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JEE Main 2019 Question Paper with Solutions (9th January - Morning)


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JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 1

A current loop, having two circular arcs joined by two radial lines is shown in the figure. It carries a current of 10 A. The magnetic field at point O will be close to :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 1





JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 2

A gas can be taken from A to B via two different processes ACB and ADB.

When path ACB is used 60 J of heat flows into the system and 30 J of work is done by the system. If path ADB is used work done by the system is 10 J. The heat Flow into the system in path ADB is :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 2


JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 3

A plane electromagnetic wave of frequency 50 MHz travels in free space along the positive xdirection. At a particular point  in space and time, The corresponding magnetic field at that point will be:

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 3



JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 4

Two coherent sources produce waves of different intensities which interfere. After interference, the ratio of the maximum intensity to the minimum intensity is 16. The intensity of the waves are in the ratio:

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 4



Using componendo & dividendo.

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 5

An L-shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure. If AB = BC, and the angle made by AB with downward vertical is θ, then :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 5


Let mass of one rod is m.
Balancing torque about hinge point.
mg (C1P) = mg (C2N)


JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 6

A mixture of 2 moles of helium gas (atomic mass = 4 u), and 1 mole of argon gas (atomic mass = 40 u) is kept at 300 K in a container. The ratio of their rms speeds  is close to

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 6

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 7

When the switch S, in the circuit shown, is closed, then the value of current i will be :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 7


Let voltage at C = xv

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 8

A resistance is shown in the figure. Its value and tolerance are given respectively by:

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 8

Color code:
Red violet orange silver
R = 27 x 103 Ω, 10%
= 27 kΩ, 10%

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 9

A bar magnet is demagnetized by inserting it inside a solenoid of length 0.2 m, 100 turns, and carrying a current of 5.2 A. The coercivity of the bar magnet is :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 9

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 10

A rod, of length L at room temperature and uniform area of cross section A, is made of a metal having coefficient of linear expansion α/ °C. It is observed that an external compressive force F, is applied on each of its ends, prevents any change in the length of the rod, when its temperature rises by ΔT K. Young's modulus, Y, for this metal is :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 10



JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 11

A block of mass m, lying on a smooth horizontal surface, is attached to a spring (of negligible mass) of spring constant k. The other end of the spring is fixed, as shown in the figure. The block is initally at rest in its equilibrium position. If now the block is pulled with a constant force F, the maximum speed of the block is :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 11

Maximum speed is at mean position (equilibrium). F = kx



JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 12

Three charges +Q, q, + Q are placed respectively, at distance, 0, d/2 and d from the origin, on the x-axis. If the net force experienced by + Q, placed at x= 0, is zero, then value of q is :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 12


JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 13

A conducting circular loop made of a thill wire, has area 3.5 x 10-3 m2 and resistance 10Ω . It is placed perpendicular to a time dependent magnetic field B(t) = (0.4T)sin(50πt). The field is uniform in space. Then the net charge flowing through the loop during t = 0 s and t = 10 ms is close to:

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 13


JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 14

Two masses m and m/2 are connected at the two ends of a massless rigid rod of length l.The rod is suspended by a thin wire of torsional constant k at the centre of mass of the rod-mass system(see figure). Because of torsional constant k, the restoring torque is π=kθ for angular displacement 0. If the rod is rotated by θ0 and released, the tension in it when it passes through its mean position will be.

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 14







JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 15

A copper wire is stretched to make it 0.5% longer. The percentage change in its electrical resistance if its volume remains unchanged is:

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 15



JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 16

A parallel plate capacitor is made of two square plates of side 'a', separated by a distance d (d<<a). The lower triangular portion is filled with a dielectric of dielectric constant K, as shown in the figure. Capacitance of this capacitor is :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 16








 

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 17

Mobility of electrons in a semiconductor is defined as the ratio of their drift velocity to the applied electric field. If, for an n-type semiconductor, the density of electrons is 1019m-3 and their mobility is 1.6 m2/(V.s) then the resistivity of the semiconductor (since it is an n-type semiconductor contribution of holes is ignored) is close to:

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 17




= 0.4 Ωm

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 18

If the angular momentum of a planet of mass m, moving around the Sun in a circular orbit is L, about the center of the Sun, its areal velocity is :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 18

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 19

A block of mass 10 kg is kept on a rough inclined plane as shown in the figure. A force of 3 N is applied on the block. The coefficient of static friction between the plane and the block is 0.6. What should be the minimum value of force P, such that the block doesnot move downward ?

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 19




JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 20

Temperature difference of 120°C is maintained between two ends of a uniform rod AB of length 2L. Another bent rod PQ, of same cross- section as AB and length 3L/2 is connected across AB (See figure). In steady state, temperature difference between P and Q will be close to :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 20



JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 21

A heavy ball of mass M is suspended from the ceiling of a car by a light string of mass m (m<<M). When the car is at rest, the speed of transverse waves in the string is 60 ms-1. When the car has acceleration a, the wave-speed increases to 60.5 ms-1. The value of a, in terms of gravitational acceleration g, is closest to :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 21





JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 22

A sample of radioactive material A, that has an activity of 10 mCi(1 Ci = 3.7 x 1010 decays/s), has twice the number of nuclei as another sample of a different radioactive material B which has an activity of 20 mCi. The correct choices for half-lives of A and B would then be respectively :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 22

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 23

Consider a tank made of glass(reiractive index 1.5) with a thick bottom. It is filled with a liquid of refractive index μ. A student finds that, irrespective of what the incident angle i (see figure) is for a beam of light entering the liquid, the light reflected from the liquid glass interface is never completely polarized. For this to happen, the minimum value of μ is :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 23

C < ib here ib is "brewester angle" and c is critical angle
sinc < sinib




slab µ = 1.5

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 24

An infinitely long current carrying wire and a small current carrying loop are in the plane of the paper as shown. The radius of the loop is a and distance of its centre from the wire is d (d»a). If the loop applies a force F on the wire then :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 24


Eqvilent dipole of given loop




JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 25

Surface of certain metal is first illuminated with light of wavelength λ1 =350 nm and then, by light of wavelength λ2=540 nm. It is found that the maximum speed of the photo electrons in the two cases differ by a factor of 2. The work function of the metal (in eV) is close to :
(Energy of photon = )

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 25



JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 26

A particle is moving with a velocity where K is a constant. The general equation for its path is:

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JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 27

A convex lens is put 10 cm from a light source and it makes a sharp image on a screen, kept 10 cm from the lens. Now a glass block (refractive index 1.5) of 1.5 cm thickness is placed in contact with the light source. To get the sharp image again, the screen is shifted by a distance d. Then d is :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 27



Shift due to slab =  in the direction of incident ray

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 28

For a uniformly charged ring of radius R, the electric field on its axis has the largest magnitude at a distance h from its centre. Then value of h is :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 28

Electric field on axis of ring

for maximum electric field

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 29

Three blocks A, B and C are lying on a smooth horizontal surface, as shown in the figure. A and B have equal masses, m while C has mass M. Block A is given an brutal speed v towards B due to which it collides with B perfectly inelastically. The combined mass collides with C, also perfectly inelastically 5/6 th of the initial kinetic energy is lost in whole process. What is value of M/m ?

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 29


JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 30

Drift speed of electrons, when 1.5 A of current flows in a copper wire of cross section 5 mm2, is v. If the electron density in copper is 9 ×1028 /m3 the value of v in mm/s is close to (Take charge of electron to be =1.6 × 10–19C)

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 30

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 31

Which one of the following statements regarding Henry's law not correct?

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 31

Liquid solution
Pgas = KH × Xgas
More is KH less is solubility, lesser solubility is at higher temperature. So more is temperature more is KH.

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 32

The correct decreasing order for acid strength is :-

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 32

EWG increasea acidic strength
NO2CH2COOH > NCCH2COOH >FCH2COOH > CICH2COOH

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 33

Two complexes [Cr(H2O6)Cl3] (A) and [Cr(NH3)6]Cl3 (B) are violet and yellow coloured, respectively. The incorrect statement regarding them is :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 33

Δ0 order will be compared by spectro chemical series not by energies of violet & yellow light so Δ0 order is
[Cr(H2O)6]Cl3 < [Cr(NH3)6]Cl3

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 34

Adsorption of a gas follows Freundlich h adsorption isotherm. In the given plot, x is the mass of the gas adsorbed on mass m of the adsorbent at pressure p. x/m is proportional to

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 34

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 35

Correct statements among a to d regarding silicones are :
(a) They are polymers with hydrophobic character
(b) They are biocompatible.
(c) In general, they have high thermal stability and low dielectric strength.
(d) Usually, they are resistant to oxidation and used as greases.

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 35

These are properties and uses of silicones.

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 36

For emission line of atomic hydrogen from ni = 8 to nf =n, the plot of wave number against will be (The Rydbergconstant, RH is in wave number unit).

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 36





m = RH
Linear with slope RH

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 37

The major product of the following reaction is:

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 37

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 38

The alkaline earth metal nitrate that does not crystallise with water molecules, is :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 38

Smaller in size of center atoms more water molecules will crystallize hence Ba(NO3)2 is answer due to its largest size of '+ve' ion.

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 39

Major product of the following reaction is :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 39


NH2(a) will wact as nucleophile as (b) is having delocalised lonepair.

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 40

The highest value of the calculated spin only magnetic moment (in BM) among all the transition metal complexs is :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 40


n = Number of unpaired electrons
n = Maximum number of unpaired electron = 5
Ex : Mn2+ complex.

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 41

20 mL of 0.1 MH2SO4  solution is added to 30 mL of 0.2 M NH4OH solution. The pH of the resulatant mixture is : [pkb of NH4OH = 4.7].

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 41


JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 42

0.5 moles of gas A and x moles of gas B exert a pressure of 200 Pa in a a container of volume 10 m3 at 1000 K. given R is the gas constant in JK–1 mol–1m, x is :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 42


JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 43

Consider the reversible isothermal expansion of an ideal gas in a closed system at two different temperatures T1 and T2 (T1 < T2). The correct graphical depiction of the dependence of work done (w) on the final volume (V) is:

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 43



Y = m x – C
So, slope of curve 2 is more than curve 1 and intercept of curve 2 is more negative then curve 1.

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 44

The major product of following reaction is :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 44

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 45

In general, the properties that decrease and increase down a group in the periodic table, respectively, are :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 45

Electronegativity decreases as we go down the group and atomic radius increases as we go down the group.

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 46

A solution of sodium sulfate contains 92 g of Na+ ions per kilogram of water. The molality of Na+ ions in that solution in mol kg–1 is:

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 46


So molality = 4

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 47

A water sample has ppm level concentration of the following metals: Fe= 0.2; Mn = 5.0; Cu = 3.0; Zn = 5.0. The metal that makes the water sample unsuitable drinking is :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 47

(i) Zn = 0.2
(ii) Fe = 0.2
(iii) Mn = 5.0
(iv) Cu = 3.0

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 48

The increasing order of pKa of the following amino acids in aqueous solution is : Gly Asp Lys Arg

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 48

Order of acidic strength :

So, pKa
Asp < Gly < Arg < Lys

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 49

According to molecular orbital theory, which of the following is true with respect to Li2+ and Li2?

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 49

Both Li2+ and Li2-​ has 0.5 bond order and hence both are stable.

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 50

The following results were obtained during kinetic studies of the reaction :
2A + B → Products

The time (in minutes) required to consume half of A is :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 50

6.93×10-3=K×(0.1)x(0.2)y
6.93×10-3=K×(0.1)x(0.25)y
So y = 0
and 1.386×10-2=K×(0.2)x(0.30)y
1/2=(1/2)x x=1
So r=K×(0.1)×(0.2)0
6.93×10−3=K×0.1×(0.2)0
K=6.93×10-2
t1/2=0.693/2K
= 0.693/(0.693×10-1×2)
= 10/2
= 5

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 51

The major product of the following reaction is:

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 51


During AES Br is o/p directing and major product will be formed on less hindrance p position :

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 52

Arrange the following amines in the decreasing order of basicity:

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 52

Order of basic strength :

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 53

Which amongst the following is the strongest acid ?

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 53

CN makes anino most stable so answer is CH(CN)3

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 54

The anodic half-cell of lead-acid battery is recharged unsing electricity of 0.05 Faraday. The amount of PbS04 electrolyzed in g during the process is: (Molar mass of PbS04 = 303 g mol-1)

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 54

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 55

The one that is extensively used as a piezoelectric material is :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 55

Quartz (Information)

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 56

Aluminium is usually found in +3 oxidation stagte. In contarast, thallium exists in +1 and +3 oxidation states. This is due to :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 56

Inert pair effect is promenent character of p block element.

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 57

The correct match between Item -I and ItemII is :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 57




JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 58

The ore that contains both iron and copper is:

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 58

Copper pyrites : CuFeS2
Malachite  : Cu(OH)2 . CuCO3
Azurite Cu(OH)2 . 2CuCO3
Dolomite CaCO3 . MgCO3

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 59

The compounds A and B in the following reaction are, respectively:

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 59

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 60

The isotopes of hydrogen are :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 60

Isotopes of hydrogen are: Proteium, Deuterium, Tritium

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 61

The area (in sq. units) bounded by the parabola y = x2 - 1, the tangent at the point (2, 3 ) to it and the y-axis is :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 61


Equation of tangent at (2,3) on
y = x2 – 1, is y = (4x – 5) ....(i)
∴ Requireds haded area

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 62

The maximum volume (in cu. m) of the right circular cone having slant height 3m is :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 62


∴ h = 3 cos θ
r = 3 sin θ
Now,


⇒ Volume is maximum,

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 63

For x≠ nπ + 1, n ∈ N (the set of natural numbers), the integral  is equal to :
(where c is a constant of integration)

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 63



 

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 64

Let α and β be two roots of the equation x2 + 2x + 2 = 0, then α15 + β15 is equal to :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 64

We have
(x + 1)2 + 1 = 0
⇒ (x + 1)2 – (i)2 = 0
⇒ (x + 1 + i) (x + 1 – i) = 0

So,   α15 + β15 = (α2)7 α + (β2)7 β
= –128 (–i + 1 + i + 1)
= – 256

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 65

If y = y( x) is the solution of the differential equation.satisfying y(1) = 1, then is equal to :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 65


JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 66

Equation of a common tangent to the circle, x2 + y2 - 6x = 0 and the parabola, y2 = 4x, is:

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 66

Let equation of tangent to the parabola y2 = 4x is

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 67

Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be fomied from this class, if there are two specific boys A and B, who refuse to be the members of the same team, is:

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 67

Required number of ways
= Total number of ways – When A and B are always included.
= 5C2 . 7C3 - 5C1 . 5C2 = 300

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 68

Three circles of radii a, b, c( a < b < c) touch each other externally. If they have x-axis as a common tangent, then :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 68


AB = AC + CB

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 69

If the fractional part of the number 2403/15 is k/15, then k is equal to :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 69


∵ 8λ is integer
⇒ fractional part of 

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 70

Axis of a parabola lies along x-axis. If its vertex and focus are at distances 2 and 4 respectively from the origin, on the positive x-axis then which of the following points does not lie on it ?

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 70


equation of parabola is
y2 = 8(x – 2)
(8, 6) does not lie on parabola.

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 71

The plane through the intersection of the planes x + y + z = 1 and 2x + 3y-z + 4 = 0 and parallel to y-axis also passes through the point :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 71

Equation of plane
(x + y + z – 1) + λ(2x + 3y – z + 4) = 0
⇒ (1 + 2λ)x + (1 + 3λ)y + (1 – λ)z – 1 +4λ = 0
dr's of normal of the plane are
1 + 2λ, 1+ 3λ, 1 – l
Since plane is parallel to y - axis, 1 + 3λ = 0
⇒ λ = –1/3
So the equation of plane is
x + 4z – 7 = 0
Point (3, 2, 1) satisfies this equation
Hence Answer is (3)

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 72

If a, b and c be three distinct real numbers in G. P. and a + b + c = xb, then x cannot be :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 72


given a + b + c = xb
⇒ b/r + b + br = xb
⇒ b = 0 (not possible)

⇒ x – 1 > 2 or x – 1 < –2
⇒ x > 3 or x < – 1
So x can't be '2'

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 73

Consider the set of all lines px + qy + r = 0 such that 3p + 2q + 4r = 0. Which one of the following statements is true ?

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 73

Given set of lines px + qy + r = 0
given condition 3p + 2q + 4r = 0

⇒ All lines pass through a fixed point
.

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 74

The system of linear equations.
x + y + z = 2
2x + 3y + 2z = 5
2x + 3y + (a2 – 1)z = a + 1

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 74





JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 75

Let  be a vector such that is equal to :-

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 75



JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 76

Let a1, a2,.........,a30 be an A. P., S =  and If a5 = 27 and S – 2T = 75, then a10 is equal to :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 76

S = a1 + a2 + ...... + a30

S = 15(a1 + a30) = 15 (a1 + a1 + 29d)
T = a1 + a3 + ..... + a29
= (a1) + (a1 + 2d) ..... + (a1 + 28d)
= 15a1 + 2d(1 + 2 + ..... + 14)
T = 15a1 + 210 d
Now use S – 2T = 75
⇒ 15 (2a1 + 29d) – 2 (15a1 + 210 d) = 75
⇒ d = 5
Given a5 = 27 = a1 + 4d ⇒ a1 = 7
Now  a10 = a1 + 9d = 7 + 9 × 5 = 52

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 77

5 students of a class have an average height 150 cm and variance 18 cm2. A new student, whose height is 156 cm, joined them. The variance (in cm2) of the height of these six students is:

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 77


 (i)

 (ii)
Given height of new student
x6 = 156



= 22821- 22801 = 20

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 78

Two cards are drawn successively with replacement from a well-shuffled deck of 52 cards. Let X denote the random variable of number of aces obtained in the two drawn cards. Then P(X = 1) + P(X = 2) eauals :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 78

Two cards are drawn successively with replacement
4 Aces  48 Non Aces


JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 79

For x ∈ R - {0, 1}, let f1(x) = 1/x, f2(x) = 1 – x and  f3(x) =  be three given functions. If a function, J(x) satisfies (f2°J°f1)(x) = f3(x) then J(x) is equal to :-

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 79




 

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 80

Let Then the sum of the elements in A is :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 80

is purely img
so real part becomes zero.

Now  Re(z) = 0


then sum of the elements in A is

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 81

If θ denotes the acute angle between the curves,y = 10 – x2 and y = 2 + x2 at a point of their intersection, then |tan θ| is equal to :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 81

Point of intersection is P (2, 6).


 

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 82

If then the matrix A–50  when   is equal to :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 82

Here, AAT = I


JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 83

Let 0 < θ < π/2. If the eccentricity of the hyperbola  is greater than 2, then the length of its latus rectum lies in the interval :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 83



= 2(sec θ – cos θ)
Which is strictly increasing, so
ℓ (L.R) ∈(3, ∞).

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 84

The equation of the line passing through (–4, 3, 1), parallel to the plane x + 2y – z – 5 = 0 and intersecting the line is:

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 84


Normal vector of plane containing two intersecting lines is parallel to vector.


∴ Required line is parallel to vector

⇒ Required equation of line is

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 85

For any θ ∈ , the expression 3(sinθ – cosθ)4 + 6(sinθ + cosθ)2 + 4sin6θ equals :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 85

We have,
3(sinθ – cosθ)4 + 6(sinθ + cosθ)2 + 4 sin6θ
= 3(1 – sin2θ)2 + 6(1 + sin2θ) + 4sin6θ
= 3(1 – 2sin2θ + sin22θ) + 6 + 6 sin2θ + 4sin6θ
= 9 + 12 sin2θ · cos2θ + 4(1 – cos2θ)3
= 13 – 4 cos6θ

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 86

If  then x is equal to :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 86






JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 87

The value of 

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 87





JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 88

If the Boolean expression  is equivalent to p ^ q, where  then the ordered pair  is:

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 88

 (given)

from truth table 

JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 89

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 89





JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 90

Let f : R → R be a function defined as :

Then, f is :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (9th January - Morning) - Question 90


f(1) = 5,   f(1) = 5,   f(1+) = a + b
f(3) = a + 3b,  f(3) = b + 15,  f(3+) = b + 15
f(5) = b + 25 ;  f(5) = 30     f(5+) = 30
from above we concluded that f is not continuous for any values of a and b.

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