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JEE Physics and Mathematics PYQs with Solutions

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

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About Physics and Mathematics PYQs

Physics and Mathematics has 74 previous year questions in the Quantrex Academy JEE Main & Advanced Physics bank. The 74 questions in this list come from Concepts Of Physics MCQ Edition [Volume 1] (74). Each question opens on its own page with the options, the correct answer and the worked solution where available.

JEE Physics and Mathematics PYQs with Solutions

About Physics and Mathematics PYQs

Physics and Mathematics questions with solutions

Consider two vectors A and B , each having a magnitude of 10 unit. If these vectors are inclined to the X-axis at angles of 30^ ^ ^ ∘ and 60^ ^ ^ ∘ respectively, determine their

Vector A has a magnitude of 3 m and is directed at an angle of 20^ ^ ^ ∘ to the X-axis, while vector B has a magnitude of 4 m and is directed at 110^ ^ ^ ∘ to the X-axis.

Given the vectors a = 4 i + 3 j and b = 3 i + 4 j , evaluate the magnitude of a .

Consider the vectors a = 4 i + 3 j and b = 3 i + 4 j . Calculate the magnitude of b .

Suppose two vectors are given by a = 4 i + 3 j and b = 3 i + 4 j . Compute the magnitude of a + b .

Two vectors are defined as a = 4 i + 3 j and b = 3 i + 4 j . Determine the magnitude of a - b .

Determine the sum of vectors A , B , and C , each possessing a magnitude of 100 units and inclined to the X-axis at angles of 45^ ^ ^ ∘ , 135^ ^ ^ ∘ , and 315^ ^ ^ ∘ respectively.

Based on the figure, determine the x and y components of the resultant of OA , BC and DE .

Based on the figure, determine the magnitude of the resultant of OA , BC and DE .

Based on the figure, determine the angle that the resultant of OA , BC and DE makes with the X-axis.

Two vectors have magnitudes of 3 unit and 4 unit, respectively. Determine the angle between them if the magnitude of the resultant is 1 unit.

Two vectors have magnitudes of 3 unit and 4 unit, respectively. Determine the angle between them if the magnitude of the resultant is 5 unit.

Two vectors have magnitudes of 3 unit and 4 unit, respectively. Determine the angle between them if the magnitude of the resultant is 7 unit.

A surveillance report concerning a suspected car details the following: 'The car travelled 2.00 km towards east, executed a perpendicular left turn, proceeded for 500 m , executed

A carrom board ( 4 ft × 4 ft square) features the queen at its centre. The queen is struck by the striker, travels to the front edge, rebounds, and goes into the hole behind the

A carrom board ( 4 ft × 4 ft square) features the queen at its centre. The queen is struck by the striker, travels to the front edge, rebounds, and goes into the hole behind the

A mosquito net positioned over a 7 ft × 4 ft bed has a height of 3 ft . A mosquito enters the net through a hole located at one of the bed's corners. It then flies to and settles

A mosquito net positioned over a 7 ft × 4 ft bed has a height of 3 ft . A mosquito enters the net through a hole located at one of the bed's corners. It then flies to and settles

Let a be a vector of magnitude 4.5 unit pointing due north. Evaluate the vector 3 a .

Let a be a vector of magnitude 4.5 unit pointing due north. Evaluate the vector -4 a .

Two vectors possess magnitudes of 2 m and 3 m . The angle between them is 60^ ^ ^ ∘ . Determine the magnitude of their vector product.

Two vectors possess magnitudes of 2 m and 3 m . The angle between them is 60^ ^ ^ ∘ . Determine the scalar product of the two vectors.

A carrom board ( 4 ft × 4 ft square) features the queen at its centre. The queen is struck by the striker, travels to the front edge, rebounds, and goes into the hole behind the

Let A_1 A_2 A_3 A_4 A_5 A_6 A_1 represent a regular hexagon, as shown in the figure. The six sides, taken in sequence, represent six vectors. By utilizing the x-components of

Determine the value of A · ( A × B ) .

Consider the vectors a = 2 i + 3 j + 4 k and b = 3 i + 4 j + 5 k . Determine the angle between these vectors.

Given the vectors A = 2 i + 3 j + 4 k and B = 4 i + 3 j + 2 k , determine the cross product A × B .

Given that the vectors A , B , and C are mutually perpendicular, evaluate C × ( A × B ) and determine whether the converse holds true.

A particle travels on a given straight line with a constant speed v . At a certain time, it is at a point P on its straight line path. O is a fixed point. The quantity OP × v is

The force acting on a charged particle due to electric and magnetic fields is expressed as F = q E + q v × B . Suppose E is directed along the X-axis and B is along the Y-axis. In

Identify an example where A · B = C · B while A ≠ C .

Construct a graph from the following data and consider tangents drawn at x = 2, 4, 6 , and 8 . Identify the correct equation of the curve and the expression for the slope of the

A curve is described by y = x . Determine the approximate change in y if x varies from (π)/(3) to (π)/(3) + (π)/(100) .

In a charging R – C circuit, the electric current is given by i = i_0 e^ -t/RC , where i_0 , R , and C are constant parameters of the circuit and t represents time. Determine the

In a charging R – C circuit, the electric current is given by i = i_0 e^ -t/RC , where i_0 , R , and C are constant parameters of the circuit and t represents time. Determine the

In a charging R – C circuit, the electric current is given by i = i_0 e^ -t/RC , where i_0 , R , and C are constant parameters of the circuit and t represents time. Determine the

In a discharging R – C circuit, the electric current is given by i = i_0 e^ -t/RC , where i_0 , R and C denote constant parameters and t represents time. If i_0 = 2.00 A , R =

In a discharging R – C circuit, the electric current is given by i = i_0 e^ -t/RC , where i_0 , R and C denote constant parameters and t represents time. If i_0 = 2.00 A , R =

In a discharging R – C circuit, the electric current is given by i = i_0 e^ -t/RC , where i_0 , R and C denote constant parameters and t represents time. If i_0 = 2.00 A , R =

Determine the area bounded by the curve y = 3x^2 + 6x + 7 and the X-axis between the ordinates x = 5 and x = 10 .

Determine the area enclosed by the curve y = x and the X-axis between x = 0 and x = π .

Determine the area bounded by the curve y = e^ -x , the X-axis and the Y-axis.

A rod of length L is positioned along the X-axis between x = 0 and x = L . The linear density (mass/length) ρ of the rod varies with the distance x from the origin as ρ = a + bx .

A rod of length L is positioned along the X-axis between x = 0 and x = L . The linear density (mass/length) ρ of the rod varies with the distance x from the origin as ρ = a + bx .

For a particle, the momentum p varies with time t such that (dp)/(dt) = (10 N) + (2 N/s)t . Assuming the momentum is zero at t = 0 , determine the momentum at t = 10 s .

The relationship between the changes in a function y and an independent variable x is given by (dy)/(dx) = x^2 . Determine y as a function of x .

Determine the number of significant digits in the value 1001 .

Determine the number of significant digits in the value 0.001001 .

Determine the number of significant digits in the value 100.10 .

Determine the number of significant digits in the value 100.1 .

A metre scale is graduated at every millimetre. How many significant digits can be present in a length measurement made with this scale?

Round the value 3472 off to 2 significant digits.

Round the value 84.16 off to 2 significant digits.

Using a slide callipers, the length and radius of a cylinder are measured as 4.54 cm and 1.75 cm , respectively. Compute the volume of the cylinder.

Round the value 2.55 off to 2 significant digits.

At three different locations, the thickness of a glass plate is measured as 2.17 mm , 2.17 mm , and 2.18 mm . Determine the average thickness of the plate from this data.

Round the value 28.5 off to 2 significant digits.

Using a metre scale, the length of the string of a simple pendulum is measured to be 90.0 cm . Measurements with a slide callipers determine the radius of the bob plus the length

Suppose the resultant of vectors A and B makes an angle α with A and an angle β with B . It follows that

Which of the following sets could represent the magnitudes of three vectors that sum to zero?

A vector remains unaltered provided that

A component of a vector is

A vector A is directed vertically upward and a vector B is directed towards north. The vector product A × B is

The radius of a circle is given as 2.12 cm . Its area must be expressed as

A physical scenario can be described by employing various sets of coordinate axes that are oriented differently. Which among the following do not depend on the orientation of

Suppose the angle between two nonzero vectors A and B is 120^ ^ ^ ∘ , and let their resultant be C .

For the resultant of several vectors, its x-component

For two vectors A and B , the magnitude of their vector product can be

Suppose C = A + B .

Suppose C = A + B .

A physical scenario can be described by employing various sets of coordinate axes that are oriented differently. Which among the following do not depend on the orientation of

For the resultant of several vectors, its x-component

Suppose the angle between two nonzero vectors A and B is 120^ ^ ^ ∘ , and let their resultant be C .

For two vectors A and B , the magnitude of their vector product can be

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