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JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1)


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90 Questions MCQ Test JEE Main & Advanced Mock Test Series | JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1)

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JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 1

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

The rms value of the force experienced by a stationary charge Q =10–4C at z = 0 is

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 1

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 2

A solid sphere of mass ‘M’ and radius ‘a’ is surrounded by a uniform concentric spherical shell of thickness 2a and mass 2M. The gravitational field at distance ‘3a’ from the centre will be:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 2

Field at 

Field = 

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 3

A moving coil galvanometer has resistance 50Ω and it indicates full deflection at 4mA current. A voltmeter is made using this galvanometer and a 5 kΩ resistance.The maximum voltage, that can be measured using this voltmeter, will be close to:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 3

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 4

For a given gas at 1 atm pressure, rms speed of the molecules is 200 m/s at 127ºC. At 2 atm pressure and at 227ºC, the rms speed of the molecules will be:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 4

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 5

Taking the wavelength of first Balmer line in hydrogen spectrum (n = 3 to n = 2) as 660 nm, the wavelength of the 2nd Balmer line (n = 4 to n = 2) will be:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 5

1st line Balmer

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 6

The pressure wave, P = 0.01sin[1000t – 3x]Nm–2 , corresponds to the sound produced
by a vibrating blade on a day when atmospheric temperature is 0ºC. On some other day when temperature is T, the speed of sound produced by the same blade and at the same frequency is found to be 336ms–1 . Approximate value of T is:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 6

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 7

The following bodies are made to roll up (without slipping) the same inclined plane from a horizontal plane :
(i) a ring of radius R,
(ii) a solid cylinder of radius R/2 and
(iii) a solid sphere of radius R/4. If, in each case, the speed of the center of mass at the bottom of the incline is same, theratio of the maximum heights they climb is:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 7


JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 8

An NPN transistor is used in common emitter configuration as an amplifier with1kΩ load resistance. Signal voltage of 10 mV is applied across the base-emitter. Thisproduces a 3 mA change in the collector current and 15μ A change in the basecurrent of the amplifier. The input resistance and voltage gain are:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 8



Voltage gain
Voltage gain = 300

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 9

A ball is thrown vertically up (taken as +z-axis) from the ground. The correct momentum – height (p-h) diagram is:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 9

v2 - u2 = -2 gh
v2 = v2 - 2 gh
p2 = A - Bh

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 10

The electric field of light wave is given as .
The light falls on a metal plate of work function 2eV. The stopping potential of the
photo-electrons is:Given, E (in eV) 

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 10

hv = hv0 + s. potential
= w + s potential

2.48 = 2ev + s. potential

stop potential = 0.4eV

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 11

A string is clamped at both the ends and it is vibrating in its 4th harmonic. The equation of the stationary wave is Y= 0.3sin(0.157x)cos(200π) . The length of the string is: (All quantities are in SI units.)

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 11

ln 4th harmonic

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 12

A signal Acosωt is transmitted using ν0 sin ω0t as carrier wave. The correct amplitude modulated (AM) signal is:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 12

Mododulater wave =

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 13

In the density measurement of a cube, the mass and edge length are\ measured as (10.00 ± 0.10) kg and ( 0.10 ± 0.01) m, respectively. The error in the measurement of density is:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 13

mass = (10 ± 0.1) kg
Length = ( 0.1 ± 0.01) m
Denisty ==D

=0.01+0.3
= 0.31 kg/m3

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 14

A simple pendulum oscillating in air has period T. The bob of the pendulum is
completely immersed in a non-viscous liquid. The density of the liquid is  of the material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 14

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 15

If ‘M’ is the mass of water that rises in a capillary tube of radius ‘r’, then mass of
water which will rise in a capillary tube of radius ‘2r’ is:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 15


mass α r2h
mass α r
So final mass rise = 2M

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 16

Following figure shows two process A and B for a gas. If ΔQA  and  ΔQB are the amount of heat absorbed by the system in two cases, and ΔUA and ΔUare changes in internal energies, respectively, then:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 16

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 17

The total number of turns and cross-section area in a solenoid is fixed. However, its length L is varied by adjusting the separation between windings. The inductance of solenoid will be proportional to:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 17

WKT
Self inductance L = μn2 x(volume) 


Self inductance 

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 18

A uniform cable of mass ‘M’ and length ‘L’ is placed on a horizontal surface such
that its part is hanging below the edge of the surface. To lift the hanging part of the cable upto the surface, the work done should be:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 18

The resultant is the centre of mass of the part AB is shifter to top i.e. 

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 19

A body of mass 2 kg makes an elastic collision with a second body at rest andcontinues to move in the original direction but with one fourth of its original speed.What is the mass of the second body?

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 19

Momentum conservation

Elatic collision
Energy conservation

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 20

A capacitor with capacitance 5μF is charged to5μC. If the plates are pulled apart to reduce the capacitance to 2μF , how much work is done?

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 20

⇒work done by force ⇒ F×S

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 21

A rectangular coil (Dimension5cm × 2.5cm) with 100 turns, carrying a current of 3A in the clock-wise direction, is kept centered at the origin and in the X-Z plane. A magnetic field of 1 T is applied along X-axis. If the coil is tilted through 45º about Z-axis, then the torque on the coil is

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 21

Torque = M×B
= Nxi×A×B×sin 4J
= 100×3×12.5×10–4 ×1×
τ =0.265

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 22

The figure shows a Young’s double slit experimental setup. It is observed that when
a thin transparent sheet of thickness t and refractive index µ is put in front of one
of the slits, the central maximum gets shifted by a distance equal to n fringe widths.
If the wavelength of light used is λ,t will be:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 22

S1 P–S2 P+(µ–1) t = 0
(µ–1) = S1 P–S2
(µ–1) t =nl

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 23

A wire of resistance R is bent to form a square ABCD as shown in the figure. The
effective resistance between E and C is: (E is mid-point of arm CD)

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 23



JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 24

A rigid square loop of side ‘a’ and carrying current I2 is lying on a horizontal surface near a long current I1 carrying wire in the same plane as shown in figure. The net force on the loop due to the wire will be:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 24


JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 25

The stream of a river is flowing with a speed of 2 km/h. A swimmer can swim at a speed of 4 km/h. What should be the direction of the swimmer with respect to the flow of the river to cross the river straight?

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 25

to cross the river straight, V along the river=0
Vsteam = Vswimmer cos θ
2 = 4cos θ ⇒ cos θ =
⇒ θ = 60º
Direction w.r.t flow of river = 180º-60º = 120º

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 26

A stationary horizontal disc is free to rotate about its axis. When a torque is applied on it, its kinetic energy as a function of θ , where θ is the angle by which it has rotated, is given as kθ2 . If its moment of inertia is I then the angular acceleration of the disc is:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 26

KE = Kθ2

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 27

A system of three charges are placed as shown in the figure:

If D > > d, the potential energy of the system is best given by:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 27

The potential energy of +q, -q system is 
The system of +q, -q act as an electric dipole as d<<D
Hence, Potential energy between Q and dipole is 
Hence,  

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 28

An HCl molecule has rotational, translational and vibrational motions. If the rms velocity of HCl molecules in its gaseous phase is  , m is its mass and KBis Boltzman constant, then its temperature will be :

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 28

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 29

A concave mirror for face viewing has focal length of 0.4 m. The distance at which you hold the mirror from your face in order to see your image upright with a magnification of 5 is:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 29

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 30

Determine the charge on the capacitor in the following circuit:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 30

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 31

Among the following, the set of parameters that represents path functions, is:
A) q+w
B) q
C) w
D) H-TS

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 31

Except q, w all other thermodynamic variables are state functions q, w are path functions.

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 32

The correct IUPAC name of following compound is

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 32


NO - Nitro Cl - Chloro CH3 - Methyl

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 33

The degenerate orbitals of [Cr (H2O)6]3+ are

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 33

dzx , dyz are degenerate in octahedral splitting.

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 34

The organic compound that gives following qualitative analysis is:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 34


insoluble in Dil. HCl, Soluble in NaOH solution , & Decolourization of Br2 / water

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 35

Excessive release of CO2 into the atmosphere results in

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 35

Excessive release of CO2 into the atmosphere results in global warming.

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 36

The element having greatest difference between its first and second ionization energies, is

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 36

In given options k has greatest difference between its first & second ionisation energies.

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 37

The major product of the following reaction is:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 37

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 38

The number of water molecules not coordinated to copper ion directly in CuSOl 4.5H2 O, is

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 38

In CnSO4 .5H2O , four water molecules are coordinates to Cu2+ ion and one water molecules is outside the coordinate sphere.
Number of water molecules not coordinated to copper ion is

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 39

C60 , an allotrope of carbon contains:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 39

In C60 , hexagonal, 12 pentagonal
⇒ 20 hexagonal, 12 petagonal

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 40

Aniline dissolved in dilute HCl is reacted with sodium nitrite at 0ºC. this solution was added dropwise to a solution containing equimolar mixture of aniline and phenol in dil. HCl. The structure of the major product is

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 40


In equimolar mixture of aniline, phenol in dil.HCl, amiline in more reactive, as slightly acidic medium supports.

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 41

The major product of the following reaction is

Ch3Cº =CH 

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 41


JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 42

The standard Gibbs energy for the given cell reaction in kJ mol-1 at 298 K is:
Zn (s) + Cu2+ (aq) ® Zn2+ (aq) + Cu (s), Eº = 2V at 298K

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 42


ΔGº = -nFEºcell
= -2 x 96000 x 2
= -4 x 96kJ = -384kJ

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 43

The given plots represent the variation of the concentration of a reactant R with time for two different reactions (i) and (ii). The respective orders of the reactions are

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 43


T is proportional [R] it is 1st order t is proportional to [R] it is 0th order

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 44

The increasing order of reactivity of the following compounds towards aromatic electrophilic substitution reaction is​

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 44


B > C > A > D(dueto + M, Directing)

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 45

The correct order of the oxidation states of nitrogen in NO, N2O, NO2 and N2O3 is

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 45

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 46

Match the catalysts (colum I) with products (column II).

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 46

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 47

Which of the following statement is not true about sucrose?​

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 47

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 48

The aerosol is a kind of colloid in which:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 48

aerosol is a kind of colloid is disersion phase(s) dispersion medium(g)

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 49

The major product of the following reaction is

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 49

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 50

Consider the van der walls constants, a and b, for the following gases 

Q. Which gas is expected to have the highest critical temperature

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 50

To have highest critical temperature a should be high b should below so, it is Kr

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 51

Among the following, the molecule expected to be stabilized by anion formation is:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 51

C2 has vacant and if eenters into this if will be stabilized

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 52

The ore that contains the metal in the form of fluoride is

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 52

Cryolife → Na3AlF6
Malachite → CuCO3.CU(OH)2
Magnetite → Fe3O4
Sphalarite ®ZnS

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 53

The one that will show optical activity is:
(en = ethane – 1,2, -diamine)

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 53

Given which will show optical activity
The Compound should not have plans of symmetry only compounds in options

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 54

For any given series of spectral lines of atomic hydrogen, let  be the difference in maximum and minimum frequencies in cm-1 . The ratio is:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 54

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 55

The major product of the following reaction is:

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 56

The osmotic pressure of a dilute solution of an ionic compound XY in water is four times that of a solution of 0.01 M BaCl2 in water. Assuming complete dissociation of the given ionic compounds is water, the concentration of XY (in mol L-1) in solution is

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 56

2 – Chloro – 1 – methyl - 4 – nitro benzene

C = 0.06 M

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 57

For a reaction, n2(g)+H2 (g) →2NH3(g): identify dihydrogen ( H2 ) as a limiting reagent in the following reaction mixtures.

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 57

N2 + 3H2 → 2NH3
56g     10g
2 mol   5 mol
Actually 6 mol of H2 is required but only 5 mol present so it is limiting reagent.

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 58

Magnesium powder burns in air to give:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 58

Mh + O2 → MgO + Mg3 N2

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 59

The major product of the following reaction is
CH3 CH = CHCO2 CH3 

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 59

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 60

Liquid ‘M’ and liquid ‘N’ form an ideal solution. The vapour pressures of pure liquids ‘M’ and ‘N’ are 450 and 700mmHg, respectively, at the same temperature. Then correct statement is:
(xM = Mole fraction of ‘M’ is solution;
xN = Mole fraction of ‘N’ in solution ;
yM = Mole fraction of ‘M’ in vapour phase;
yN = Mole fraction of ‘N’ in vapour phase)

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 60

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 61

Let S = {θ ∈ [ -2π, 2π] : 2 cos2 θ + 3sin θ = 0} . Then the sum of the elements of S is: 

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 61

solving the trigonometric equation, we get sin θ 

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 62

If the standard deviation of the numbers -1, 0,1, k is √5 where k > 0 , then k is equal to:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 62

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 63

​All the points in the set  lie on a:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 63


So x2 + y2 = 1, is a circle of radius 1 

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 64

​For any two statements p and q, the negation of the expression p V ( ~ p ∧ q ) is:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 64

pV(~ p ∧ q) = (pV ~ p) ∧ (p V q) = T∧ (p V q) = p V q
So ~ ( p V ( ~ p ∧ q ) ) =~ ( p V q ) =~ p∧ ~ q (or) draw truth tables

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 65

If the function f : R - {1, -1} → A defined by  , is surjective, then A is equal to:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 65


x2 (1 + y) = y

y (y + 1)≥ 0 ⇒ y ∈(-∝, -1) ∪ [0, ∝)
So A = R - [ -1, 0)

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 66

If the fourth term in the Binomial expansion of  , then a value of x is:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 66

equate T4 = 20 × 87

Take logaritham on both side to base 8, we get

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 67

Slope of a line passing through P ( 2, 3) and intersecting the line, x + y = 7 at a distance of 4 units from P, is:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 67



JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 68

If f ( x ) is a non-zero polynomial of degree four, having local extreme points at x = -1, 0,1 ; Then the set S = {x ∈ R : f ( x ) = f ( 0)} contains exactly:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 68


JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 69

Let is parallel to is perpendicular to  is equal to:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 69



JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 70

If the function f defined on   is continuous, then k is equal to:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 70

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 71

Let α and β be the roots of the equation x2 + x + 1 = 0 . Then for y ≠ 0 in R,
 is equal to:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 71


R1 → R1 + R2 + R3 & take common ( y + 1 + α + β )
Given determinant  expanding simplify = y ( y2 ) = y3

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 72

If the line y = mx + 7√3 is normal to the hyperbola , then a value of m is:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 72


Simplify we get m = 2/√5

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 73

The value of 

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 73


Simplify we get, given integral 

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 74

If the line,  meets the plane, x + 2y + 3z = 15 at a point P, then the distance of P from the origin is:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 74

Let P(2t + 1, 3t - 1, 4t + 2) be any point on the line, P lies on plane also
 

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 75

Let = 16(210 - 1), where the function f satisfies f ( x + y ) = f ( x ) f ( y ) for all natural numbers x, y and f (1) = 2 . Then the natural number 'a' is

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 75

f ( x ) = 2x & simplify (using G.P formula) we get a = 3

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 76

​If one end of a focal chord of the parabola, y2 = 16x is at (1, 4 ) , then the length of this focal chord is:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 76


So Q(16, -16 ) , ( P (1, 4) given ) PQ = 25

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 77

The solution of the differential equation  with y (1) = 1, is: 

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 77

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 78

If the tangent to the curve, y = x3 + ax - b at the point (1, -5) is perpendicular to the line, - x + y + 4 = 0 , then which one of the following points lies on the curve?

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 78

f (1) = -5 ⇒ 1 + a - b = -5 ⇒ a - b = -6 ......(1)
f1(x) = 3x2 +a f1(1) = 3+a = -1⇒ a = -4
b = a + 6 = 2
f ( x ) = x3 - 4 x - 2 check options (( 2, -2) satisfies )

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 79

If   then the inverse of  is

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 79


(n -1) n =156 = 13 × 2 ⇒ n =13 (n ∈ N)
So increase of 

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 80

The value of is cos2 100 - cos100 cos 500 + cos2 500 is :

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 80

cos2 A + cos2 B - cos A cos B = 3/4, A + b = 600 

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 81

Let the sum of the first n terms of a non-constant A.P., a1 , a2 , a3 , ... be  A, where A is a constant, If d is the common difference of this A.P., then the ordered pair ( d, a50 ) is equal to:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 81


d = A, a50 = 46A + 50

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 82

A committee of 11 members is to be formed from 8 males and 5 females. If m is the number of ways the committee is formed with at least 6 males and n is the number of ways the committee is formed with at least 3 females, then:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 82

m = 8C6 . 5C5 + 8C7 . 5C4 + 8C8 . 5C3 = 28 + 40 + 10 = 78
n = 8C6 . 5C3 + 8C7 . 5C4 + 8C6 . 5C5 = 78

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 83

Four persons can hit a target correctly with probabilities

respectively. If all hit at the target independently, then the probability that the target would be hit, is:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 83

1 P ( no one hiting the t arg et )

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 84

Let S be the set of all values of x for which the tangent to the curve y = f ( x ) = x3 - x2 - 2x at ( x, y ) is parallel to the line segment joining the points (1, f (1) ) , and ( -1, f ( -1) ) , then S is equal to:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 84

(1, f (1) ) = (1, -2 ) , ( -1, f ( -1) ) = ( -1, 0)
slope = -1 ⇒ 3x2 - 2x - 2 = -1
3x2 - 2x -1 = 0 ⇒ x -1)(3x +1) = 0

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 85

The integral   is equal to (Here C is a constant of integration)

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 85

put 

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 86

Let p, q ∈ R. If 2 - √3 is a root of the quadratic equation, x2 + px + q = 0, then :

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 86

2 + √3 also root, S.R = 2 + √3 + 2 - √3 = -P ⇒ p = -4
P.R = 4-3=q ⇒ q =1
So p2 - 4q - 12 = 16 - 4 - 12 = 0

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 87

If a tangent to the circle x2 + y2 = 1 intersects the coordinate axes at distinct points P and Q, then the locus of the mid-point of PQ is:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 87

Let P ( cos θ, sin θ ) be any point on circle, tangent at P is x cos θ + y sin θ = 1

P x1 , y1 ) be mid point of AB = 

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 88

The area (in sq. units) of the region A = {( x, y ) : x2 ≤ y ≤ x + 2} is:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 88

x2 ≤ y ≤ x + 2
x2 - x - 2 = 0

Draw diagram and find 

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 89

Let f ( x ) = 15 - |x - 10|; x ∈ R. Then the set of all values of x, at which the function, g ( x ) = f ( f ( x ) ) is not differentiable, is:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 89

f ( x) = 15 - x -10 , x ∈ R

JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 90

A plane passing through the points ( 0, -1, 0) and ( 0, 0,1) and making an angle π/4 with the plane y - z + 5 = 0 , also passes through the point:

Detailed Solution for JEE Main 2019 Paper-1 with Solutions (9 April, Slot-1) - Question 90

 is the equation of plane ……(1)
y - z = 0 ..........(2)


So plane equation is

Check options ( √2,1, 4 ) satisfies second equation 

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