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# JEE Main 2019 Question Paper with Solutions (12th January - Evening)

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JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 1

### A load of mass M kg is suspended from a steel wire of length 2 m and radius 1.0 mm in Searle's apparatus experiment. The increase in length produced in the wire is 4.0 mm. Now the load is fully immersed in a liquid of relative density 2. The relative density of the material of load is 8. The new value of increase in length of the steel wire is :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 1

...(1)
T = mg

T = mg – fB

From (1)

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 2

### Formation of real image using a biconvex lens is shown below : If the whole set up is immersed in water without disturbing the object and the screen position, what will one observe on the screen?

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 2

From

Focal length of lens will change hence image disappears from the screen.

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 3

### A vertical closed cylinder is separated into two parts by a frictionless piston of mass m and of negligible thickness. The piston is free to move along the length of the cylinder. The length of the cylinder above the piston is ℓ1, and that below the piston is ℓ2 , such that ℓ1 > ℓ2. Each part of the cylinder contains n moles of an ideal gas at equal temperature T. If the piston is stationary, its mass, m, will be given by : (R is universal gas constant and g is the acceleration due to gravity)

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 3

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 4

A simple harmonic motion is represented by:

The amplitude and time period of the motion are:

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 4

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 5

In the given circuit diagram, the currents , I1 =–0.3A, I4 = 0.8 A and I5 = 0.4 A, are flowing as shown. The currents I2,I3 and I6,respectively, are :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 5

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 6

A particle of mass 20 g is released with an initial velocity 5 m/s along the curve from the point A, as shown in the figure. The point A is at height h from point B. The particle slides along the frictionless surface. When the particle reaches point B, its angular momentum about O will be : (Take g= 10 m/s2)

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 6

Work Energy Theorem from A to B

Angular momentum about 0

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 7

In the above circuit,     Current in L-R1 path is I1 and in C-R2 path it is I2. The voltage of A.C source is given by  volts. The phase difference  between I1 and I2 is :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 7

So phase difference comes out 90 + 60 = 150.
Therefore Ans. is Bonus If R2 is 20 KΩ then phase difference comes out to be 60+30 = 90°

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 8

A paramagnetic material has 1028atoms/m3. Its magnetic susceptibility at temperature 350 K is 2.8 ×10–4. Its susceptibility at 300 K is :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 8

curie law for paramagnetic substane

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

A 10 m long horizontal wire extends from North East to South West. It is falling with a speed of 5.0ms–1, at right angles to the horizontal component of the earth's magnetic field, of 0.3 × l0–4Wb/m2.The value of the induced emf in wire is :

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

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 10

In the figure, given that VBB supply can vary from 0 to 5.0 V, VCC = 5V, βdc = 200, RB = 100 kW, RC=l kΩ and VBE=1.0 V, The minimum base current and the input voltage at which the transistor will go to saturation, will be, respectively :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 10

given

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 11

In the circuit shown, find C if the effective capacitance of the whole circuit is to be 0.5 μF.
All values in the circuit are in μF.

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 11

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

Two satellites, A and B, have masses m and 2m respectively. A is in a circular orbit of radius R, and B is in a circular orbit of radius 2R around the earth. The ratio of their kinetic energies, TA/TB, is:

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

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 13

The moment of inertia of a solid sphere, about an axis parallel to its diameter and at a distance of x from it, is I(x)'. Which one of the graphs represents the variation of I(x) with x correctlv?

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 13

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 14

When a certain photo sensistive surface is illuminated with monochromatic light of frequency n, the stopping potential for the photo current is - V0/2. When the surface is illuminated by monochromatic light of frequency v/2, the stopping potential is -V0. The threshold frequency for photoelectric emission is:

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 14

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 15

A galvanometer, whose resistance is 50 ohm, has 25 divisions in it. When a current of 4 ×10–4 A passes through it, its needle (pointer) deflects by one division. To use this galvanometer as a voltmeter of range 2.5 V, it should be connected to a resistance of:

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 15

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 16

A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is 5 cm and its rotational speed is 2 rotations per second, then the difference in the heights between the centre and the sides, in cm, will be:

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 16

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 17

Two particles A, B are moving on two concentric circles of radii R1 and R2 with equal angular speed ω. At t = 0, their positions and direction of motion are shown in the figure :

The relative velocity  is given by:

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 17

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 18

A plano-convex lens (focal length f2, refractive index μ2, radius of curvature R) fits exactly into a plano-concave lens (focal length f1, refractive index μ1, radius of curvature R). Their plane surfaces are parallel to each other. Then, the focal length of the combination will be :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 18

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 19

Let ℓ, r, c and v represent inductance, resistance, capacitance and voltage, respectively. The dimension of  in SI units will be:

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 19

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 20

In a radioactive decay chain, the initial nucleus is  . At the end there are 6 α-particles and 4 β-particles which are emitted. If the end nucleus, If , A and Z are given by :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 20

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 21

The mean intensity of radiation on the surface of the Sun is about 108 W/m2. The rms value of the corresponding magnetic field is closest to :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 21

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 22

A resonance tube is old and has jagged end. It is still used in the laboratory to determine velocity of sound in air. A tuning fork of frequency 512 Hz produces first resonance when the tube is filled with water to a mark 11 cm below a reference mark, near the open end of the tube. The experiment is repeated with another fork of frequency 256 Hz which produces first resonance when water reaches a mark 27 cm below the reference mark.
The velocity of sound in air, obtained in the experiment, is close to:

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 22

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 23

An ideal gas is enclosed in a cylinder at pressure of 2 atm and temperature, 300 K. The mean time between two successive collisions is 6 × 10–8 s.If the pressure is doubled and temperature is increased to 500 K, the mean time between two successive collisions will be close to:

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 23

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 24

The charge on a capacitor plate in a circuit, as a function of time, is shown in the figure: What is the value of current at t = 4s ?

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 24

since

Therefore current = 0

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 25

A block kept on a rough inclined plane, as shown in the figure, remaias at rest upto a maximum force 2 N down the inclined plane. The maximum external force up the inclined plane that does not move the block is 10 N. The coefficient of static friction betwreen the block and the plane is : [Take g = 10 m/s2]

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 25

2 + mg sin30 = µmg cos30°
10 = mgsin 30 + µ mg cos30°
= 2µmg cos30 –2
6 = µmg cos 30
4 = mg sin 30

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 26

An alpha - particle of mass m suffer s 1-dimensional elastic coolision with a nucleus at rest of unknown mass. It is scattered directly backwards losing, 64% of its initial kinetic energy.The mass of the nucleus is :-

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 26

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 27

A soap bubble, blown by a mechanical pump at the mouth of a tube, increases in volume, with time, at a constant rate. The graph that correctly depicts the time dependence of pressure inside the bubble is given by :-

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 27

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 28

To double the coverging range of a TV transmittion tower, its height should be multiplied by :-

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 28

Range

To double the range h have to be made 4 times

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 29

A parallel plate capacitor with plates of area 1m2 each, are at a separation of 0.1 m. If the electric field between the plates is 100 N/C, the magnitude of charge each plate is :-

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 29

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 30

In a Frank-Hertz experiment, an electron of energy 5.6 eV passes through mercury vapour and emerges with an energy 0.7 eV. The minimum wavelength of photons emitted by mercury atoms is close to :-

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 30

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 31

An open vessel at 27°C is heated until two fifth of the air (assumed as an ideal gas) in it has escaped from the vessel. Assuming that the volume of the vessel remains constant, the temperature at which the vessel has been heated is

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 31

Initial number of moles of an ideal gas = n1
Find number of moles of the ideal gas

At constant volume and pressure, the number of moles of an ideal gas is inversely proportional to temperature

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 32

Given

Based on the above thermochemical equations, find out which one of the following algebraic relationships is correct?

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 32

According to Hess’s law, the enthalpy change of a reaction does not depend on the number of steps involved in the reaction.

** in reaction ii, Product should be CO (gas) instead of CO2 (gas).

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 33

The increasing order of the reactivity of the following with LiAlH4 is

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 33

The reactivity order of carboxylic acid derivatives depends on the leaving tendency of the leaving group. Higher the leaving tendency of the leaving group, higher will be the reactivity of the compound.
Therefore, reactivity order towards LiAlH4 is

Acid halide > Acid anhydride > Ester > Amide

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 34

Among the following, the false statement is

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 34

Latex is colloidal solution of rubber particles which are negatively charged.

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 35

The major product of the following reaction is

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 35

High temperature and strong base favours elimination reaction forming more stable alkene according to Saytzeff rule.

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 36

The magnetic moment of an octahedral homoleptic Mn(II) complex is 5.9 BM. The suitable ligand for this complex is

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 36

Electronic configuration of Mn2+ is
Mn+2 : 3d5

It has 5 unpaired electrons which corresponds to magnetic moment of   This shows that the homoleptic complex of Mn2+ has only weak field ligands and that is NCS. The remaining three ligands are strong field ligands.

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 37

The major product of the following reaction is

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 37

NaBH4 does not reduces the double bond in β - γ unsaturated aldehydes/ ketones.
Only the keto group will be reduced.

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 38

If Ksp of Ag2CO3 is 8 × 10–12, the molar solubility of Ag2CO3 in 0.1 M AgNO3 is

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 38

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 39

for NaCl, HCl and NaA are 126.4, 425.9 and 100.5 S cm2mol–1, respectively. If the conductivity of 0.001 M HA is 5 × 10–5 S cm–1, degree of dissociation of HA is

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 39

(NaCl) = 126.4 S cm2 mol–1

(HCl) = 425.9 S cm2 mol–1

(NaA) = 100.5 S cm2 mol–1

(HA) = 425.9 – 126.4 + 100.5 = 400 S cm2 mol–1

K(HA) = 5 × 10–5 S cm–1

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 40

The major product of the following reaction is

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 40

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 41

The aldehydes which will not form Grignard product with one equivalent Grignard reagent are

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 41

Grignard reagent will not react with aldehydes if it has a functional group which contains acidic hydrogen. Options (B) and (D) have —COOH and — CH2OH respectively which contan acidic H-atom.

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 42

For a reaction, consider the plot of In k versus 1/T given in the figure. If the rate constant of this reaction at 400 K is 10–5 s–1, then the rate constant at 500 K is

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 42

⇒ K2 = 10K1 = 10–5 × 10 = 10–4 S–1

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 43

The major product of the following reaction is

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 43

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 44

The compound that is NOT a common component of photochemical smog is:

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 44

CF2Cl2 is not a common component of photochemical smog.

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 45

The major product in the following conversion is

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 45

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 46

The major product of the following reaction is

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 46

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 47

Molecules of benzoic acid (C6H5COOH) dimerise in benzene. ‘w’ g of the acid dissolved in 30 g of benzene shows a depression in freezing point equal to 2 K. If the percentage association of the acid to form dimer in the solution is 80, then w is
(Given that Kf = 5 K kg mol–1, Molar mass of benzoic acid = 122 g mol–1)

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 47

Moles at equilibrium = 1 – 2α + α = 1 - α

2α = 0.8, α = 0.4

Moles at equilibrium = 0.6

i = 0.6

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 48

Chlorine on reaction with hot and concentrated sodium hydroxide gives

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 48

3Cl2 + 6NaOH → 5NaCl + NaClO3 + 3H2O

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 49

The correct statement(s) among I to III with respect to potassium ions that are abundant within the cell fluids is/are I. They activate many enzymes
II. They participate in the oxidation of glucose to produce ATP
III. Along with sodium ions, they are responsible for the transmission of nerve signals

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 49

K+ ions act as carriers for nerve signals, are activators for many enzymes and participate in the oxidation of glucose to form ATP.

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 50

If the de Broglie wavelength of the electron in nth Bohr orbit in a hydrogenic atom is equal to 1.5 pa0 (a0 is Bohr radius), then the value of n/z is

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 50

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 51

The volume strength of 1M H2O2 is (Molar mass of H2O2 = 34 g mol–1)

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 51

Volume strength ≈ 11.2 × M
≈ 11.2

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 52

The correct order of atomic radii is

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 52

Atomic radii follows the order

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 53

The element that does NOT show catenation is

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 53

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 54

The two monomers for the synthesis of nylon 6, 6 are

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 54

Monomer of Nylon–6, 6 are adipic acid and hexamethylene diammine.

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 55

The pair that does NOT require calcination is

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 55

ZnO and MgO
They are oxides while other are carbonates or hydrated oxides which require calcination.

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 56

The upper stratosphere consisting of the ozone layer protects us from the sun’s radiation that falls in the wavelength region of

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 56

Ozone layer protects from ultra violet radiation.
∴  Wavelength range lies in 200 – 315 nm

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 57

The combination of plots which does not represent isothermal expansion of an ideal gas is

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 57

(B) and (D) are not correct representation for isothermal expansion of ideal gas.

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 58

8 g of NaOH is dissolved in 18 g of H2O. Mole fraction of NaOH in solution and molality (in mol kg–1) of the solution respectively are

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 58

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 59

The element that shows greater ability to form pπ – pπ multiple bonds, is

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 59

Carbon has small size so effective, lateral overlapping between 2p and 2p.

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 60

The correct structure of histidine in a strongly acidic solution (pH = 2) is

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 60

Histidine (in strongly acidic solution)

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 61

Let Z be the set of integers. If   and  , then the number of subsets of the set A × B, is :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 61

A × B has is 15 elements so number of subsets of A × B is 215.

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 62

If  is equal to :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 62

given that

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 63

If an angle between the line,  and the plane, x – 2y – kz = 3 is then a value of k is:

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 63

DR's of line are 2, 1, –2

normal vector of plane is

...1
... 2

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 64

If a straight line passing thourgh the point P(–3, 4) is such that its intercepted portion between the coordinate axes is bisected at P, then its equation is :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 64

equation of line is 4x – 3y + 24 = 0

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 65

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

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 65

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 66

There are m men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by 84, then the value of m is :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 66

Let m-men, 2-women

m2 – 5m – 84 = 0 ⇒ (m – 12) (m + 7) = 0 m = 12

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 67

If the function f given by f(x) = x3 –3(a – 2)x2 + 3ax + 7, for some a∈R is increasing in (0, 1] and decreasing in [1, 5), then a root of the equation,

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 67

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 68

Let f be a differentiable function such that f(1) = 2 and f'(x) = f(x) for all x∈ R. If h(x) = f(f(x)),then h'(1) is equal to :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 68

Intergrate & use f(1) = 2

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 69

The tangent to the curve y = x2 – 5x + 5, parallel to the line 2y = 4x + 1, also passes through the point.

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 69

Equation of tangent at

Now check options

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 70

Let S be the set of all real values of λ such that a plane passing through the points (–λ2, 1, 1), (1, –λ2, 1) and (1, 1, –λ2) also passes through the point (–1, –1, 1). Then S is equal to :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 70

All four points are coplaner so

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 71

If a circle of radius R passes through the origin O and intersects the coordinate axes at A and B, then the locus of the foot of perpendicular from O on AB is :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 71

Slope of AB = -h/k

Equation of AB is hx + ky = h2 + k2

AB = 2R
⇒ (h2 + k2)3 = 4R2h2k2
⇒ (x2 + y2)3 = 4R2x2y2

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 72

The equeation of a tangent to the parabola , x2 = 8y,  which makes an angle θ with the positive direction of x-axis, is :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 72

Equation of tangent :-
y – 2tan2θ = tan θ (x – 4tan θ)
⇒ x = y cot θ + 2 tan θ

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 73

If the angle of elevation of a cloud from a point P which is 25 m above a lake be 30º and the angle of depression of reflection of the cloud in the lake from P be 60º, then the height of the cloud (in meters) from the surface of the lake is :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 73

..(1)

∴ Height of cloud from surface = 25+25 = 50m

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 74

The integral  is equal to :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 74

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 75

is equal to :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 75

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 76

The set of all values of λ for which the system of linear equations.
x – 2y – 2z = λx
x + 2y + z = λy
–x – y = λz
has a non-trivial solution.

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 76

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 77

If nC4, nC5 and nC6 are in A.P., then n can be :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 77

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 78

Let  be three unit vectors, out of which vectors  are non-parallel. If  α and β are the angles which vector  makes with vectors  respectively and then  |α - β| is equal to :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 78

(All given vectors are unit vectors)

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 79

If  then for all  lies in the interval :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 79

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 80

equal to

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 80

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 81

The expression  is logically equvalent to :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 81

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 82

The total number of irrational terms in the binomial expansion of (71/ 5 - 31/10 )60  is:

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 82

General term

∴ for rational term, r = 0, 10, 20, 30, 40, 50, 60
⇒ no of rational terms = 7
∴ number of irrational terms = 54

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 83

The mean and the variance of five observation are 4 and 5.20, respectively. If three of the observations are 3, 4 and 4; then then absolute value of the difference of the other two observations, is :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 83

Using (i) and (ii) (x4 – x5)2 = 49
|x4 – x5| = 7

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 84

If the sum of the first 15 tems of the series is equal to 225 k, then k is equal to :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 84

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 85

Let S and S' be the foci of the ellipse and B be any one of the extremities of its minor axis. If ΔS'BS is a right angled triangle with right angle at B and area (ΔS'BS) = 8 sq. units, then the length of a latus rectum of the ellipse is :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 85

mSB  . mS'B  = –1

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 86

In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 opted for both NCC and NSS. If one of these students is selected at random, then the probability that the student selected has opted neither for NCC nor for NSS is :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 86

A →opted NCC
B →opted NSS

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 87

The number of integral values of m for which the quadratic expression. (1 + 2m)x2 – 2(1 + 3m)x + 4(1 + m), x∈R, is always positive, is :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 87

Exprsssion is always positve it

∴ Common interval is

∴ Intgral value of m  {0,1,2,3,4,5,6}

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 88

In a game, a man wins Rs. 100 if he gets 5 of 6 on a throw of a fair die and loses Rs. 50 for getting any other number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three throws, then his expected gain/ loss (in rupees) is :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 88

Expected Gain/ Loss =
= w × 100 + Lw (–50 + 100) + L2w (–50 –50 + 100) + L3 (–150)

here w denotes probability that outcome 5 or 6 (w = 2/6 = 1/3)

here L denotes probability that outcome

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 89

If a curve passes through the point (1, –2) and has slope of the tangent at any point (x, y) on it as then the curve also passes through the point :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 89

hence bpasses through (1, –2) ⇒C = -9/4

Now check option(s) , Which is satisly by option (ii)

JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 90

Let Z1 and Z2 be two complex numbers satisfying |Z1| = 9 and |Z2–3–4i|=4 . Then the minimum value of |Z1–Z2| is :

Detailed Solution for JEE Main 2019 Question Paper with Solutions (12th January - Evening) - Question 90

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