The resultant of these forces → OP , → OQ , → OR , → OS and → OT is approximately ______ N . [Take 3 = 1 . 7, 2 = 1 . 4 Given ^ i and ^ j unit vectors along x, y axis]

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64

If the length of the pendulum in pendulum clock increases by 0 . 1 % , then the error in time per day is:

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65

The angle between vector ( → A ) and ( → A - → B ) is :

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66

The acceleration due to gravity is found up to 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

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67

The magnitude of vectors → OA , → OB and → OC in the given figure are equal. The direction of → OA + → OB - → OC with x - axis will be:

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68

A physical quantity y is represented by the formula y = m ^ 2 r ^ - 4 g ^ x l ^ - (3)/(2) If the percentage errors found in y, m, r, l and g are 18, 1, 0 . 5, 4 and p

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69

AssertionA: If A, B, C, D are four points on a semi-circular arc with a centre at O such that | → AB | = | → BC | = | → CD | . Then, → AB + → AC + → AD = 4 → AO + → OB + → OC

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70

Two vectors → X and → Y have equal magnitude. The magnitude of ( → X - → Y ) is n times the magnitude of ( → X + → Y ) . The angle between → X and → Y is :

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71

Match List I with List II. List I List II (a) → C - → A - → B = 0 (i) (b) → A - → C - → B = 0 (ii) (c) → B - → A - → C = 0 (iii) (d) → A + → B = - → C (iv) Choose the correct

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72

What will be the projection of vector → A = ^ i + ^ j + ^ k on vector → B = ^ i + ^ j ?

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73

Three particles P, Q and R are moving along the vectors → A = ^ i + ^ j , → B = ^ j + ^ k and → C = - ^ i + ^ j , respectively. They strike on a point and start to move in

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74

Three students S _ 1 , S _ 2 and S _ 3 perform an experiment for determining the acceleration due to gravity ( g ) using a simple pendulum. They use different lengths of pendulum

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75

Two vectors → P and → Q have equal magnitudes. If the magnitude of → P + → Q is n times the magnitude of → P - → Q , then angle between → P and → Q is

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76

If → A and → B are two vectors satisfying the relation → A · → B = | → A × → B | . Then the value of | → A - → B | will be:

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77

The radius of a sphere is measured to be ( 7 . 50 ± 0 . 85 ) cm . Suppose the percentage error in its volume is x . The value of x , to the nearest x , is ___ .

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78

The time period of a simple pendulum is given by T = 2π (l)/(g) . The measured value of the length of the pendulum is 10cm known to a 1mm accuracy. The time for 200 oscillations

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79

In order to determine the Young's Modulus of a wire of radius 0 . 2cm (measured using a scale of least count = 0 . 001cm ) and length 1m (measured using a scale of least count

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80

The resistance R = (V)/(I) , where V = (50 ± 2)V and I = (20 ± 0 . 2)A . The percentage error in R is x % . The value of x to the nearest integer is ________.

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81

A wire of 1Ω has a length of 1m . It is stretched till its length increases by 25 % . The percentage change in resistance to the nearest integer is :

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82

If → P × → Q = → Q × → P , the angle between → P and → Q is θ(0 ° < θ < 360 °) . The value of θ will be ___ ° .

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83

In an octagon ABCDEFGH of equal side, what is the sum of → AB + → AC + → AD + → AE + → AF + → AG + → AH , if, → AO = 2 ^ i + 3 ^ j - 4 ^ k

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84

The period of oscillation of a simple pendulum is T = 2π (L)/(g) . Measured value of L is 1 . 0m from meter scale having a minimum division of 1mm and time of one complete

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85

Two capacitors with capacitance values C _ 1 = (2000 ± 10)pF and C _ 2 = (3000 ± 15)pF are connected in series. The voltage applied across this combination is V = (5 . 00 ± 0 .

JEE Advanced 2020 Solution
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86

The density of a solid metal sphere is diameter. The maximum error in the density of the sphere is ((x)/(100)) % . If the relative errors in measuring the mass and the diameter

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87

A physical quantity z depends on four observables a, b, c and d , as z = a ^ 2 b ^ 2 / 3 c d ^ 3 . The percentage of error in the measurement of a, b, c and d are 2 % , 1 . 5 %

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88

For the four sets of three measured physical quantities as given below. Which of the following options is correct? (i) A _ 1 = 24.36, B _ 1 = 0.0724, C _ 1 = 256.2 (ii) A _ 2 =

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89

A simple pendulum is being used to determine the value of gravitational acceleration g at a certain place. The length of the pendulum is 25.0cm and a stopwatch with 1s resolution

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90

The sum of two forces → P and → Q is → R such that | → R | = | → P |. Find the angle between resultant of2 → P and → Q and → Q , ________

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91

The resultant of two vectors is perpendicular to first vector of magnitude 6N . If the resultant has magnitude 6 3 N , then magnitude of second vector is

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92

Two forces A and B whose magnitude are in the ratio 3: 5 give a resultant of 28N . If the angle of their inclination is 60 ^ ° , then the magnitude of force B will be ----- N .

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93

The area of a square is 5.29c m ^ 2 . The area of 7 such squares taking into account the significant figures is:

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94

In the density measurement of a cube, the mass and edge length are measured as (10.00 ± 0.10)kg and (0.10 ± 0.01)m, respectively. The error in the measurement of density is:

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95

Let | → A _ 1 | = 3, | → A _ 2 | = 5 and | → A _ 1 + → A _ 2 | = 5 . The value of (2 → A _ 1 + 3 → A _ 2 ) ∙ (3 → A _ 1 - 2 → A _ 2 ) is:

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96

In a simple pendulum experiment for determination of acceleration due to gravity ( g ) , time taken for 20 oscillations is measures by using a watch of 1 second least count. The

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97

Ship A is sailing towards north-east with velocity) → v = 30 ^ i + 50 ^ j km h ^ - 1 where ^ i points east and ^ j , north. The ship B is at a distance of 80km east and 150km

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98

A person standing on an open ground hears the sound of a jet aeroplane, coming from north at an angle 60 ^ o with ground level, but he finds the aeroplane right vertically above

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99

A particle moves from the point (2.0 i +4.0 j ) m, at t=0 , with an initial velocity (5.0 i +4.0 j ) ms^ -1 . It is acted upon by a constant force which produces a constant

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100

The diameter and height of a cylinder are measured by a meter scale to be 12.6 ± 0.1cm and 34.2 ± 0.1cm , respectively. What will be the value of its volume in appropriate

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101

Two vectors → A and → B have equal magnitudes. The magnitude of ( → A + → B ) is &#39; n &#39; times the magnitude of ( → A - → B ) . The angle between → A and → B is:

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102

Two forces P and Q , of magnitude 2F and 3F , respectively, are at an angle θ with each other. If the force Q is doubled, then their resultant also gets doubled. Then, the angle θ

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103

In the cube of side &#39;a&#39; shown in the figure, the vector from the central point of the face ABOD to the central point of the face BEFO will be:

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104

The position co-ordinates of a particle moving in a 3D coordinate system is given by x = acos ⁡ y = asin ⁡ and z = a The speed of the particle is:

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105

A particle is moving with a velocity → v = K(y ^ i + x ^ j ), where K is a constant. The general equation for its path is:

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106

A copper wire is stretched to make it 0.5% longer. The percentage change in its electrical resistance if its volume remains unchanged is:

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107

Paragraph: 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

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108

Let → A = ( ^ i + ^ j )and → B = ( 2 ^ i - ^ j ) . The magnitude of a coplanar vector → C such that → A . → C = → B . → C = → A . → B is given by:

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109

The percentage errors in quantities P , Q , R and S are 0 . 5 % , 1 % , 3 % and 1 . 5 % respectively in the measurement of a physical quantity A= P ^ 3 Q ^ 2 R S . The maximum

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110

The relative error in the determination of the surface area of a sphere is α . Then the relative error in the determination of its volume is

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111

The relative error in the determination of the surface area of a sphere is α . The relative error in the determination of its volume is

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112

The density of a material, in the shape of a cube, is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are 1 .

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113

A person measures the depth of a well by measuring the time interval between dropping a stone and receiving the sound of impact with the bottom of the well. The error in his

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114

A physical quantity P is described by the relation P = a ^ (1)/(2) b ^ 2 c ^ 3 d ^ - 4 . If the relative errors in the measurement of a , b , c and d respectively, are 2 % , 1 %

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115

The following observations were taken for determining surface tension T of water by capillary method: diameter of capillary, D = 1.25 × 10 ^ - 2 m rise of water, h = 1.45 × 10 ^

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116

In an experiment to determine the acceleration due to gravity g, the formula used for the time period of a periodic motion is T = 2π (7(R - r))/(5g) . The values of R and r are

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117

A thin 1m long rod has a radius of 5mm . A force of 50 π × 10 ^ 3 N is applied at one end to determine its Young&#39;s modulus. Assume that the force is exactly known. If the

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118

A student measures the time period of 100 oscillations of a simple pendulum four times. The data set is 90 s, 91 s, 95 s and 92 s. If the minimum division in the measuring clock

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119

The energy of a system as a function of time t is given as E(t) = A ^ 2 (- ) , where α = 0.2 s ^ - 1 . The measurement of A has an error of 1.25%. If the error in the measurement

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120

A vector → A is rotated by a small angle ∆ θ radians (∆ θ ≪ 1) to get a new vector → B . In that case | → B - → A | is :

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