JEE Main 2019 April 10 Shift 1 Paper & Solutions - JEE MCQ

One Plano-convex and one plane of-concave lens of same radius of Curvature ‘R’ but of different materials are joined side by side as shown in the figure . If refractive index of the material of 1 is µ₁ and that of 2 is µ₂ ,then the focal length of the combination is

n a photoelectric effect experiment the threshold wavelength of the is 380nm. If the wavelength of indent is 260nm, the  maximum kinetic energy of emitted electrons will be: given E{in ev}= 1237/λ (innm)

The electric field of a plane electromagnetic wave is given by  The corresponding magnetic field   is then given by :

A transformer consisting of 300 turns in the primary and 150 turns in the secondary gives output power of 2.2kw. if the current in the secondary coil is 10A, then the input voltage and current in the primary Coil are:

A cylinder with fixed capacity of 67.2lit contains helium gas at STP. The amount of heat needed to raise the temperature of the gas by 20⁰C is : [Given that  R=8.31J mol ^-1k ^-1 ]

Two radioactive materials A and B have decay constants 10λ and λ,respectively . If initially they have the same number of nuclei, then the ratio of the number of nuclei, then the ratio of the number of nuclei of A to that of B will be 1/e after a time

In the  given circuit,an ideal voltmeter connected  across the 10 Ω resistance reads 2V. The internal resistance r, of each cell is

A ray of light AO in vacuum is incident on a glass slab at angle 60⁰ and refracted at angle 30⁰ along OB as shown in the figure.The optical path length of light ray from A to B is:

A current of 5A passes through a copper conductor (resistivity= 1.7 ´10^-8 Ωm) radius of cross section 5mm.Find the mobility of the charges if their drift velocity is 1.1x10^-3 m/s.

Figure shows charge (q) versus voltage (v) graph for series and parallel combination  of two given capacitors . The capacitances are :

The value of acceleration due to gravity at Earth‘s surface is 9.8ms^-2 . The altitude above  its surface at which the acceleration due to gravity decreases to 4.9 ms^-2, is close to (Radius of earth = 6.4 x10⁶ m. )

Two wires A&B are carrying  currents I₁ & I₂ as shown in the figure . the separation between them is d . A third wire C carrying a current I is to be kept parallel to them at a distance x from A such that the net force acting on it is Zero . The possible values of x are:

In a meter bridge experiment the circuit diagram and the corresponding observation table are shown in figure.
                                       

Q. Which of the readings is inconsistent ?

An npn transistor operates as a common emitter amplifier , with a power gain of 60dB. The input circuit  resistance is 100 Ω and the output load resitance is 10K Ω .The common emitter current gain β is :

A massage signal of frequency 100MHz and peak voltage 100V is used to execute amplitude modulation on a carrier wave of frequency 300GHz and peak voltage 400 V . The modulation index and difference between the two side band frequencies are​

A uniformly charged ring of radius 3a and total charge q is placed in xy-plane centred at orign. A point charge q is moving towards the ring along the z-axis and has speed  v at z = 4a The minimum value of v such that it crosses the origin is:

A proton,an electron, and a Helium nucleus, have the same energy. they are in circular orbits in a plane due to magnetic field perpendicular to the plane. Let r_p , r_e and r_He be their respective radii, then,

The ratio of surface tensions of mercury and water is given to be 7.5 while the ratio of their densities  is 13.6. Their contact angles, with glass, are close to 135⁰ and 0⁰ respectively. it is observed that mercury gets depressed by an amount h in a capillary tube of radius r₁ , while water rises by the same amount h in a capillary tube of radius r₂ ,the ratio, (r₁/ r₂) is then close to:

a moving Coil galvanometer allows a full scale current 10^-4 A.A series resistance of2-M Ω is required  to convert the above galvanometer  into a voltmeter of range 0-5V.Therefore the value of shunt resistance  required to convert the above galvanometer in to ammeter of range 0-10mA is :

A ball is thrown upward with an initial velocity V₀ from the surface of the earth. the motion of the ball is affected by a drag force equal to myV ² ( where m is mass of the ball v is its instaneous velocity and g is a constant) . Time taken by the ball to rise to its  zenith is :

A thin disc of mass M and radius R has mass per unit area σ (r ) =kr² where r is the distance from its center . Its moment of inertia about an axis going through its centre of mass and perpendicular to its plane is :

Given below in the left column are different modes of communication using the kinds of waves given in  the right column .

From the options given below , find the most appropriate match between  entries in the left and the right column.

In an experiment , the resistance of a material is plotted as a function of temperature ( in some range) .As shown in the figure , It is a straight line

A 25 x10^-3 m³ volume cylinder is field with 1 mol O₂ gas room temperature (300k) The molicular diameter of O2,and its root mean square speed , are found to be 0.3 nm and 200m/s, respectively.what is the average collision rate (per second) for an O₂ Molecule?

Two Coaxial discs , having moments of inertia I₁and I₁/2 are  rotating with respective angular velocity ω₁ and ω₁/2, about their  common axis.They are brought in contact with each other and thereafter they rotate with a common angular velocity . If E_f and E_i `, are the final and initial total energies,then ( E_f - E_i ) is

Two Particles , of masses M and 2M moving , as shown,with speeds of 10m/s and 5m/s , collied elastically at the origin. After the collision , they move along the indicated directions  with speeds  v₁ and v₂ ,respectively , The value of v₁ and v₂ are nearly:

The displacement of a damped harmonic oscillator is given by x (t) = e^-0.1t cos (10πt + φ) Here t it is in seconds.The time taken for its amplitude of vibration to drop to half of its initial value is close to: