Solved papers for JEE Main & Advanced JEE Main Paper (Held on 09-4-2019 Afternoon)

JEE Main Paper (Held on 09-4-2019 Afternoon) Total Questions - 90

1) Two coils 'P' and 'Q' are separated by some distance. When a current of 3 A flows through coil 'P', a magnetic flux of \[{{10}^{-3}}\]Wb passes through 'Q'. No current is passed through 'Q'. When no current passes through 'P' and a current of 2 A passes through 'Q', the flux through 'P' is:-          [JEE Main 9-4-2019 Afternoon]

A)

\[6.67\times {{10}^{3}}Wb\]

B)

\[6.67\times {{10}^{4}}Wb\]

C)

\[3.67\times {{10}^{4}}Wb\]

D)

\[3.67\times {{10}^{3}}Wb\]

View Answer
2) A metal wire of resistance \[3\Omega \]is elongated to make a uniform wire of double its previous length. This new wire is now bent and the ends joined to make a circle. If two points on this circle make an angle \[60{}^\circ \] at the centre, the equivalent resistance between these two points will be :-          [JEE Main 9-4-2019 Afternoon]

A)

\[\frac{12}{5}\Omega \]

B)

\[\frac{5}{3}\Omega \]

C)

\[\frac{5}{2}\Omega \]

D)

\[\frac{7}{2}\Omega \]

View Answer
3) The resistance of a galvanometer is 50 ohm and the maximum current which can be passed through it is 0.002 A. What resistance must be connected to it in order to convert it into an ammeter of range 0 - 0.5 A? [JEE Main 9-4-2019 Afternoon]

A)

0.2 ohm

B)

0.002 ohm

C)

0.02 ohm

D)

0.5 ohm

View Answer
4) The position of a particle as a function of time t, is given by \[x(t)=at\,+b{{t}^{2}}-c{{t}^{3}}\] where a, b and c are constants. When the particle attains zero acceleration, then its velocity will be:                         [JEE Main 9-4-2019 Afternoon]

A)

\[a+\frac{{{b}^{2}}}{4c}\]

B)

\[a+\frac{{{b}^{2}}}{c}\]

C)

\[a+\frac{{{b}^{2}}}{2c}\]

D)

\[a+\frac{{{b}^{2}}}{3c}\]

View Answer
5) A thin convex lens L (refractive index = 1.5) is placed on a plane mirror M. When a pin is placed at A, such that OA = 18 cm, its real inverted image is formed at A itself, as shown in figure. When a liquid of refractive index \[{{\mu }_{1}}\] is put between the lens and the mirror, The pin has to be moved to A', such that OA' = 27 cm, to get its inverted real image at A' itself. The value of μ1 will be :-             [JEE Main 9-4-2019 Afternoon]

A)

\[\sqrt{2}\]

B)

\[\frac{4}{3}\]

C)

\[\sqrt{3}\]

D)

\[\frac{3}{2}\]

View Answer
6) A moving coil galvanometer has a coil with 175 turns and area \[1c{{m}^{2}}.\]It uses a torsion band of torsion constant \[{{10}^{-6}}\] N-m/rad. The coil is placed in a maganetic field B parallel to its plane. The coil deflects by\[1{}^\circ \]for a current of 1 mA. The value of B (in Tesla) is approximately :- [JEE Main 9-4-2019 Afternoon]

A)

\[{{10}^{-3}}\]

B)

\[{{10}^{-1}}\]

C)

\[{{10}^{-4}}\]

D)

\[{{10}^{-2}}\]

View Answer
7) A very long solenoid of radius R is carrying current \[I(t)=kt{{e}^{-\alpha t}}(k>0),\]as a function of time \[(t\ge 0).\]counter clockwise current is taken to be positive. A circular conducting coil of radius 2R is placed in the equatorial plane of the solenoid and concentric with the solenoid. The current induced in the outer coil is correctly depicted, as a function of time, by :- [JEE Main 9-4-2019 Afternoon]

A)

B)

C)

D)

View Answer
8) A massless spring (k = 800 N/m), attached with a mass (500 g) is completely immersed in 1 kg of water. The spring is stretched by 2 cm and released so that it starts vibrating. What would be the order of magnitude of the change in the temperature of water when the vibrations stop completely? (Assume that the water container and spring receive negligible heat and specific heat of mass = 400 J/kg K, specific heat of water = 4184 J/kg K) [JEE Main 9-4-2019 Afternoon]

A)

\[{{10}^{-3}}K\]

B)

\[{{10}^{-4}}K\]

C)

\[{{10}^{-1}}K\]

D)

\[{{10}^{-5}}K\]

View Answer
9) A particle 'P' is formed due to a completely inelastic collision of particles 'x' and 'y' having de-Broglie wavelengths \['{{\lambda }_{x}}'\]and \['{{\lambda }_{y}}'\] respectively. If x and y were moving in opposite directions, then the de-Broglie wavelength of 'P' is :- [JEE Main 9-4-2019 Afternoon]

A)

\[{{\lambda }_{x}}+{{\lambda }_{y}}\]

B)

\[\frac{{{\lambda }_{x}}{{\lambda }_{y}}}{{{\lambda }_{x}}+{{\lambda }_{y}}}\]

C)

\[\frac{{{\lambda }_{x}}{{\lambda }_{y}}}{|{{\lambda }_{x}}-{{\lambda }_{y}}|}\]

D)

\[{{\lambda }_{x}}-{{\lambda }_{y}}\]

View Answer
10) A convex lens of focal length 20 cm produces images of the same magnification 2 when an object is kept at two distances \[{{x}_{1}}\] and \[{{x}_{2}}\] \[({{x}_{1}}>{{x}_{2}})\]from the lens. The ratio of \[{{x}_{1}}\] and \[{{x}_{2}}\] is :-             [JEE Main 9-4-2019 Afternoon]

A)

5 : 3

B)

             2 : 1

C)

4 : 3

D)

3 : 1

View Answer
11) Diameter of the objective lens of a telescope is 250 cm. For light of wavelength 600nm. coming from a distant object, the limit of resolution of the telescope is close to :- [JEE Main 9-4-2019 Afternoon]

A)

\[1.5\times {{10}^{7}}rad\]

B)

\[~2.0\times {{10}^{7}}rad\]

C)

\[3.0\times {{10}^{7}}rad\]

D)

\[4.5\times {{10}^{7}}rad\]

View Answer
12) Moment of inertia of a body about a given axis is 1.5 kg \[{{m}^{2}}\]. Initially the body is at rest. In order to produce a rotational kinetic energy of 1200 J, the angular acceleration of \[20\text{ }rad/{{s}^{2}}\] must be applied about the axis for a duration of :- [JEE Main 9-4-2019 Afternoon]

A)

2 s

B)

5s

C)

2.5 s

D)

3 s

View Answer
13) The logic gate equivalent to the given logic circuit is :- [JEE Main 9-4-2019 Afternoon]

A)

OR

B)

AND

C)

NOR

D)

NAND

View Answer
14) \[50W/{{m}^{2}}\]energy density of sunlight is normally incident on the surface of a solar panel. Some part of incident energy (25%) is reflected from the surface and the rest is absorbed. The force exerted on \[1{{m}^{2}}\]surface area will be close to \[\left( c=3\times {{10}^{8}}m/s \right)\]:- [JEE Main 9-4-2019 Afternoon]

A)

\[15\times {{10}^{8}}N\]

B)

\[35\times {{10}^{8}}N\]

C)

\[10\times {{10}^{8}}N\]

D)

\[20\times {{10}^{8}}N\]

View Answer
15) The area of a square is 5.29 \[c{{m}^{2}}\]. The area of 7 such squares taking into account the significant figures is :- [JEE Main 9-4-2019 Afternoon]

A)

\[37c{{m}^{2}}\]

B)

\[37.0\text{ }c{{m}^{2}}\]

C)

\[37.03\text{ }c{{m}^{2}}\]

D)

\[37.030\text{ }c{{m}^{2}}\]

View Answer
16) The physical sizes of the transmitter and receiver antenna in a communication system are :- [JEE Main 9-4-2019 Afternoon]

A)

proportional to carrier frequency

B)

inversely proportional to modulation frequency

C)

inversely proportional to carrier frequency

D)

independent of both carrier and modulation frequency

View Answer
17) Four point charges \[q,+q,+q\]and -q are placed on y-axis at \[y=2d,y=d,y=+d\] and \[y=+2d,\]respectively. The magnitude of the electric field E at a point on the x-axis at \[x=D,\] with \[D>>d,\]will behave as :- [JEE Main 9-4-2019 Afternoon]

A)

\[E\propto \frac{1}{D}\]

B)

\[E\propto \frac{1}{{{D}^{3}}}\]

C)

\[E\propto \frac{1}{{{D}^{2}}}\]

D)

\[E\propto \frac{1}{{{D}^{4}}}\]

View Answer
18) The specific heats, \[{{C}_{P}}\] and \[{{C}_{V}}\] of a gas of diatomic molecules, A, are given (in units of \[J\,mo{{l}^{-1}}{{K}^{-1}}\]) by 29 and 22, respectively. Another gas of diatomic molecules, B, has the corresponding values 30 and 21. If they are treated as ideal gases, then :- [JEE Main 9-4-2019 Afternoon]

A)

A has one vibrational mode and B has two

B)

Both A and B have a vibrational mode each

C)

A is rigid but B has a vibrational mode

D)

A has a vibrational mode but B has none

View Answer
19) The position vector of a particle changes with time according to the relation \[\vec{r}(t)=15{{t}^{2}}\hat{i}+(4-{{20}^{2}})\hat{j}.\] What is the magnitude of the acceleration at t = 1 ? [JEE Main 9-4-2019 Afternoon]

A)

40

B)

100

C)

25

D)

50

View Answer
20) A test particle is moving in a circular orbit in the gravitational field produced by a mass density \[\rho (r)=\frac{K}{{{r}^{2}}}.\]Identify the correct relation between the radius R of the particle's orbit and its period T : [JEE Main 9-4-2019 Afternoon]

A)

\[T/{{R}^{2}}\] is a constant

B)

\[TR\] is a constant

C)

\[{{T}^{2}}/{{R}^{3}}\] is a constant

D)

\[T/R\] is a constant

View Answer
21) A particle of mass 'm' is moving with speed '2v' and collides with a mass '2m' moving with speed 'v' in the same direction. After collision, the first mass is stopped completely while the second one splits into two particles each of mass 'm', which move at angle\[45{}^\circ \]with respect to the original direction. The speed of each of the moving particle will be :- [JEE Main 9-4-2019 Afternoon]

A)

\[\text{v/}\left( 2\sqrt{2} \right)\]

B)

\[2\sqrt{2}\text{v}\]

C)

\[\sqrt{2}\text{v}\]

D)

\[\text{v}/\sqrt{2}\]

View Answer
22) A wooden block floating in a bucket of water has\[\frac{4}{5}\]of its volume submerged. When certain amount of an oil is poured into the bucket, it is found that the block is just under the oil surface with half of its volume under water and half in oil. The density of oil relative to that of water is :- [JEE Main 9-4-2019 Afternoon]

A)

0.5

B)

0.7

C)

0.6

D)

0.8

View Answer
23) Two cars A and B are moving away from each other in opposite directions. Both the cars are moving with a speed of \[20\,m{{s}^{-1}}\]with respect to the ground. If an observer in car A detects a frequency 2000 Hz of the sound coming from car B, what is the natural frequency of the sound source in car B? (speed of sound in air \[=340\,m{{s}^{-1}}\]) :- [JEE Main 9-4-2019 Afternoon]

A)

2250 Hz

B)

2060 Hz

C)

2150 Hz

D)

2300 Hz

View Answer
24) A wedge of mass M = 4m lies on a frictionless plane. A particle of mass m approaches the wedge with speed v. There is no friction between the particle and the plane or between the particle and the wedge. The maximum height climbed by the particle on the wedge is given by :- [JEE Main 9-4-2019 Afternoon]

A)

\[\frac{2{{\text{v}}^{2}}}{7g}\]

B)

\[\frac{{{\text{v}}^{2}}}{g}\]

C)

\[\frac{\text{2}{{\text{v}}^{2}}}{5g}\]

D)

\[\frac{{{\text{v}}^{2}}}{2g}\]

View Answer
25) A \[H{{e}^{+}}\] ion is in its first excited state. Its ionization energy is:- [JEE Main 9-4-2019 Afternoon]

A)

6.04 eV

B)

13.60 eV

C)

54.40 eV

D)

48.36 eV

View Answer
26) Two materials having coefficients of thermal conductivity '3K' and 'K' and thickness 'd' and '3d', respectively, are joined to form a slab as shown in the figure. The temperatures of the outer surfaces are \['{{\theta }_{2}}'\]and \['{{\theta }_{1}}'\]respectively, \[({{\theta }_{2}}>{{\theta }_{1}}).\]The temperature at the interface is :- [JEE Main 9-4-2019 Afternoon]

A)

\[\frac{{{\theta }_{2}}+{{\theta }_{1}}}{2}\]

B)

\[\frac{{{\theta }_{1}}}{10}+\frac{9{{\theta }_{2}}}{10}\]

C)

\[\frac{{{\theta }_{1}}}{3}+\frac{2{{\theta }_{2}}}{3}\]

D)

\[\frac{{{\theta }_{1}}}{6}+\frac{5{{\theta }_{2}}}{6}\]

View Answer
27) A thin smooth rod of length L and mass M is rotating freely with angular speed\[{{\omega }_{0}}\]about an axis perpendicular to the rod and passing through its center. Two beads of mass m and negligible size are at the center of the rod initially. The beads are free to slide along the rod. The angular speed of the system , when the beads reach the opposite ends of the rod, will be :- [JEE Main 9-4-2019 Afternoon]

A)

\[\frac{M{{\omega }_{0}}}{M+3m}\]

B)

\[\frac{M{{\omega }_{0}}}{M+m}\]

C)

\[\frac{M{{\omega }_{0}}}{M+2m}\]

D)

\[\frac{M{{\omega }_{0}}}{M+6m}\]

View Answer
28) The parallel combination of two air filled parallel plate capacitors of capacitance C and nC is connected to a battery of voltage, V. When the capacitors are fully charged, the battery is removed and after that a dielectric material of dielectric constant K is placed between the two plates of the first capacitor. The new potential difference of the combined system is :- [JEE Main 9-4-2019 Afternoon]

A)

\[\frac{V}{K+n}\]

B)

(v)\[V\]

C)

\[\frac{(n+1)V}{(K+n)}\]

D)

\[\frac{nV}{K+n}\]

View Answer
29) In a conductor, if the number of conduction electrons per unit volume is \[8.5\times {{10}^{28}}\text{ }{{m}^{3}}\] and mean free time is 25?s (fem to second), it's approximate resistivity is :- \[\left( {{m}_{e}}=9.1\times {{10}^{31}}kg \right)\] [JEE Main 9-4-2019 Afternoon]

A)

\[{{10}^{-5}}\Omega m\]

B)

\[{{10}^{-6}}\Omega m\]

C)

\[{{10}^{-7}}\Omega m\]

D)

\[{{10}^{-8}}\Omega m\]

View Answer
30) A string 2.0 m long and fixed at its ends is driven by a 240 Hz vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is :- [JEE Main 9-4-2019 Afternoon]

A)

320m/s, 120 Hz

B)

180m/s, 80 Hz

C)

180m/s, 120 Hz

D)

320m/s, 80 Hz

View Answer
31) Increasing order of reactivity of the following compounds for \[{{S}_{N}}1\]substitution is:

[A] [B]

[C] [D]

[JEE Main 9-4-2019 Afternoon]

A)

\[\left( B \right)<\left( C \right)<\left( D \right)<\left( A \right)\]

B)

\[\left( A \right)<\left( B \right)<\left( D \right)<\left( C \right)\]

C)

\[\left( B \right)<\left( A \right)<\left( D \right)<\left( C \right)\]

D)

\[\left( B \right)<\left( C \right)<\left( A \right)<\left( D \right)\]

View Answer
32) The one that is not a carbonate is : [JEE Main 9-4-2019 Afternoon]

A)

bauxite

B)

siderite

C)

calamine

D)

malachite

View Answer
33) During compression of a spring the work done is 10kJ and 2kJ escaped to the surroundings as heat. The change in internal energy, \[\Delta U\](in kJ) is: [JEE Main 9-4-2019 Afternoon]

A)

8

B)

12

C)

- 12

D)

-8

View Answer
34) The amorphous form of silica is : [JEE Main 9-4-2019 Afternoon]

A)

quartz

B)

kieselguhr

C)

cristobalite

D)

tridymite

View Answer
35) The major products A and B for the following reactions are, respectively: [JEE Main 9-4-2019 Afternoon]

A)

B)

C)

D)

View Answer
36) Which one of the following about an electron occupying the 1s orbital in a hydrogen atom is incorrect ? (The Bohr radius is represented by \[{{a}_{0}}\]) [JEE Main 9-4-2019 Afternoon]

A)

The electron can be found at a distance \[2{{a}_{0}}\]from the nucleus

B)

The probability density of finding the electron is maximum at the nucleus.

C)

The magnitude of potential energy is double that of its kinetic energy on an average.

D)

The total energy of the electron is maximum when it is at a distance \[{{a}_{0}}\] from the nucleus.

View Answer
37) The maximum possible dent cities of a ligand given below towards a common transition and inner-transition metal ion, respectively, are : [JEE Main 9-4-2019 Afternoon]

A)

6 and 8

B)

8 and 6

C)

8 and 8

D)

6 and 6

View Answer
38) The correct statements among I to III regarding group 13 element oxides are,

(I) Boron trioxide is acidic.

(II) Oxides of aluminium and gallium are amphoteric.

(III) Oxides of indium and thalliumare basic.

[JEE Main 9-4-2019 Afternoon]

A)

(I), (II) and (III)

B)

(II) and (III) only

C)

(I) and (III) only

D)

(I) and (II) only

View Answer
39) Among the following species, the diamagnetic molecule is :- [JEE Main 9-4-2019 Afternoon]

A)

\[{{O}_{2}}\]

B)

\[NO\]

C)

\[{{B}_{2}}\]

D)

\[CO\]

View Answer
40) The peptide that gives positive ceric ammonium nitrate and carbylamine tests is : [JEE Main 9-4-2019 Afternoon]

A)

Lys-Asp

B)

Ser-Lys

C)

Gln-Asp

D)

Asp-Gln

View Answer
41) Assertion: For the extraction of iron, haematite ore is used.

Reason: Haematite is a carbonate ore of iron.

[JEE Main 9-4-2019 Afternoon]

A)

Only the reason is correct.

B)

Both the assertion and reason are correct and the reason is the correct explanation for the assertion.

C)

Only the assertion is correct.

D)

Both the assertion and reason are correct, but the reason is not the correct explanation for the assertion.

View Answer
42) 10 mL of 1mM surfactant solution forms a monolayer covering \[0.24c{{m}^{2}}\]on a polar substrate. If the polar head is approximated as cube, what is its edge length? [JEE Main 9-4-2019 Afternoon]

A)

2.0 pm

B)

2.0 nm

C)

1.0 pm

D)

0.1 nm

View Answer
43) Consider the given plot of enthalpy of the following reaction between A and B. \[A+B\to C+D\] Identify the incorrect statement. [JEE Main 9-4-2019 Afternoon]

A)

C is the thermodynamically stable product.

B)

Formation of A and B from C has highest enthalpy of activation.

C)

D is kinetically stable product.

D)

Activation enthalpy to form C is \[5kJ\,mo{{l}^{-1}}\]less than that to form D.

View Answer
44) At a given temperature T, gases Ne, Ar, Xe and Kr are found to deviate from ideal gas behaviour. Their equation of state is given as \[p=\frac{RT}{V-b}\]at T. Here, b is the van der Waals constant. Which gas will exhibit steepest increase in the plot of Z (compression factor) vs p? [JEE Main 9-4-2019 Afternoon]

A)

Ne

B)

Ar

C)

Xe

D)

Kr

View Answer
45) A solution of\[Ni{{(N{{O}_{3}})}_{2}}\]is electrolysed between platinum electrodes using 0.1 Faraday electricity. How many mole of Ni will be deposited at the cathode? [JEE Main 9-4-2019 Afternoon]

A)

0.20

B)

0.05

C)

0.10

D)

0.15

View Answer
46) In the following reaction carbonyl compound \[+MeOH\] acetal Rate of the reaction is the highest for : [JEE Main 9-4-2019 Afternoon]

A)

Acetone as substrate and methanol in stoichiometric amount

B)

Propanal as substrate and methanol in stoichiometric amount.

C)

Acetone as substrate and methanol in excess

D)

Propanal as substrate and methanol in excess

View Answer
47) The structures of beryllium chloride in the solid state and vapour, phase, respectively,are : [JEE Main 9-4-2019 Afternoon]

A)

chain and dimeric

B)

chain and chain

C)

dimeric and dimeric

D)

dimeric and chain

View Answer
48) Which of the following potential energy (PE) diagrams represents the \[{{S}_{N}}1\]reaction? [JEE Main 9-4-2019 Afternoon]

A)

B)

C)

D)

View Answer
49) The major product of the following reaction is:           [JEE Main 9-4-2019 Afternoon]

A)



B)

C)



D)

View Answer
50) The maximum number of possible oxidation states of actinoides are shown by [JEE Main 9-4-2019 Afternoon]

A)

berkelium (Bk) and californium (Cf)

B)

nobelium (No) and lawrencium (Lr)

C)

actinium (Ac) and thorium (Th)

D)

neptunium (Np) and plutonium (Pu)

View Answer
51) Molal depression constant for a solvent is \[4.0kg\,mo{{l}^{-1}}.\]The depression in the freezing point of the solvent for \[0.03\,mol\,k{{g}^{-1}}\]solution of \[{{K}_{2}}S{{O}_{4}}\]is : (Assume complete dissociation of the electrolyte)             [JEE Main 9-4-2019 Afternoon]

A)

0.12 K

B)

0.36 K

C)

0.18 K

D)

0.24 K

View Answer
52) Noradrenaline is a /an :- [JEE Main 9-4-2019 Afternoon]

A)

Neurotransmitter

B)

Antidepressant

C)

Antihistamine

D)

Antacid

View Answer
53) Hinsberg's reagent is : [JEE Main 9-4-2019 Afternoon]

A)

\[{{C}_{6}}{{H}_{5}}S{{O}_{2}}Cl\]

B)

\[{{C}_{6}}{{H}_{5}}COCl\]

C)

\[SOC{{l}_{2}}\]

D)

\[{{(COCl)}_{2}}\]

View Answer
54) The layer of atmosphere between 10 km to 50 km above the sea level is called as : [JEE Main 9-4-2019 Afternoon]

A)

troposphere

B)

mesosphere

C)

stratosphere

D)

thermosphere

View Answer
55) HF has highest boiling point among hydrogen halides, because it has : [JEE Main 9-4-2019 Afternoon]

A)

lowest dissociation enthalpy

B)

strongest van der Waals' interactions

C)

strongest hydrogen bonding

D)

lowest ionic character

View Answer
56) What would be the molality of 20% (mass/ mass) aqueous solution of KI?

(molar mass of \[KI=166g\,mo{{l}^{-1}}\])

[JEE Main 9-4-2019 Afternoon]

A)

1.08

B)

1.48

C)

1.51

D)

1.35

View Answer
57) Which of the following compounds is a constituent of the polymer [JEE Main 9-4-2019 Afternoon]

A)

Formaldehyde

B)

Ammonia

C)

Methylamine

D)

N-Methyl urea

View Answer

58) The correct statements among I to III are:

(I) Valence bond theory cannot explain the color exhibited by transition metal complexes.

(II) Valence bond theory can predict quantitatively the magnetic properties of transtition metal complexes.

(III) Valence bond theory cannot distinguish ligands as weak and strong field ones.

[JEE Main 9-4-2019 Afternoon]

(I) and (II) only

(I), (II) and (III)

(I) and (III) only

(II) and (III) only

View Answer

59) In an acid-base titration, 0.1 M HCl solution was added to the NaOH solution of unknown strength. Which of the following correctly shows the change of pH of the titraction mixture in this experiment? [JEE Main 9-4-2019 Afternoon]

(A) (B)

(C) (D)

A)

[A]

B)

[C]

C)

[D]

D)

[B]

View Answer
60) p-Hydroxybenzophenone upon reaction with bromine in carbon tetrachloride gives: [JEE Main 9-4-2019 Afternoon]

A)

B)

C)

D)

View Answer
61) If the tangent to the parabola \[{{y}^{2}}=x\]at a point \[(\alpha ,\beta ),(\beta >0)\]is also a tangent to the ellipse, \[{{x}^{2}}+2{{y}^{2}}=1,\] then \[\alpha \]is equal to : [JEE Main 9-4-2019 Afternoon]

A)

\[2\sqrt{2}+1\]

B)

\[\sqrt{2}-1\]

C)

\[\sqrt{2}+1\]

D)

\[2\sqrt{2}-1\]

View Answer
62) Some identical balls are arranged in rows to form an equilateral triangle. The first row consists of one ball, the second row consists of two balls and so on. If 99 more identical balls are addded to the total number of balls used in forming the equilateral triangle, then all these balls can be arranged in a square whose each side contains exactly 2 balls less than the number of balls each side of the triangle contains. Then the number of balls used to form the equilateral triangle is :- [JEE Main 9-4-2019 Afternoon]

A)

190

B)

262

C)

225

D)

157

View Answer
63) If \[f:R\to R\] is a differentiable function and \[f(2)=6,\]then\[\underset{x\to 2}{\mathop{\lim }}\,\int\limits_{6}^{f(x)}{\frac{2tdt}{(x-2)}}\]is:- [JEE Main 9-4-2019 Afternoon]

A)

0

B)

2f'(2)

C)

12f'(2)

D)

24f'(2)

View Answer
64) If the system of equations \[2x+3yz=0,\]\[x+ky2z=0\]and \[2xy+z=0\]has a non-trival solution \[\left( x,y,z \right),\]then \[\frac{x}{y}+\frac{y}{z}+\frac{z}{x}+k\]is equal to:- [JEE Main 9-4-2019 Afternoon]

A)

\[\frac{3}{4}\]

B)

\[-4\]

C)

\[\frac{1}{2}\]

D)

\[-\frac{1}{4}\]

View Answer
65) The common tangent to the circles \[{{x}^{2}}+{{y}^{2}}=4\]and \[{{x}^{2}}+{{y}^{2}}+6x+8y24=0\] also passes through the point :-                                                 [JEE Main 9-4-2019 Afternoon]

A)

(-4, 6)

B)

(6, -2)

C)

(-6, 4)

D)

(4, -2)

View Answer
66) If the sum and product of the first three term in an A.P. are 33 and 1155, respectively, then a value of its 11th term is :- [JEE Main 9-4-2019 Afternoon]

A)

-25

B)

25

C)

-36

D)

-35

View Answer
67) The value of the integral \[\int\limits_{0}^{1}{x}{{\cos }^{-1}}(1-{{x}^{2}}+{{x}^{4}})dx\]is :- [JEE Main 9-4-2019 Afternoon]

A)

\[\frac{\pi }{4}-\frac{1}{2}{{\log }_{e}}2\]

B)

\[\frac{\pi }{2}-{{\log }_{e}}2\]

C)

\[\frac{\pi }{2}-\frac{1}{2}{{\log }_{e}}2\]

D)

\[\frac{\pi }{4}-{{\log }_{e}}2\]

View Answer
68) The value of \[sin\text{ }10{}^\text{o}\text{ }sin30{}^\text{o}\text{ }sin50{}^\text{o}\text{ }sin70{}^\text{o}\]is :-             [JEE Main 9-4-2019 Afternoon]

A)

\[\frac{1}{36}\]

B)

\[\frac{1}{32}\]

C)

\[\frac{1}{18}\]

D)

\[\frac{1}{16}\]

View Answer
69) Let \[z\in C\]be such that \[\left| z \right|<1.\]If \[\omega =\frac{5+3z}{5(1-z)},\] then:-             [JEE Main 9-4-2019 Afternoon]

A)

\[5\operatorname{Im}(\omega )<1\]

B)

\[4\operatorname{Im}(\omega )>5\]

C)

\[5Re(\omega )>1\]

D)

\[5Re(\omega )>4\]

View Answer
70)             If some three consecutive in the binomial expansion of \[{{\left( x+1 \right)}^{n}}\]is powers of x are in the ratio 2 : 15 : 70, then the average of these three coefficient is :-             [JEE Main 9-4-2019 Afternoon]

A)

964

B)

625

C)

227

D)

232

View Answer
71) If \[\cos x\frac{dy}{dx}-y\sin x=6x,(0<x<\frac{\pi }{2})\] and\[y\left( \frac{\pi }{3} \right)=0,\]then\[y\left( \frac{\pi }{6} \right)\]is equal to :- [JEE Main 9-4-2019 Afternoon]

A)

\[-\frac{{{\pi }^{2}}}{4\sqrt{3}}\]

B)

\[-\frac{{{\pi }^{2}}}{2}\]

C)

\[-\frac{{{\pi }^{2}}}{2\sqrt{3}}\]

D)

\[\frac{{{\pi }^{2}}}{2\sqrt{3}}\]

View Answer
72) If the two lines \[x+\left( a1 \right)y=1\]and \[2x+{{a}^{2}}y=1\]\[(a\in R-\{0,1\})\]are perpendicular, then the distance of their point of intersection from the origin is :-        [JEE Main 9-4-2019 Afternoon]

A)

\[\frac{2}{5}\]

B)

\[\frac{2}{\sqrt{5}}\]

C)

\[\frac{\sqrt{2}}{5}\]

D)

\[\sqrt{\frac{2}{5}}\]

View Answer
73) A water tank has the shape of an inverted right circular cone, whose semi-vertical angle is\[{{\tan }^{-1}}\left( \frac{1}{2} \right).\]Water is poured into it at a constant rage of 5 cubic meter per minute. The the rate (in m/min.), at which the level of water is rising at the instant when the depth of water in the tank is 10m; is :-                                                 [JEE Main 9-4-2019 Afternoon]

A)

\[2/\pi \]

B)

\[1/5\pi \]

C)

\[1/10\pi \]

D)

\[1/15\pi \]

View Answer
74) Two poles standing on a horizontal ground are of heights 5m and 10 m respectively. The line joining their tops makes an angle of \[15{}^\text{o}\] with ground. Then the distance (in m) between the poles, is :-             [JEE Main 9-4-2019 Afternoon]

A)

\[\frac{5}{2}(2+\sqrt{3})\]

B)

\[5(\sqrt{3}+1)\]

C)

\[5(2+\sqrt{3})\]

D)

\[10(\sqrt{3}-1)\]

View Answer
75) The vertices B and C of a \[\Delta ABC\]lie on the line, \[\frac{x+2}{3}=\frac{y-1}{0}=\frac{z}{4}\]such that BC = 5 units. Then the area (in sq. units) of this triangle, given that the point A(1, -1, 2), is :-             [JEE Main 9-4-2019 Afternoon]

A)

\[2\sqrt{34}\]

B)

\[\sqrt{34}\]

C)

\[6\]

D)

\[5\sqrt{17}\]

View Answer
76) The total number of matrices for which \[{{A}^{T}}A=3{{I}_{3}}\] is :-                                                                         [JEE Main 9-4-2019 Afternoon]

A)

6

B)

2

C)

3

D)

4

View Answer
77) The area (in sq. units) of the smaller of the two circles that touch the parabola, \[{{y}^{2}}=4x\] at the point (1, 2) and the x-axis is :-             [JEE Main 9-4-2019 Afternoon]

A)

\[4\pi (2-\sqrt{2})\]

B)

\[8\pi (3-2\sqrt{2})\]

C)

\[4\pi (3+\sqrt{2})\]

D)

\[8\pi (2-\sqrt{2})\]

View Answer
78) If the function f(x) = \[\left\{ \begin{align} & a|\pi -x|+1,x\le 5 \\ & b|x-\pi |+3,x>5 \\ \end{align} \right.\]is continuous at \[x=5,\]then the value of \[ab\] is :- [JEE Main 9-4-2019 Afternoon]

A)

\[\frac{2}{5-\pi }\]

B)

\[\frac{2}{\pi -5}\]

C)

\[\frac{2}{\pi +5}\]

D)

\[\frac{-2}{\pi +5}\]

View Answer
79) If\[f(x)=[x]-\left[ \frac{x}{4} \right],x\in R,\], where [x] denotes the greatest integer function, then : [JEE Main 9-4-2019 Afternoon]

A)

Both \[\underset{x\to 4-}{\mathop{\lim }}\,f(x)\] and \[\underset{x\to 4+}{\mathop{\lim }}\,f(x)\] exist but are not equal

B)

\[\underset{x\to 4-}{\mathop{\lim }}\,f(x)\] exists but \[\underset{x\to 4+}{\mathop{\lim }}\,f(x)\] does not exist

C)

\[\underset{x\to 4+}{\mathop{\lim }}\,f(x)\] exists but \[\underset{x\to 4-}{\mathop{\lim }}\,f(x)\]does not exist

D)

f is continuous at x = 4

View Answer
80) If \[\int_{{}}^{{}}{{{e}^{\sec x}}}(sec\,x\,tan\,xf(x)+(sec\,x\,tan\,x+se{{c}^{2}}x)dx\]\[={{e}^{\sec \,x}}f(x)+C,\]then a possible choice of \[f\left( x \right)\] is :- [JEE Main 9-4-2019 Afternoon]

A)

\[\sec x-\tan x-\frac{1}{2}\]

B)

\[x\sec x+\tan x+\frac{1}{2}\]

C)

\[\sec x+x\tan x-\frac{1}{2}\]

D)

\[\sec x+\tan x+\frac{1}{2}\]

View Answer
81) If m is chosen in the quadratic equation \[({{m}^{2}}+1){{x}^{2}}-3x+{{({{m}^{2}}+1)}^{2}}=0\]such that the sum of its roots is greatest, then the absolute difference of the cubes of its roots is :-             [JEE Main 9-4-2019 Afternoon]

A)

\[8\sqrt{3}\]

B)

\[4\sqrt{3}\]

C)

\[10\sqrt{5}\]

D)

\[8\sqrt{5}\]

View Answer
82) Two newspapers A and B are published in a city. It is known that \[25%\]of the city populations reads A and \[20%\]reads B while \[8%\]reads both A and B. Further, \[30%\]of those who read A but not B look into advertisements and \[40%\]of those who read B but not A also look into advertisements, while \[50%\]of those who read both A and B look into advertisements. Then the percentage of the population who look into advertisement is :- [JEE Main 9-4-2019 Afternoon]

A)

12.8

B)

13.5

C)

13.9

D)

13

View Answer
83) Let P be the plane, which contains the line of intersection of the planes, \[x+y+z6=0\] and \[2x+3y+z+5=0\]and it is perpendicular to the xy-plane. Then the distance of the point (0, 0, 256) from P is equal to :-             [JEE Main 9-4-2019 Afternoon]

A)

\[63\sqrt{5}\]

B)

\[205\sqrt{5}\]

C)

\[17/\sqrt{5}\]

D)

\[11/\sqrt{5}\]

View Answer
84) If \[P\Rightarrow (q\vee r)\] is false, then the truth values of p, q, r are respectively :-             [JEE Main 9-4-2019 Afternoon]

A)

F, T, T

B)

T, F, F

C)

T, T, F

D)

F, F, F

View Answer
85) The domain of the definition of the function \[f(x)=\frac{1}{4-{{x}^{2}}}+{{\log }_{10}}({{x}^{3}}-x)\]is :- [JEE Main 9-4-2019 Afternoon]

A)

\[(1,2)\cup (2,\infty )\]

B)

\[(-1,0)\cup (1,2)\cup (3,\infty )\]

C)

\[(-1,0)\cup (1,2)\cup (2,\infty )\]

D)

\[(-2,-1)\cup (-1,0)\cup (2,\infty )\]

View Answer
86) The sum of the series \[1+2\times 3+3\times 5+4\times 7+....\] upto 11th term is :-             [JEE Main 9-4-2019 Afternoon]

A)

915

B)

946

C)

945

D)

916

View Answer
87)           The mean and the median of the following ten numbers in increasing order \[10,22,26,29,34,x42,67,70,y\] are 42 and 35 respectively, then \[\frac{y}{x}\] is equal to :-             [JEE Main 9-4-2019 Afternoon]

A)

7/3

B)

9/4

C)

7/2

D)

8/3

View Answer
88) The area (in sq. units) of the region \[A=\{(x,y):\frac{{{y}^{2}}}{2}\le x\le y+4\}\]is :-             [JEE Main 9-4-2019 Afternoon]

A)

\[\frac{53}{3}\]

B)

18

C)

30

D)

16

View Answer
89)             If a unit vector \[\vec{a}\] makes angles \[\pi /3\] with \[\hat{i},\pi /4\]with \[\hat{j}\] and \[\theta \in (0,\pi )\] with \[\hat{k},\] then a value of \[\theta \]is :-             [JEE Main 9-4-2019 Afternoon]

A)

\[\frac{5\pi }{12}\]

B)

\[\frac{5\pi }{6}\]

C)

\[\frac{2\pi }{3}\]

D)

\[\frac{\pi }{4}\]

View Answer
90) A rectangle is inscribed in a circle with a diameter lying along the line \[3y=x+7.\] If the two adjacent vertices of the rectangle are (-8, 5) and (6, 5), then the area of the rectangle (in sq. units) is :-             [JEE Main 9-4-2019 Afternoon]

A)

72

B)

84

C)

98

D)

56

View Answer