JEE Main entrance exam Question Bank Solutions

In Bohr's atomic model of hydrogen, let K. P and E are the kinetic energy, potential energy and total energy of the electron respectively. Choose the correct option when the electron undergoes transitions to a higher level:

According to Bohr atom model, in which of the following transitions will the frequency be maximum?

The electron in a hydrogen atom first jumps from the third excited state to the second excited state and subsequently to the first excited state. The ratio of the respective wavelengths, λ₁/λ₂, of the photons emitted in this process is ______. 

The energy required to remove the electron from a singly ionized Helium atom is 2.2 times the energy required to remove an electron from Helium atom. The total energy required to ionize the Helium atom completely is ______. 

Orbits of a particle moving in a circle are such that the perimeter of the orbit equals an integer number of de-Broglie wavelengths of the particle. For a charged particle moving in a plane perpendicular to a magnetic field, the radius of the n^th orbital will therefore be proportional to:

If 13.6 eV energy is required to ionize the hydrogen atom, then the energy required to remove an electron from n = 2 is ______.

A transmitting antenna has a height of 320 m and that of receiving antenna is 2000 m. The maximum distance between them for satisfactory communication in line of sight mode is 'd'. The value of 'd' is ______ km.

A cyclic process ABCA is shown in the V-T diagram. A process on the P-V diagram is ______.

A 100 eV electron collides with a stationary helium ion (He⁺) in its ground state and exits to a higher level. After the collision, He⁺ ions emit two photons in succession with wavelengths 1085 Å and 304 Å. The energy of the electron after the collision will be ______ eV.

Given h = 6.63 × 10^-34 Js.

A balloon has mass of 10 g in air. The air escapes from the balloon at a uniform rate with velocity 4.5 cm/s. If the balloon shrinks in 5 s completely. Then, the average force acting on that balloon will be (in dyne).

This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements.

Statement 1: If you push on a cart being pulled by a horse so that it does not move, the cart pushes you back with an equal and opposite force.

Statement 2: The cart does not move because the force described in statement 1 cancel each other.

A cylindrical container of volume 4.0 × 10^-3 m³ contains one mole of hydrogen and two moles of carbon dioxide. Assume the temperature of the mixture is 400 K. The pressure of the mixture of gases is ______.

[Take gas constant as 8.3 J mol^-1 K^-1]

The photocurrent in an experiment on photoelectric effect increases if ______.

A spherical shell of 1 kg mass and radius R is rolling with angular speed ω on horizontal plane (as shown in figure). The magnitude of angular momentum of the shell about the origin O is `a/3 R^2` ω. The value of a will be:

A person whose mass is 100 kg travels from Earth to Mars in a spaceship. Neglect all other objects in the sky and take acceleration due to gravity on the surface of the Earth and Mars as 10 m/s² and 4 m/s² respectively. Identify from the below figures, the curve that fits best for the weight of the passenger as a function of time.

Region I and II are separated by a spherical surface of a radius of 25 cm. An object is kept in the region I at a distance of 40 cm from the surface. The distance of the image from the surface is ______.

An audio signal v_m = 20sin2π(1500t) amplitude modulates a carrier v_c = 80 sin 2π (100,000t). The value of percent modulation is ______.

An amplitude-modulated wave is represented by C_m(t) = 10(1 + 0.2 cos 12560t) × sin (111 × 10⁴t) volts. The modulating frequency in kHz will be ______.

An electric fan has blades of length 30 cm as measured from the axis of rotation. If the fan is rotating at 1200 r.p.m. The acceleration of a point on the tip of the blade is about:

A rod of mass 'm' hinged at one end is free to rotate in a horizontal plane. A small bullet of mass m/4 travelling with speed 'u' hits the rod and attaches to it at its centre. Find the angular speed of rotation of rod just after the bullet hits the rod 3. [take length of the rod as 'l']