JEE Main 2026 · 4 Apr 2026 Shift 1

In a screw gauge when the circular scale is given five complete rotations it moves linearly by 2.5 mm. If the circular scale has 100 divisions, the least count of screw gauge is ________ mm.

1. A1 × 10⁻²
2. B1 × 10⁻³
3. C5 × 10⁻²
4. D5 × 10⁻³

The increase in the pressure required to decrease the volume (ΔV) of water is 6.3 × 10⁷ N/m². The percentage decrease in the volume is _______. (Bulk modulus of water = 2.1 × 10⁹ N/m².)

1. A2 %
2. B3 %
3. C6 %
4. D4 %

The time taken by a block of mass m to slide down from the highest point to the lowest point on a rough inclined plane is 50 % more compared to the time taken by the same block on identical inclined smooth plane. Both inclined planes are at 45° with the horizontal. The coefficient of kinetic friction between the rough inclined surface and block is ________.

1. A3/4
2. B2/3
3. C5/9
4. D4/9

Two nuclei of mass number 3 combine with another nucleus of mass number 4 to yield a nucleus of mass number 10. If the binding energy per nucleon for the mass numbers 3, 4 and 10 are 5.6 MeV, 7.4 MeV and 6.1 MeV, respectively, then in the process, ΔMc² = ______ MeV.

1. A6.9
2. B7.9
3. C2.2
4. D4.3

A solid sphere of mass M and radius R is divided into two unequal parts. The smaller part having mass M/8 is converted into a sphere of radius r and the larger part is converted into a circular disc of thickness t and radius 2R. If I₁ is moment of inertia of a sphere having radius r about an axis through its centre and I₂ is the moment of inertia of a disc about its diameter, the ratio of their moment of inertia I₂/I₁ = ______.

1. A35
2. B70
3. C140
4. D210

The two projectiles are projected with the same initial velocities at the 15° and 30° with respect to the horizontal. The ratio of their ranges is 1:x. The value of x is

1. A√2
2. B√3
3. C2√3
4. D1/√2

A slit of width a is illuminated by light of wavelength λ. The linear separation between 1st and 3rd minima in the diffraction pattern produced on a screen placed at a distance D from the slit system is __________.

1. ADλ/a
2. B1.5 Dλ/a
3. C2Dλ/a
4. D3Dλ/a

A string A of length 0.314 m and Young's modulus 2 × 10¹⁰ N/m² is connected to another string B of length and Young's modulus both twice of those of A. This series combination of strings is then suspended from a rigid support and its free end is fixed to a load of mass 0.8 kg. The net change in length of the combination is ________ mm. (radius of both the strings is 0.2 mm and acceleration due to gravity =10 m/s²) (Mass of both strings is to be neglected as compared to the mass of load)

1. A3
2. B2
3. C1.9
4. D1