JEE Main entrance exam Question Bank Solutions

The figure shows a small wheel fixed coaxially on a bigger one of double the radius. The system rotates about the common axis. The strings supporting A and B do not slip on the wheels. If x and y be the distances travelled by A and B in the same time interval, then ______.

A thin circular plate of mass M and radius R has its density varying as ρ(r) = ρ₀r with ρ₀ as constant and r is the distance from its center. The moment of Inertia of the circular plate about an axis perpendicular to the plate and passing through its edge is I = a MR². The value of the coefficient a is ______.

A boy's catapult is made of rubber cord which is 42 cm long, with a 6 mm diameter of cross-section and negligible mass. The boy keeps a stone weighing 0.02 kg on it and stretches the cord by 20 cm by applying a constant force. When released, the stone flies off with a velocity of 20 ms^-1. Neglect the change in the area of the cross-section of the cord while stretched. Young's modulus of rubber is closest to ______.

If at same temperature and pressure, the densities for two diatomic gases are respectively d₁ and d₂ then the ratio of velocities of sound in these gases will be ______.

A physical quantity A is dependent on other four physical quantities p, q, r and s as given below A = `sqrt("pq"/("r"^2"s"^3))`. The percentage error of measurement in p, q, r and s are 1%, 3%, 0.5% and 0.33% respectively, then the maximum percentage error in A is ______ %.

A plano convex lens has diameter of 10 cm and its thickness at the centre is 0.5 cm. Speed of light in the lens is 2 × 10⁸ ms^-1. What is the focal length of the lens?

An aeroplane, with its wings spread 10 m, is flying at a speed of 180 km/h in a horizontal direction. The total intensity of earth's field at that part is 2.5 × 10^-4 Wb/m² and the angle of dip is 60°. The emf induced between the tips of the plane wings will be ______.

Match List I with List II.

Choose the correct answer from the options given below:

The density of a material in SI unit is 128 kg m^-3. In certain units in which the unit of length is 25 cm and the unit of mass is 50 g, the numerical value of density of the material is _____.

A uniform metal rod of 2 mm² cross section is heated from 0°C to 20°C. The coefficient of linear expansion of the rod is 12 × 10^-6/°C, it's Young's modulus is 10¹¹ N/m². The energy stored per unit volume of the rod is ______.

A cubical block of mass 6 kg and side 16.1 cm is placed on a frictionless horizontal surface. It is hit by a cue at the top to impart impulse in the horizontal direction. The minimum impulse imparted to topple the block must be greater than ______ kg m/s.

If the length of a wire is made double and the radius is halved of its respective values. Then, Young's modules of the material of the wire will ______.

The force required to stretch a wire of cross section 1 cm² to double its length will be ______.

(Given Young's modulus of the wire = 2 × 10¹¹ N/m²)

A block of ice of mass 120 g at temperature 0°C is put in 300 gm of water at 25°C. The xg of ice melts as the temperature of the water reaches 0°C. The value of x is ______.

[Use: Specific heat capacity of water = 4200 Jkg^-1K^-1, Latent heat of ice = 3.5 × 10⁵ Jkg^-1]

A geyser heats water flowing at a rate of 2.0 kg per minute from 30°C to 70°C. If the geyser operates on a gas burner, the rate of combustion of fuel will be ______ g min^-1.

[Heat of combustion = 8 × 10³ Jg^-1 Specific heat of water = 4.2 Jg^-1°C^-1]

The Vernier constant of Vernier callipers is 0.1 mm and it has zero error of (-0.05) cm. While measuring the diameter of a sphere, the main scale reading is 1.7 cm and the coinciding vernier division is 5. The corrected diameter will be ______ × 10^-2 cm.

If speed V, area A and force F are chosen as fundamental units, then the dimension of Young's modulus will be :

The fractional change in the magnetic field intensity at a distance 'r' from centre on the axis of the current-carrying coil of radius 'a' to the magnetic field intensity at the centre of the same coil is ______.

(Take r < a).

A block of mass m is taken from A to B slowly under the action of a constant force R Work done by this force is ______.

A monkey of mass 20 kg rides on a 40 kg trolley moving with constant speed of 8 m/s along a horizontal track If the monkey jumps vertically to grab the overhanging branch of a tree, the speed of the trolley after the monkey has jumped off is ______.