JEE Main 2024 · 31 Jan 2024 Shift 1

A force is represented by F = ax² + bt¹⁄² where x = distance and t = time. The dimensions of b²/a are:

1. A[MLT⁻²]
2. B[ML⁻¹T⁻¹]
3. C[ML²T⁻³]
4. D[ML³T⁻³]

The relation between time 't' and distance 'x' is t = αx² + βx, where α and β are constants. The relation between acceleration (a) and velocity (v) is :

1. Aa = −2αv³
2. Ba = −3αv²
3. Ca = −4αv⁴
4. Da = −5αv⁵

A coin is placed on a disc. The coefficient of friction between the coin and the disc is μ. If the distance of the coin from the center of the disc is r, the maximum angular velocity which can be given to the disc, so that the coin does not slip away, is :

1. Aμg/r
2. B√(μg/r)
3. C√(r/μg)
4. Dμ/√(rg)

An artillery piece of mass M₁ fires a shell of mass M₂ horizontally. Instantaneously after the firing, the ratio of kinetic energy of the artillery and that of the shell is:

1. AM₁/M₂
2. BM₂/M₁
3. CM₁/(M₁ + M₂)
4. DM₂/(M₁ + M₂)

Four identical particles of mass m are kept at the four corners of a square. If the gravitational force exerted on one of the masses by the other masses is ((2√2 + 1)/32) Gm²/L², the length of the sides of the square is

1. AL/2
2. B4L
3. C2L
4. D3L

The parameter that remains the same for molecules of all gases at a given temperature is :

1. Amass
2. Bspeed
3. Cmomentum
4. Dkinetic energy

Two conductors have the same resistances at 0°C but their temperature coefficients of resistance are α₁ and α₂. The respective temperature coefficients for their series and parallel combinations are :

1. A(α₁ + α₂)/2, (α₁ + α₂)/2
2. B(α₁ + α₂)/2, α₁ + α₂
3. Cα₁ + α₂, (α₁ + α₂)/2
4. Dα₁ + α₂, α₁α₂/(α₁ + α₂)

A coil is places perpendicular to a magnetic field of 5000 T. When the field is changed to 3000 T in 2 s, an induced emf of 22 V is produced in the coil. If the diameter of the coil is 0.02 m, then the number of turns in the coil is:

1. A7
2. B140
3. C35
4. D70