JEE Main 2026 · 6 Apr 2026 Shift 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 20.20 ± 0.02 mm, respectively. Calculated percentage fractional error in ρ is ________.

1. A0.63%
2. B0.82%
3. C0.72%
4. D0.25%

The potential energy of a particle changes with distance x from a fixed origin as V = A√x/(x + B), where A and B are constant with appropriate dimensions. The dimensions of AB are ________.

1. A[M¹ L⁵ᐟ² T⁻²]
2. B[M³ᐟ² L⁵ᐟ² T⁻²]
3. C[M¹ L² T⁻²]
4. D[M¹ L⁷ᐟ² T⁻²]

The rain drop of mass 1 g, starts with zero velocity from a height of 1 km. It hits the ground with a speed of 5 m/s. The work done by the unknown resistive force is ________ J. (take g = 10 m/s²)

1. A− 8.75
2. B− 8.35
3. C− 9.55
4. D− 9.98

A lift of mass 1600 kg is supported by thick iron wire. If the maximum stress which the wire can withstand is 4 × 10⁸ N/m² and its radius is 4 mm, then maximum acceleration the lift can take is ______ m/s². (take g = 10 m/s² and π = 3.14)

1. A2.56
2. B3.89
3. C4.32
4. D5.16

A solid sphere of radius 4 cm and mass 5 kg is rotating (rotation axis is passing through the centre of the sphere) with an angular velocity of 1200 rpm. It is brought to rest in 10 s by applying a constant torque. The torque applied and the number of rotations it made before it comes to rest are ______ and ______ respectively.

1. A0.128 π Nm, 100
2. B0.0128 π Nm, 50
3. C0.128 π Nm, 50
4. D0.0128 π Nm, 100

The two wires A and B of equal cross-section but of different materials are joined together. The ratio of Young's modulus of wire A and wire B is 20/11. When the joined wire is kept under certain tension the elongations in the wires A and B are equal. If the length of wire A is 2.2 m, then the length of wire B is ________ m.

1. A1.1
2. B2.22
3. C1.21
4. D4.44

Two closed vessels of same volume are joined through a narrow tube and both vessels are filled with air of pressure 90 kPa and temperature 400 K. Keeping the temperature of one vessel constant at 400 K the second vessel temperature is raised to 500 K. The final pressure in the vessels is ________ kPa.

1. A100
2. B120
3. C90
4. D105

In interference experiment the path difference between two interfering waves at a point A on the screen is λ/3, where λ is the wavelength of these waves, and at another point B the path difference is λ/6. The ratio of intensities at points A and B is ________.

1. A3
2. B4
3. C1/3
4. D1/4