JEE Main Mock Test - 20 - JEE MCQ

Suppose refractive index μ is given as where A and B are constants and λ is wavelength, then dimensions of B are same as that of

Assertion : Machine parts are jammed in winter.
Reason : The viscosity of lubricant used in machine parts increase at low temperature.

Assertion: In S.H.M., the velocity and displacement of the particle are in the same phase.
Reason: Velocity is the ratio of displacement to the time taken.

A mass is attached to one end of a spring of spring constant k. The spring is stretched and then released such that its amplitude of oscillation is A. For a displacement y from the mean position, if the kinetic energy is 44% of its potential energy, then y in terms of A is

A circular disc of radius r and thickness r/6 has moment of inertia I about an axis passing through its centre and perpendicular to its plane. It is melted and recasted to a solid sphere. The moment of inertia of the sphere about its diameter as axis of rotation is

When an UV light of 10¹⁵ Hz and intensity 2 W/m² is directed at a metal surface, photoelectrons emitted were found to have a maximum kinetic energy of 1.6 eV. If the work functions for different materials are as follows: Potassium 2.2 eV, Sodium 2.3 eV, Lithium 2.5 eV and Calcium 3.2 eV, identify the metal in the given problem.

Two sources of sound S₁ and S₂ each emitting waves of wavelength A are kept symmetrically on either side of the centre 0 of a circle ABCD such that S₁O = S₂O = K . When the detector is moved along the circumference of the circle, the number of maxima recorded by the detector in one revolution is

A boat capable of a speed v in still water wants to cross a river of width d. The speed of the water current increases linearly from zero at either bank to a maximum of u at the middle of the river. When the boat is rowed at right angles to the bank, its downstream drift is

Figure shows the plot of a potential energy function of a conservative system U versus x. Which of the following statements is correct ?

A sphere with some cavity has outer radius R. It rolls down an inclined plane without slipping and attains a speed v at the bottom. When this sphere slides down without rolling on the frictionless inclined plane of same height its speed at the bottom is 5v/4. The radius of gyration of the sphere is

The antenna current of an AM transmitter is 8 A when only carrier wave is sent but the current increases to 8.88 A when the carrier wave is sinusoidally modulated. The percentage of modulation is

A square metal wire loop of side 20 cm and resistance 1 Ω is moved with a constant velocity Vo in a uniform magnetic field of induction B = 4 Wb/m². The magnetic field lines are perpendicular to the plane of the loop and directed inwards. The loop is connected to a network of resistors each of value 2 Ω . The resistance of load wires AB and CD are negligible. To get a current of 2 mA in the loop, the speed of motion of the loop is

Four identical hollow cylindrical columns of steel, support a big structure of mass 60,000 kg. The inner and outer radii of each column are 40 cm and 50 cm respectively. When the load distribution is uniform, the compressional strain on each column is (Young’s modulus of steel is 2 x 10¹¹ Pa)

A steel ball of mass 60 g falls from a height 0.8 m on the horizontal surface of a massive slab. The coefficient of restitution between the ball and the slab is e = 0.4; the total momentum imparted to the slab by the ball after numerous bounces is

An alternating voltage having frequency of 50 cycles/sec and maximum voltage 220 V is supplied to a circuit containing a pure inductance of 0.02 H and a pure resistance of 10 Ω in series. The value of maximum current in circuit is-

A beam of light traveling in water strikes a glass plate which is also immersed in water. When the angle of incidence is 50 ° the reflected beam is found to be plane polarised. The refractive index of water is 4/3. The refractive index of the glass plate is (Given tan 50 ° = 1.198)

A man pulls a loaded sledge of mass 60 kg along a horizontal surface at constant velocity as shown in figure. The coefficient of kinetic friction between the sledge and the surface is 0.15. The tension in the rope during pulling when it makes an angle of cp = 40 ° with the horizontal is (cos 40 0 = 0.766, sin 40 ° = 0.643 and g = 10 ms'2)

Which of the following statements are correct?
(i) Inductive effect and resonance effect is possible in chlorobenzene.
(ii) Resonance effect dominates over inductive effect in anisole.
(iii) p-nitrobenzoic acid is less acidic than m-nitrobenzoic acid.
(iv) Diphenylamine is more basic than aniline.

Statement I: Lothar Meyer arranged elements in increasing order of atomic number and observed periodic trends in their physical properties.
Statement II: Newlands' Law of Octaves states that every eighth element has properties similar to the first when elements are arranged in increasing order of atomic weight.
In the light of the above statements, choose the correct answer from the options given below:

Pick out the incorrect statement(s) from the following.
1. Glucose exists in two different crystalline forms, α-D-glucose and β-D-glucose.
2. α-D-glucose and β-D-glucose are anomers.
3. α-D-glucose and β-D-glucose are enantiomers.
4. Cellulose is a straight chain polysaccharide made of only β-D-glucose units.
5. Starch is a mixture of amylase and amylopectin, both contain unbranched chain of α-D-glucose units.

The intermediate formed in the following reaction is-

The compound present in brorax bead is

A proton is fired from very far away towards a nucleus with charge Q = 120 e, where, e is the electronic charge. It makes the closest approach of 10 fm to the nucleus. The de Broglie wavelength (in units of fm) of the proton at its start is : (take the proton mass,  h/e = 4⋅2 × 10⁻¹⁵ J s C⁻¹; = 9 × 10⁹m F⁻¹ ; 1 fm = 10⁻¹⁵)

A circular coil of area 0.01 m² and 40 turns is rotated about its vertical diameter with an angular speed of 50 rads⁻¹ in a uniform horizontal magnetic field 0.05 T. If the average power loss due to joule heating is 25 mW, then the closed loop resistance of the coil is

Gravitational acceleration on the surface of planet is where  is the gravitational acceleration on the surface of earth. The average mass density of the planet is 2/3 times that of the earth. If escape speed on the surface of the earth is taken to be 11kms^–1, escape speed on the surface of the planet in kms^–1, will be:

A radioactive substance A decays in to B. It is known that only A is present at t = 0. Find the number of half lives at which the probability of getting B in the mixture is 15 times that of finding A, if we pick out randomly from the sample.

A single electron orbits round a stationary nucleus of charge Ze, where Z is a constant and - e is the electron charge. It is observed that it requires 47.2 eV to excite the electron from second Bohr orbit to third orbit. Then to ionise the atom from ground state, required wavelength of electromagnetic(EM) radiations is found to be 4nÅ. Find the value of n. [Take energy of electron in ground state of hydrogen atom is - 13.6 eV.]