AIPMT-MAINS Questions

The dimensions of (μ₀ε₀)⁻¹/² are :

A stone is dropped from a height h. It hits the ground with a certain momentum P. If the same stone is dropped from a height 100% more than the previous height, the momentum when it hits the ground will change by :

A car of mass m is moving on a level circular track of radius R. If μₛ represents the static friction between the road and tyres of the car, the maximum speed of the car in circular motion is given by :

A car of mass m starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude P₀. The instantaneous velocity of this car is proportional to :

A circular platform is mounted on a frictionless vertical axle. Its radius R = 2m and its moment of inertia about the axle is 200 kgm². It is initially at rest. A 50 kg man stands on the edge of the platform and begins to walk along the edge at the speed of 1ms⁻¹ relative to the ground. Time taken by the man to complete one revolution is:

The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through:

Three masses are placed on the x-axis: 300 g at origin, 500 g at x = 40 cm and 400 g at x = 70 cm. The distance of the centre of mass from the origin is:

If vₑ is escape velocity and v₀ is orbital velocity of a satellite for orbit close to the earth’s surface, then these are related by:

Which one of the following plots represents the variation of gravitational field on a particle with distance r due to a thin spherical shell of radius R? (r is measured from the centre of the spherical shell)

A slab of stone of area 0.36 m² and thickness 0.1 m is exposed on the lower surface to steam at 100°C. A block of ice at 0°C rests on the upper surface of the slab. In one hour 4.8 kg of ice is melted. The thermal conductivity of slab is: (Given latent heat of fusion of ice = 3.36 × 10⁵ J kg⁻¹)

An ideal gas goes from state A to state B via three different processes as indicated in the P⁻V diagram: If Q₁, Q₂, Q₃ indicate the heat a absorbed by the gas along the three processes and ΔU₁, ΔU₂, ΔU₃ indicate the change in internal energy along the three processes respectively, then

The equation of a simple harmonic wave is given by y = 3 sin(π/2 (50t - x)). Where x and y are in meters and t is in seconds. The ratio of maximum particle velocity to the wave velocity is

A train moving at a speed of 220 ms⁻¹ towards a stationary object, emits a sound of frequency 1000 Hz. Some of the sound reaching the object gets reflected back to the train as echo. The frequency of the echo as detected by the train is: (speed of sound in air is 330 ms⁻¹)

A parallel plate capacitor has a uniform electric field E in the space between the plates. If the distance between the plates is d and area of each plate is A, the energy stored in the capacitor is:

Two metallic spheres of radii 1 cm and 3 cm are given charges of −1×10⁻² C and 5×10⁻² C, respectively. If these are connected by a conducting wire, the final charge on the bigger sphere is:

The power dissipated in the circuit shown in the figure is 30 Watts. The value of R is:

Cell having an emf ε and internal resistance r is connected across a variable external resistance R. As the resistance R is increased, the plot of potential difference V across R is given by:

A proton carrying 1 MeV kinetic energy is moving in a circular path of radius R in uniform magnetic field. What should be the energy of an α-particle to describe a circle of same radius in the same field?

A magnetic needle suspended parallel to a magnetic field requires √3 J of work to turn it through 60°. The torque needed to maintain the needle in this position will be:

The instantaneous values of alternating current and voltages in a circuit are given as i = 1/√2 sin(100πt) amper and e = 1/√2 sin(100πt + π/3) Volt. The average power in Watts consumed in the circuit is:

In a coil of resistance 10 Ω, the induced current developed by changing magnetic flux through it, is shown in figure as a function of time. The magnitude of change in flux through the coil in Weber is:

The ratio of amplitude of magnetic field to the amplitude of electric field for an electromagnetic wave propagating in vacuum is equal to:

For the angle of minimum deviation of a prism to be equal to its refracting angle, the prism must be made of a material whose refractive index:

A rod of length 10 cm lies along the principal axis of a concave mirror of focal length 10 cm in such a way that its end closer to the pole is 20 cm away from the mirror. The length of the image is:

If the momentum of electron is changed by P, then the de Broglie wavelength associated with it changes by 0.5%. The initial momentum of electron will be:

Two radiations of photons energies 1 eV and 2.5 eV, successively illuminate a photosensitive metallic surface of work function 0.5 eV. The ratio of the maximum speeds of the emitted electrons is:

The transition from the state n = 3 to n = 1 in a hydrogen like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition from:

The half life of a radioactive nucleus is 50 days. The time interval (t₂ - t₁) between the time t₂ when 2/3 of it has decayed and the time t₁ when 1/3 of it had decayed is:

The input resistance of a silicon transistor is 100 Ω. Base current is changed by 40 μA which results in a change in collector current by 2 mA. This transistor is used as a common emitter amplifier with a load resistance of 4 kΩ. The voltage gain of the amplifier is:

To get an output Y = 1 in given circuit which of the following input will be correct:

Given that the equilibrium constant for the reaction 2SO₂(g) + O₂(g) ⇌ 2SO₃(g) has a value of 278 at a particular temperature. What is the value of the equilibrium constant for the following reaction at the same temperature? SO₃(g) ⇌ SO₂(g) + 1/2 Ω₂(g)

Structure of a mixed oxide is cubic close-packed (c.c.p). The cubic unit cell of mixed oxide is composed of oxide ions. One fourth of the tetrahedral voids are occupied by divalent metal A and the octahedral voids are occupied by a monovalent metal B. The formula of the oxide is:

Given the reaction between 2 gases represented by A₂ and B₂ to give the compound AB(g). A₂(g) + B₂(g) ⇌ 2 AB(g). At equilibrium, the concentration of A₂ = 3.0 × 10⁻³ M, B₂ = 4.2 × 10⁻³ M, and AB = 2.8 × 10⁻³ M. If the reaction takes place in a sealed vessel at 527°C, then the value of Kc will be:

Activation energy (Eₐ) and rate constants (k₁ and k₂) of a chemical reaction at two different temperatures (T₁ and T₂) are related by:

During change of O₂ to O₂⁻ ion, the electron adds on which one of the following orbitals?

Standard reduction potentials of the half reactions are given below: F₂(g) + 2e⁻ → 2F⁻ (aq) ; E° = +2.85 V Cl₂(g) + 2e⁻ → 2Cl⁻ (aq) ; E° = +1.36 V Br₂(l) + 2e⁻ → 2Br⁻ (aq) ; E° = +1.06 V I₂(s) + 2e⁻ → 2I⁻ (aq) ; E° = +0.53 V The strongest oxidising and reducing agents respectively are:

A certain gas takes three times as long to effuse out as helium. Its molecular mass will be:

The orbital angular momentum of a p-electron is given as:

Vapour pressure of chloroform (CHCl₃) and dichloromethane (CH₂Cl₂) at 25°C are 200 mm Hg and 41.5 mm Hg respectively. Vapour pressure of the solution obtained by mixing 25.5 g of CHCl₃ and 40 g of CH₂Cl₂ at the same temperature will be: (Molecular mass of CHCl₃ = 119.5 u and molecular mass of CH₂Cl₂ = 85 u).

Molar conductivities (Λ°) at infinite dilution of NaCl, HCl and CH₃COONa are 126.4, 425.9 and 91.0 S cm² mol⁻¹ respectively. Λ° for CH₃COOH will be:

For real gases van der Waals equation is written as \( \left( p + \frac{an^2}{v^2} \right) (V - nb) = nRT \) where 'a' and 'b' are van der Waals constants. Two sets of gases are: (I) Ω₂, CO₂, He and (II) CH₄, O₂, H₂. The gases given in set-I in increasing order of 'b' and gases given in set-II in decreasing order of 'a', are arranged below. Select the correct order from the following:

Equal volumes of two monoatomic gases, A and B, at same temperature and pressure are mixed. The ratio of specific heats \( \left( \frac{C_p}{C_v} \right) \) of the mixture will be:

Red precipitate is obtained when ethanol solution of dimethylglyoxime is added to ammoniacal Ni(II). Which of the following statements is not true?

Low spin complex of d⁶-cation in an octahedral field will have the following energy: (Δ₀ = Crystal Field Splitting Energy in an octahedral field, P = Electron pairing energy)

Which one of the following does not correctly represent the correct order of the property indicated against it?

Four successive members of the first series of the transition metals are listed below. For which one of them the standard potential (E°_{M²⁺/M}) value has a positive sign?

In the replacement reaction RCl + MF → RF + MCl The reaction will be most favourable if M happens to be:

In which of the following arrangements the given sequence is not strictly according to the property indicated against it?

Four diatomic species are listed below. Identify the correct order in which the bond order is increasing in them:

The catalytic activity of transition metals and their compounds is ascribed mainly to: