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Mathematics in Physics — JEE Main & Advanced Physics PYQs

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

222 questionsPhysicsSolutions on every page
1

The density 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 20.20 0.02

JEE Main 2026 Solution View → 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 :

JEE Main 2026 Solution View → 3

In an experiment the values of two spring constants were measured as k₁=(10 0.2) N / m and k₂=(20 0.3) N / m . If these springs are connected in parallel, then the percentage error

JEE Main 2026 Solution View → 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 ~m , respectively. Which of the following option(s) give(s) t

JEE Advanced 2025 Solution View → 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. The max

JEE Main 2025 Solution View → 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 %

JEE Main 2025 Solution View → 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 the per

JEE Main 2025 Solution View → 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

JEE Main 2025 Solution View → 9

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

JEE Main 2025 Solution View → 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 vect

JEE Main 2025 Solution View → 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 ]

JEE Main 2025 Solution View → 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

JEE Advanced 2024 Solution View → 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 ______ .

JEE Main 2024 Solution View → 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 ____

JEE Main 2024 Solution View → 15

In an expression a 10^ b ;

JEE Main 2024 Solution View → 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

JEE Main 2024 Solution View → 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 ________ .

JEE Main 2024 Solution View → 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 perce

JEE Main 2024 Solution View → 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 _________

JEE Main 2024 Solution View → 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 :

JEE Main 2024 Solution View → 21

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

JEE Main 2024 Solution View → 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 mea

JEE Main 2024 Solution View → 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 u and

JEE Main 2024 Solution View → 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 magnitude. T

JEE Main 2024 Solution View → 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 ans

JEE Main 2024 Solution View → 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 in resist

JEE Main 2024 Solution View → 27

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

JEE Main 2024 Solution View → 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:

JEE Main 2024 Solution View → 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 respectively

JEE Main 2024 Solution View → 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, the

JEE Main 2024 Solution View → 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 :

JEE Main 2024 Solution View → 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 . 1 cm and the distance of its real image from

JEE Advanced 2023 Solution View → 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 :

JEE Main 2023 Solution View → 34

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

JEE Main 2023 Solution View → 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:

JEE Main 2023 Solution View → 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 the

JEE Main 2023 Solution View → 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

JEE Main 2023 Solution View → 38

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

JEE Main 2023 Solution View → 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 c

JEE Main 2023 Solution View → 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 _ _ _ _ _ _ _ _ .

JEE Main 2023 Solution View → 41

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

JEE Main 2023 Solution View → 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 . 25 mm and

JEE Main 2023 Solution View → 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 ^ )

JEE Main 2023 Solution View → 44

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

JEE Main 2023 Solution View → 45

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

JEE Main 2023 Solution View → 46

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

JEE Main 2022 Solution View → 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

JEE Main 2022 Solution View → 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 acc

JEE Main 2022 Solution View → 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 .

JEE Main 2022 Solution View → 50

In an experiment of determine the Young's modulus of wire of a length exactly 1 m , the extension in the length of the wire is measured as 0 . 4 mm with an uncertainty of &#177

JEE Main 2022 Solution View → 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 err

JEE Main 2022 Solution View → 52

A person moved from A to B on a circular path as shown in figure. If the distance travelled by him is 60 m , then the magnitude of displacement would be : (Given cos 135 ° = -

JEE Main 2022 Solution View → 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 betwe

JEE Main 2022 Solution View → 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

JEE Main 2022 Solution View → 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

JEE Main 2022 Solution View → 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 percentag

JEE Main 2022 Solution View → 57

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

JEE Main 2022 Solution View → 58

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

JEE Main 2022 Solution View → 59

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

JEE Main 2022 Solution View → 60

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

JEE Main 2021 Solution View → 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

JEE Main 2021 Solution View → 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 result

JEE Main 2021 Solution View → 63

The resultant of these forces O P → , O Q → , O R → , O S → and O T → is approximately ______ N . [Take 3 = 1 . 7 , 2 = 1 . 4 Given i ^ and j ^ unit v

JEE Main 2021 Solution View → 64

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

JEE Main 2021 Solution View → 65

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

JEE Main 2021 Solution View → 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 i

JEE Main 2021 Solution View → 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:

JEE Main 2021 Solution View → 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 respectively, then

JEE Main 2021 Solution View → 69

Assertion A : If A , B , C , D are four points on a semi-circular arc with a centre at O such that | A B → | = | B C → | = | C D → | . Then, A B → + A C &#8

JEE Main 2021 Solution View → 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 &#8

JEE Main 2021 Solution View → 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 (ii

JEE Main 2021 Solution View → 72

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

JEE Main 2021 Solution View → 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

JEE Main 2021 Solution View → 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

JEE Main 2021 Solution View → 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 &#8594

JEE Main 2021 Solution View → 76

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

JEE Main 2021 Solution View → 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 ___ .

JEE Main 2021 Solution View → 78

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

JEE Main 2021 Solution View → 79

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

JEE Main 2021 Solution View → 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 ________.

JEE Main 2021 Solution View → 81

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

JEE Main 2021 Solution View → 82

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

JEE Main 2021 Solution View → 83

In an octagon A B C D E F G H of equal side, what is the sum of A B → + A C → + A D → + A E → + A F → + A G → + A H → , if, AO → = 2

JEE Main 2021 Solution View → 84

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

JEE Main 2021 Solution View → 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 ±

JEE Advanced 2020 Solution View → 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 are 6 . 0

JEE Main 2020 Solution View → 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 % , 4 %

JEE Main 2020 Solution View → 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 i i A 2 = 24.44 , B 2

JEE Main 2020 Solution View → 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 25.0 c m and a stopwatch with 1 s resolutio

JEE Main 2020 Solution View → 90

The sum of two forces P → and Q → is R → such that R → = P → . Find the angle between resultant of 2 P → and Q → and Q → , ________

JEE Main 2020 Solution View → 91

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

NTA Abhyas JEE Main 2020 Solution View → 92

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

NTA Abhyas JEE Main 2020 Solution View → 93

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

JEE Main 2019 Solution View → 94

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

JEE Main 2019 Solution View → 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:

JEE Main 2019 Solution View → 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 me

JEE Main 2019 Solution View → 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 80 k m east and 150 k

JEE Main 2019 Solution View → 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 his

JEE Main 2019 Solution View → 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 accele

JEE Main 2019 Solution View → 100

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

JEE Main 2019 Solution View → 101

Two vectors A → and B → have equal magnitudes. The magnitude of A → + B → is ' n ' times the magnitude of A → - B → . The angle between

JEE Main 2019 Solution View → 102

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

JEE Main 2019 Solution View → 103

In the cube of side 'a' shown in the figure, the vector from the central point of the face A B O D to the central point of the face B E F O will be:

JEE Main 2019 Solution View → 104

The position co-ordinates of a particle moving in a 3 D coordinate system is given by x = a cos ⁡ ω t y = a sin ⁡ ω t and z = a ω t The speed of the part

JEE Main 2019 Solution View → 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:

JEE Main 2019 Solution View → 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:

JEE Main 2019 Solution View → 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 s

JEE Advanced 2018 Solution View → 108

Let A → = i ^ + j ^ a n d B → = ( 2 i ^ - j ^ ) . The magnitude of a coplanar vector C → such that A → . C → = B → . C → = A → . B &

JEE Main 2018 Solution View → 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 percenta

JEE Main 2018 Solution View → 110

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

JEE Main 2018 Solution View → 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

JEE Main 2018 Solution View → 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 .

JEE Main 2018 Solution View → 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 measur

JEE Advanced 2017 Solution View → 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 % , 3 % and 5 %

JEE Main 2017 Solution View → 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 ×

JEE Main 2017 Solution View → 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 = 2 π 7 R - r 5 g . The values of R and r are m

JEE Advanced 2016 Solution View → 117

A thin 1 m long rod has a radius of 5 mm . A force of 50 π×10 3 N is applied at one end to determine its Young's modulus. Assume that the force is exactly known. If t

JEE Main 2016 Solution View → 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 is

JEE Main 2016 Solution View → 119

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

JEE Advanced 2015 Solution View → 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 :

JEE Main 2015 Solution View →
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