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JEE Main 2019 Paper-1 with Solutions - Question 1

### Four identical particles of mass M are located at the corners of a square of side ‘a’. What should be their speed if each of them revolves under the influence of others’gravitational field in a circular orbit circumscribing the square?

Detailed Solution for JEE Main 2019 Paper-1 with Solutions - Question 1

JEE Main 2019 Paper-1 with Solutions - Question 2

### Two particles move at right angle to each other. Their de Broglie wavelengths are λ1  and λ2 respectively. The particles suffer perfectly inelastic collision. The de Broglie wavelength λ , of the final particle, is given by:

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JEE Main 2019 Paper-1 with Solutions - Question 3

### In SI units, the dimensions of

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JEE Main 2019 Paper-1 with Solutions - Question 4

A particle moves in one dimension from rest under the influence of a force that varies with the distance travelled by the particle as shown in the figure. The kinetic energy of the particle after it has travelled 3 m is:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions - Question 4

Final K.E.=6.5 J

JEE Main 2019 Paper-1 with Solutions - Question 5

An alternating voltage volt is applied to a purely resistive load of 50Ω . The time taken for the current to rise from half of the peak value to the peak value is:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions - Question 5

JEE Main 2019 Paper-1 with Solutions - Question 6

A boy's catapult is made of rubber cord which is 42 cm long, with 6 mm diameter of cross-section and of 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 crosssection
of the cord while stretched. The Young's modulus of rubber is closest to:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions - Question 6

JEE Main 2019 Paper-1 with Solutions - Question 7

The reverse breakdown voltage of a Zener diode is 5.6 V in the given circuit.

The current Iz through the Zener is:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions - Question 7

Current through 800
Current through 200
Then current Iz is 10 mA.

JEE Main 2019 Paper-1 with Solutions - Question 8

Two identical beakers A and B contain equal volumes of two different liquids at 60°C each and left to cool down. Liquid in A has density of 8 x102 kg/ m3 and specific heat of 2000J kg-1 K-1 while liquid in B has density of 103 kg m-3 and specific heat of 4000J kg-1K-1. Which of the following best describes their temperature versus time graph schematically? (Assume the emissivity of both the beakers to be the same)

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JEE Main 2019 Paper-1 with Solutions - Question 9

A plane electromagnetic wave travels in free space along the x-direction. The electric field component of the wave at a particular point of space and time is E = 6 Vm-1 along y-direction. Its corresponding magnetic field component, B would be:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions - Question 9

Along z-direction

JEE Main 2019 Paper-1 with Solutions - Question 10

A wire of length 2L, is made by joining two wires A and B of same length but different radii r and 2r and made of the same material. It is vibrating at a frequency such that the joint of the two wires forms a node. If the number of antinodes in wire A is p and that in B is q then the ratio p: q is:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions - Question 10

JEE Main 2019 Paper-1 with Solutions - Question 11

Radiation coming from transitions n =2 to n=1 of hydrogen atoms fall on He+ ions in n=1 and n=2 states. The possible transition of helium ions as they absorb energy from the radiation is:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions - Question 11

For hydrogen,
For He+,
2 → 4 transition.

JEE Main 2019 Paper-1 with Solutions - Question 12

For the circuit shown, with and the
potential difference between the points ’a' and ‘b’ is approximately (in V) :

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JEE Main 2019 Paper-1 with Solutions - Question 13

Voltage rating of a parallel plate capacitor is 500 V. Its dielectric can withstand a maximum electric field of 106 V/ m. The plate area is 10-4 m2. What is the dielectric constant if the capacitance is 15 pF ?

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JEE Main 2019 Paper-1 with Solutions - Question 14

A solid conducting sphere, having a charge Q, is surrounded by an uncharged conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V. If the shell is now given a charge of -4 Q, the new potential difference between the same two surfaces is :

Detailed Solution for JEE Main 2019 Paper-1 with Solutions - Question 14

Potential difference doesn’t change.

JEE Main 2019 Paper-1 with Solutions - Question 15

A thin strip 10 cm long is on a U shaped wire of negligible resistance and it is connected to a spring of spring constant 0.5 Nm-1 (see figure). The assembly is kept in a uniform magnetic field of 0.1 T. If the strip is pulled from its equilibrium position and released, the number of oscillations it performs before its amplitude decreases by a factor of e is N. If the mass of the strip is 50 grams, its resistance 10 Ω . and air drag negligible, N will be close to :

Detailed Solution for JEE Main 2019 Paper-1 with Solutions - Question 15

Force on oscillating wire if it’s speed v is

Time period T is
No. of oscillations is and t is given by

JEE Main 2019 Paper-1 with Solutions - Question 16

An upright object is placed at a distance of 40 cm in front of a convergent lens of focal length 20 cm. A convergent mirror of focal length 10 cm is placed at a distance of 60 cm on the other side of the lens. The position and size of the final image will be:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions - Question 16

Actual final image (3rd image) is formed at object itself with same size but according to the options best answer is taken for second image.

JEE Main 2019 Paper-1 with Solutions - Question 17

A steel wire having a radius of 2.0 mm, carrying a load of 4 kg, is hanging from a ceiling. Given that g=3.1 πms-2 what will be the tensile stress that would be developed in the wire?

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JEE Main 2019 Paper-1 with Solutions - Question 18

A thermally insulated vessel contains 150 g of water at 0°C. Then the air from the vessel is pumped out adiabatically. A fraction of water turns into ice and the rest evaporates at 0°C itself. The mass of evaporated water will be closest to: (Latent heat of vaporization of water = 2.10 x 106J kg-1 and Latent heat of Fusion of water =3.36x 105J kg-1)

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JEE Main 2019 Paper-1 with Solutions - Question 19

A thin circular plate of mass M and radius R has its density varying as with 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
The value of the coefficient a is:

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JEE Main 2019 Paper-1 with Solutions - Question 20

A 20 Henry inductor coil is connected to a 10 ohm resistance in series as shown in figure. The time at which rate of dissipation of energy (Joule's heat) across resistance is equal to the rate at which magnetic energy is stored in the inductor, is:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions - Question 20

JEE Main 2019 Paper-1 with Solutions - Question 21

Four particles A, B, C and D with masses mA=m, mB=2m, mC=3m and mD=4m are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles is:

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JEE Main 2019 Paper-1 with Solutions - Question 22

A circular coil having N turns and radius r carries a current I. It is held in the XZ plane in a magnetic field The torque on the coil due to the magnetic field is:

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JEE Main 2019 Paper-1 with Solutions - Question 23

If 1022 gas molecules each of mass 10-26 kg collide with a surface (perpendicular to it) elastically per second over an area 1 m2 with a speed 104 m/s, the pressure exerted by the gas molecules will be of the order of :

Detailed Solution for JEE Main 2019 Paper-1 with Solutions - Question 23

Pressure = 2Nm-2

JEE Main 2019 Paper-1 with Solutions - Question 24

In figure, the optical fiber is l=2 m long and has a diameter of d =20 μm. If a ray of light is incident on one end of the fiber at angle the number of reflections it makes before emerging from the other end is close to : (refractive index of fiber is 1.31 and sin 400= 0.64)

Detailed Solution for JEE Main 2019 Paper-1 with Solutions - Question 24

x=d / tanθ2
No. of collisions

JEE Main 2019 Paper-1 with Solutions - Question 25

A 200Ω resistor has a certain color code. If one replaces the red color by green in
the code, the new resistance will be :

Detailed Solution for JEE Main 2019 Paper-1 with Solutions - Question 25

In the given resistance 200Ω  , 2 stands for red. If it is replaced by green, then the resistance becomes 500Ω .

JEE Main 2019 Paper-1 with Solutions - Question 26

The bob of a simple pendulum has mass 2 g and a charge of 5.0μ C. It is at rest in a uniform horizontal electric field of intensity 2000 V/ m. At equilibrium, the angle that the pendulum makes with the vertical is (take g = 10 m/s2)

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JEE Main 2019 Paper-1 with Solutions - Question 27

Ship A is sailing towards north-east with velocity where points east and north. Ship B is at a distance of 80 km east and 150 km north of Ship A and is sailing towards west at 10 km/hr. A will be at minimum distance from B in:

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Velocity of A w.r.t B is

JEE Main 2019 Paper-1 with Solutions - Question 28

In an interference experiment the ratio of amplitudes of coherent waves is The ratio of maximum and minimum intensities of fringes will be:

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JEE Main 2019 Paper-1 with Solutions - Question 29

Water from a pipe is coming at a rate of 100 liters per minute. If the radius of the pipe is 5 cm, the Reynolds number for the flow is of the order of : (density of water =1000 kg/m3, coefficient of viscosity of water= 1 mPas)

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JEE Main 2019 Paper-1 with Solutions - Question 30

The wavelength of the carrier waves in a modern optical fiber communication network is close to:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions - Question 30

Wavelength used for communication are 1300nm and 1500nm.

JEE Main 2019 Paper-1 with Solutions - Question 31

For the reaction the values of initial rate at different reactant concentrations are given in the table below. The rate law for the reaction is:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions - Question 31

⇒ a =1

⇒b = 2
Therefore,

JEE Main 2019 Paper-1 with Solutions - Question 32

The major product of the following reaction is:

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JEE Main 2019 Paper-1 with Solutions - Question 33

If solubility product of is denoted by KSP and its molar solubility is denoted by S, then which of the following relation between S and KSP is correct ?

Detailed Solution for JEE Main 2019 Paper-1 with Solutions - Question 33

Let “s” be the solubility, then

JEE Main 2019 Paper-1 with Solutions - Question 34

Maltose on treatment with dilute HCI gives:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions - Question 34

Maltose on treatment with dil.HCl gives D-glucose.

JEE Main 2019 Paper-1 with Solutions - Question 35

The IUPAC name of the following compound is:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions - Question 35

3-hydroxy-4-methylpentanoic acid

JEE Main 2019 Paper-1 with Solutions - Question 36

The quantum number of four electrons are given below:

The correct order of their increasing energies will be:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions - Question 36

lower (n +l) value, and followed by lower ‘n’ value (aufbau rule)
IV < II< III< I
(3p)(3d) (4p) (4d)

JEE Main 2019 Paper-1 with Solutions - Question 37

Diborane (B2 H6) reacts independently with O2 and H2O to produce, respectively:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions - Question 37

Diborane burns in O2 forming B2O3

Diborane hydrolyses in water producing H2BO3

JEE Main 2019 Paper-1 with Solutions - Question 38

100 mL of a water sample contains 0.81 g of calcium bicarbonate and 0.73 g of magnesium bicarbonate. The hardness of this water sample expressed in terms of equivalents of CaCO3 is: (molar mass of calcium bicarbonate is 162 g mol-1 and magnesium bicarbonate is 146 g mol-1)

Detailed Solution for JEE Main 2019 Paper-1 with Solutions - Question 38

100 ml sample contain 0.81g of i.e., equal to 5g of and 0.73 g of per 100ml is equal to 5g of per lit. total hardness is 10g per litre or 10,000 ppm

JEE Main 2019 Paper-1 with Solutions - Question 39

The correct order of hydration enthalpies of alkali metal ions is:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions - Question 39

Hydration enthalpies of alkali metal ions decrease down two group

JEE Main 2019 Paper-1 with Solutions - Question 40

For silver, If the temperature (T) of 3 moles of silver is raised from 300 K to 1000 K at 1 atm pressure, the value of ΔH will be close to :

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JEE Main 2019 Paper-1 with Solutions - Question 41

The correct order of the spin-only magnetic moment of metal ions in the following low- spin complexes,

Detailed Solution for JEE Main 2019 Paper-1 with Solutions - Question 41

configuration of which all the 3 are unpaired electrons,
configuration. On low spin the 4 electrons are arranged as one pair and 2 unpaired electrons,
configuration. In low spin the 5 electrons are arranged as 2 pairs ard 1 electron remain unpaired
configuration. In low spin complex all the six electrons are paired so no unpaired electrons

JEE Main 2019 Paper-1 with Solutions - Question 42

Coupling of benzene diazonium chloride with 1-naphthol in alkaline medium will give:

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JEE Main 2019 Paper-1 with Solutions - Question 43

Which of the following amines can be prepared by Gabriel phthalimide reaction ?

Detailed Solution for JEE Main 2019 Paper-1 with Solutions - Question 43

Only primary amine can be prepared by Gabriel Pthalimide reaction with better SN2.

JEE Main 2019 Paper-1 with Solutions - Question 44

Given that

The strongest oxidizing agent is:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions - Question 44

Strongest oxidizing agent may have higher reduction potential in standard state

JEE Main 2019 Paper-1 with Solutions - Question 45

Assertion : Ozone is destroyed by CFCs in the upper stratosphere.
Reason : Ozone holes increase the amount of UV radiation reaching the earth.

Detailed Solution for JEE Main 2019 Paper-1 with Solutions - Question 45

Ozone is destroyed by due to which ozone holes are formed. Through these holes the amount u.v radiation reaching the earth increases

JEE Main 2019 Paper-1 with Solutions - Question 46

Adsorption of a gas follows Freundlich adsorption isotherm. x is the mass of the gas adsorbed on mass m of the adsorbent. The plot of versus log p is shown in the given graph. is proportional to :

Detailed Solution for JEE Main 2019 Paper-1 with Solutions - Question 46

JEE Main 2019 Paper-1 with Solutions - Question 47

With respect to an ore, Ellingham diagram helps to predict the feasibility of its

Detailed Solution for JEE Main 2019 Paper-1 with Solutions - Question 47

Ellingham diagrams are related to the values for the formation of oxides and can be used for the thermal reduction of ores

JEE Main 2019 Paper-1 with Solutions - Question 48

The major product of the following reaction is:

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JEE Main 2019 Paper-1 with Solutions - Question 49

In order to oxidise a mixture of one mole of each of andin acidic medium, the number of moles of KMnO4 required is:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions - Question 49

have valence factors as 3, 6, 1 and 0 and that of KMnO4 is 5. Therefore two moles of oxidizing agent is required

JEE Main 2019 Paper-1 with Solutions - Question 50

The following ligand is

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