# Solved papers for JEE Main & Advanced JEE Main Paper (Held on 12-4-2019 Morning)

### done JEE Main Paper (Held on 12-4-2019 Morning) Total Questions - 90

• question_answer1) The value of numerical aperature of the objective lens of a microscope is 1.25. If light of wavelength $5000\overset{\text{o}}{\mathop{\text{A}}}\,$ is used, the minimum separation between two points, to be seen as distinct, will be :                                          [JEE Main Held on 12-4-2019 Morning]

A)
$0.24\mu m$

B)
$0.48\mu m$

C)
$0.12\mu m$

D)
$0.38\mu m$

• question_answer2) A progressive wave travelling along the positive x-direction is represented by $y\left( x,\text{ }t \right)=A\sin$$(kx-\omega t+\phi )$. Its snapshot at $t=0$is given in the figure: For this wave, the phase $\phi$is :                                         [JEE Main Held on 12-4-2019 Morning]

A)
$0$

B)
$-\frac{\pi }{2}$

C)
$\pi$

D)
$\frac{\pi }{2}$

• question_answer3) A circular disc of radius b has a hole of radius a at its centre (see figure). If the mass per unit area of the disc varies as $\left( \frac{{{\sigma }_{0}}}{r} \right),$then the radius of gyration of the disc about its axis passing through the centre is :                                                   [JEE Main Held on 12-4-2019 Morning]

A)
$\frac{a+b}{2}$

B)
$\frac{a+b}{3}$

C)
$\sqrt{\frac{{{a}^{2}}+{{b}^{2}}+ab}{2}}$

D)
$\sqrt{\frac{{{a}^{2}}+{{b}^{2}}+ab}{3}}$

• question_answer4) Shown in the figure is a shell made of a conductor. It has inner radius a and outer radius b, and carries charge Q. At its centre is a dipole $\vec{p}$ as shown. In this case:                                                     [JEE Main Held on 12-4-2019 Morning]

A)
Electric field outside the shell is the same as that of a point charge at the centre of the shell.

B)
Surface charge density on the inner surface of the shell is zero everywhere.

C)
Surface charge density on the inner surface is uniform and equal to $\frac{(Q/2)}{4\pi {{a}^{2}}}.$

D)
Surface charge density on the outer surface depends on $\left| {\vec{p}} \right|$

• question_answer5) A person of mass M is, sitting on a swing of length L and swinging with an angular amplitude ${{\theta }_{0}}$. If the person stands up when the swing passes through its lowest point, the work done by him, assuming that his centre of mass moves by a distance $\ell (\ell <<L),$is close to: [JEE Main Held on 12-4-2019 Morning]

A)
$Mg\ell$

B)
$Mg\ell (1+{{\theta }_{0}}^{2})$

C)
$Mg\ell (1-{{\theta }_{0}}^{2})$

D)
$Mg\ell \left( 1+\frac{{{\theta }_{0}}^{2}}{2} \right)$

• question_answer6) A concave mirror has radius of curvature of 40 cm. It is at the bottom of a glass that has water filled up to 5 cm (see figure). If a small particle is floating on the surface of water, its image as seen, from directly above the glass, is at a distance d from the surface of water. The value of d is close to : (Refractive index of water = 1.33)                                                        [JEE Main Held on 12-4-2019 Morning]

A)
8.8 cm

B)
11.7 cm

C)
6.7 cm

D)
13.4 cm

• question_answer7) Two identical parallel plate capacitors, of capacitance C each, have plates of area A, separated by a distance d. The space between the plates of the two capacitors, is filled with three dielectrics, of equal thickness and dielectric constants ${{K}_{1}},{{K}_{2}}$and ${{K}_{3}}.$The first capacitor is filled as shown in fig. I, and the second one is filled as shown in fig. II. If these two modified capacitors are charged by the same potential V, the ratio of the energy stored in the two, would be (${{E}_{1}}$refers to capacitor (I) and ${{E}_{2}}$to capacitor (II)):                              [JEE Main Held on 12-4-2019 Morning]

A)
$\frac{{{E}_{1}}}{{{E}_{2}}}=\frac{9{{K}_{1}}{{K}_{2}}{{K}_{3}}}{({{K}_{1}}+{{K}_{2}}+{{K}_{2}})({{K}_{2}}{{K}_{3}}+{{K}_{3}}{{K}_{1}}+{{K}_{1}}{{K}_{2}})}$

B)
$\frac{{{E}_{1}}}{{{E}_{2}}}=\frac{{{K}_{1}}{{K}_{2}}{{K}_{3}}}{({{K}_{1}}+{{K}_{2}}+{{K}_{2}})({{K}_{2}}{{K}_{3}}+{{K}_{3}}{{K}_{1}}+{{K}_{1}}{{K}_{2}})}$

C)
$\frac{{{E}_{1}}}{{{E}_{2}}}=\frac{({{K}_{1}}+{{K}_{2}}+{{K}_{2}})({{K}_{2}}{{K}_{3}}+{{K}_{3}}{{K}_{1}}+{{K}_{1}}{{K}_{2}})}{{{K}_{1}}{{K}_{2}}{{K}_{3}}}$

D)
$\frac{{{E}_{1}}}{{{E}_{2}}}=\frac{({{K}_{1}}+{{K}_{2}}+{{K}_{2}})({{K}_{2}}{{K}_{3}}+{{K}_{3}}{{K}_{1}}+{{K}_{1}}{{K}_{2}})}{9{{K}_{1}}{{K}_{2}}{{K}_{3}}}$

• question_answer8) A point dipole $\vec{p}=-{{p}_{0}}\hat{x}$is kept at the origin. The potential and electric field due to this dipole on the y-axis at a distance d are, respectively:                         [JEE Main Held on 12-4-2019 Morning]  (Take V = 0 at infinity):

A)
$\frac{|\vec{p}|}{4\pi {{\varepsilon }_{0}}{{d}^{2}}},\frac{-\vec{p}}{4\pi {{\varepsilon }_{0}}{{d}^{3}}}$

B)
$0,\frac{{\vec{p}}}{4\pi {{\varepsilon }_{0}}{{d}^{3}}}$

C)
$\frac{|\vec{p}|}{4\pi {{\varepsilon }_{0}}{{d}^{3}}},\frac{{\vec{p}}}{4\pi {{\varepsilon }_{0}}{{d}^{3}}}$

D)
$0,\frac{-\vec{p}}{4\pi {{\varepsilon }_{0}}{{d}^{3}}}$

• question_answer9) When ${{M}_{1}}$gram of ice at $10{}^\text{o}C$ (specific heat $=0.5\text{ }cal\text{ }{{g}^{1}}{}^\text{o}{{C}^{1}})$is added to M2 gram of water at $50{}^\text{o}C,$ finally no ice is left and the water is at 0ºC. The value of latent heat of ice, in cal ${{g}^{-1}}$is:                      [JEE Main Held on 12-4-2019 Morning]

A)
$\frac{5{{M}_{1}}}{{{M}_{2}}}-50$

B)
$\frac{50{{M}_{2}}}{{{M}_{1}}}$

C)
$\frac{50{{M}_{2}}}{{{M}_{1}}}-5$

D)
$\frac{5{{M}_{2}}}{{{M}_{1}}}-5$

• question_answer10) The trajectory of a projectile near the surface of the earth is given as $y=2x-9{{x}^{2}}.$. If it were launched at an angle ${{\theta }_{0}}$with speed ${{\text{v}}_{0}}$then $\left( g=10\text{ }m{{s}^{2}} \right)$: [JEE Main Held on 12-4-2019 Morning]

A)
${{\theta }_{0}}={{\cos }^{-1}}\left( \frac{1}{\sqrt{5}} \right)$and${{\text{v}}_{0}}=\frac{5}{3}m{{s}^{-1}}$

B)
${{\theta }_{0}}={{\sin }^{-1}}\left( \frac{1}{\sqrt{5}} \right)$and${{\text{v}}_{0}}=\frac{5}{3}m{{s}^{-1}}$

C)
${{\theta }_{0}}={{\sin }^{-1}}\left( \frac{2}{\sqrt{5}} \right)$and${{\text{v}}_{0}}=\frac{3}{5}m{{s}^{-1}}$

D)
${{\theta }_{0}}={{\cos }^{-1}}\left( \frac{2}{\sqrt{5}} \right)$and${{\text{v}}_{0}}=\frac{3}{5}m{{s}^{-1}}$

• question_answer11) The truth table for the circuit given in the fig. is:          [JEE Main Held on 12-4-2019 Morning]

A)
$\left| \begin{matrix} A & B & Y \\ 0 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 0 & 0 \\ 1 & 1 & 0 \\ \end{matrix} \right|$

B)
$\left| \begin{matrix} A & B & Y \\ 0 & 0 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 1 \\ 1 & 1 & 1 \\ \end{matrix} \right|$

C)
$\left| \begin{matrix} A & B & Y \\ 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \\ 1 & 1 & 0 \\ \end{matrix} \right|$

D)
$\left| \begin{matrix} A & B & Y \\ 0 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 1 \\ \end{matrix} \right|$

• question_answer12)           A shell is fired from a fixed artillery gun with an initial speed u such that it hits the target on the ground at a distance R from it. If ${{t}_{1}}$ and ${{t}_{2}}$are the values of the time taken by it to hit the target in two possible ways, the product ${{t}_{1}}{{t}_{2}}$is:                                     [JEE Main Held on 12-4-2019 Morning]

A)
$R/g$

B)
$R/4g$

C)
$2R/g$

D)
$R/2g$

• question_answer13) A submarine [A] travelling at 18 km/hr is being chased along the line of its velocity by another submarine [B] travelling at 27 km/hr. B sends a sonar signal of 500 Hz to detect A and receives a reflected sound of frequency n. The value of n is close to:                                 [JEE Main Held on 12-4-2019 Morning] (Speed of sound in water $=1500\text{ }m{{s}^{1}}$)

A)
499 Hz

B)
502 Hz

C)
507 Hz

D)
504 Hz

• question_answer14) Two moles of helium gas is mixed with three moles of hydrogen molecules (taken to be rigid). What is the molar specific heat of mixture at constant volume? $\left( R=8.3\text{ }J/mol\text{ }K \right)$                                                                         [JEE Main Held on 12-4-2019 Morning]

A)
21.6 J/mol K

B)
19.7 J/mol K

C)
17.4 J/mol K

D)
15.7 J/mol K

• question_answer15) The stopping potential ${{V}_{0}}$(in volt) as a function of frequency (v) for a sodium emitter, is shown in the figure. The work function of sodium, from the data plotted in the figure, will be:  (Given : Planck's constant$\left( h \right)=6.63\times {{10}^{34}}Js,$electron charge $e=1.6\times {{10}^{19}}C$)
[JEE Main Held on 12-4-2019 Morning]

A)
1.95 eV

B)
1.82 eV

C)
1.66 eV

D)
2.12 eV

• question_answer16) At $40{}^\text{o}C,$a brass wire of 1 mm radius is hung from the ceiling. A small mass, M is hung from the free end of the wire. When the wire is cooled down from $40{}^\text{o}C$to $20{}^\text{o}C$ it regains its original length of 0.2 m. The value of M is close to : (Coefficient of linear expansion and Young's modulus of brass are ${{10}^{5}}/{}^\text{o}C$and ${{10}^{11}}N/{{m}^{2}},$ respectively; $g=10\,m{{s}^{-2}}$)                                         [JEE Main Held on 12-4-2019 Morning]

A)
$1.5\,kg$

B)
$9\text{ }kg$

C)
$0.9\text{ }kg$

D)
$0.5\text{ }kg$

• question_answer17) A uniform rod of length$\ell$is being rotated in a horizontal plane with a constant angular speed about an axis passing through one of its ends. If the tension generated in the rod due to rotation is T(x) at a distance x from the axis, then which of the following graphs depicts it most closely? [JEE Main Held on 12-4-2019 Morning]

A)

B)

C)

D)

• question_answer18) Which of the following combinations has the dimension of electrical resistance (${{\varepsilon }_{0}}$is the permittivity of vacuum and ${{\mu }_{0}}$is the permeability of vacuum)?          [JEE Main Held on 12-4-2019 Morning]

A)
$\sqrt{\frac{{{\varepsilon }_{0}}}{{{\mu }_{0}}}}$

B)
$\frac{{{\mu }_{0}}}{{{\varepsilon }_{0}}}$

C)
$\sqrt{\frac{{{\mu }_{0}}}{{{\varepsilon }_{0}}}}$

D)
$\frac{{{\varepsilon }_{0}}}{{{\mu }_{0}}}$

• question_answer19) In a double slit experiment, when a thin film of thickness t having refractive index m is introduced in front of one of the slits, the maximum at the centre of the fringe pattern shifts by one fringe width. The value of t is ($\lambda$is the wavelength of the light used) :                    [JEE Main Held on 12-4-2019 Morning]

A)
$\frac{\lambda }{2(\mu -1)}$

B)
$\frac{\lambda }{(2\mu -1)}$

C)
$\frac{2\lambda }{(\mu -1)}$

D)
$\frac{\lambda }{(\mu -1)}$

• question_answer20) An electromagnetic wave is represented by the electric field $\vec{E}={{E}_{0}}\hat{n}\sin [\omega t+(6y-8z)]$ . Taking unit vectors in x, y and z directions to be $\hat{i}.\hat{j},\hat{k},$the direction of propagation $\hat{s},$ is :                                                                                                 [JEE Main Held on 12-4-2019 Morning]

A)
$\hat{s}=\frac{4\hat{j}-3\hat{k}}{5}$

B)
$\hat{s}=\frac{3\hat{j}-4\hat{j}}{5}$

C)
$\hat{s}=\left( \frac{-3\hat{j}+4\hat{k}}{5} \right)$

D)
$\hat{s}=\frac{-4\hat{j}+3\hat{j}}{5}$

• question_answer21) The figure shows a square loop L of side 5 cm which is connected to a network of resistances. The whole setup is moving towards right with a constant speed of $1cm{{s}^{-1}}.$ At some instant, a part of L is in a uniform magnetic field of 1T, perpendicular to the plane of the loop. If the resistance of L is $1.7\Omega ,$the current in the loop at that instant will be close to:           [JEE Main Held on 12-4-2019 Morning]

A)
$115\mu A$

B)
$170\mu A$

C)
$60\mu A$

D)
$150\mu A$

• question_answer22) The transfer characteristic curve of a transistor, having input and output resistance $100\Omega$ and $100k\Omega$respectively, is shown in the figure. The Voltage and Power gain, are respectively :                          [JEE Main Held on 12-4-2019 Morning]

A)
$5\times {{10}^{4}},5\times {{10}^{5}}$

B)
$5\times {{10}^{4}},5\times {{10}^{6}}$

C)
$5\times {{10}^{4}},2.5\times {{10}^{6}}$

D)
$2.5\times {{10}^{4}},2.5\times {{10}^{6}}$

• question_answer23) A galvanometer of resistance $100\Omega$has 50 divisions on its scale and has sensitivity of $20\mu A/$division. It is to be converted to a voltmeter with three ranges, of 0-2 V, 0-10 V and 0-20 V. The appropriate circuit to do so is :                             [JEE Main Held on 12-4-2019 Morning]

A)

B)

C)

D)

• question_answer24) To verify Ohm's law, a student connects the voltmeter across the battery as, shown in the figure. The measured voltage is plotted as a function of the current, and the following graph is obtained:  If V0 is almost zero, identify the correct statement:
[JEE Main Held on 12-4-2019 Morning]

A)
The value of the resistance R is $1.5\Omega$

B)
The emf of the battery is 1.5 V and the value of R is $1.5\Omega$

C)
The emf of the battery is 1.5 V and its internal resistance is $1.5\Omega$

D)
The potential difference across the battery is 1.5 V when it sends a current of 1000 mA.

• question_answer25) An excited He+ ion emits two photons in succession, with wavelengths 108.5 nm and 30.4 nm, in making a transition to ground state. The quantum number n, corresponding to its initial excited state is (for photon of wavelength $\lambda ,$energy                                                [JEE Main Held on 12-4-2019 Morning] $E=\frac{1240eV}{\lambda (in\,nm)}:$

A)
n = 5

B)
n = 4

C)
n = 6

D)
n = 7

• question_answer26) A sample of an ideal gas is taken through the cyclic process abca as shown in the figure. The change in the internal energy of the gas along the path ca is -180J. The gas absorbs 250 J of heat along the path ab and 60 J along the path bc. The work done by the gas along the path abc is :                                                     [JEE Main Held on 12-4-2019 Morning]

A)
100 J

B)
120 J

C)
140 J

D)
130 J

• question_answer27) A thin ring of 10 cm radius carries a uniformly distributed charge. The ring rotates at a constant angular speed of $40\pi \,rad\,{{s}^{-1}}$about its axis, perpendicular to its plane. If the magnetic field at its centre is $3.8\times {{10}^{9}}T,$then the charge carried by the ring is close to $({{\mu }_{0}}=4\pi \times {{10}^{7}}\text{ }N/{{A}^{2}})$ : [JEE Main Held on 12-4-2019 Morning]

A)
$2\times {{10}^{-6}}C$

B)
$3\times {{10}^{-5}}C$

C)
$4\times {{10}^{-5}}C$

D)
$7\times {{10}^{-6}}C$

• question_answer28) A magnetic compass needle oscillates 30 times per minute at a place where the dip is $45{}^\text{o},$and 40 times per minute where the dip is $30{}^\text{o}$. If ${{B}_{1}}$and ${{B}_{2}}$are respectively the total magnetic field due to the earth at the two places, then the ratio ${{B}_{1}}/{{B}_{2}}$is best given by:               [JEE Main Held on 12-4-2019 Morning]

A)
2.2

B)
1.8

C)
0.7

D)
3.6

• question_answer29)           A man (mass = 50 kg) and his son (mass = 20 kg) are standing on a frictionless surface facing each other. The man pushes his son so that he starts moving at a speed of $0.70\,m{{s}^{-1}}$ with respect to the man. The speed of the man with respect to the surface is :                      [JEE Main Held on 12-4-2019 Morning]

A)
$0.20\,m{{s}^{-1}}$

B)
$0.14\,m{{s}^{-1}}$

C)
$0.47\,m{{s}^{-1}}$

D)
$0.28\,m{{s}^{-1}}$

• question_answer30) The resistive network shown below is connected to a D.C. source of 16V. The power consumed by the network is 4 Watt. The value of R is :                               [JEE Main Held on 12-4-2019 Morning]

A)
$8\Omega$

B)
$6\Omega$

C)
$1\Omega$

D)
$16\Omega$

• question_answer31)           5 moles of $A{{B}_{2}}$weigh $125\times {{10}^{3}}kg$and 10 moles of ${{A}_{2}}{{B}_{2}}$weigh $300\times {{10}^{3}}kg$. The molar mass of $A({{M}_{A}})$and molar mass of $B({{M}_{B}})$in $kg\,mo{{l}^{-1}}$are:                   [JEE Main Held on 12-4-2019 Morning]

A)
${{M}_{A}}=50\times {{10}^{-3}}$and ${{M}_{B}}=25\times {{10}^{-3}}$

B)
${{M}_{A}}=25\times {{10}^{-3}}$ and ${{M}_{B}}=50\times {{10}^{-3}}$

C)
${{M}_{A}}=5\times {{10}^{-3}}$ and ${{M}_{B}}=10\times {{10}^{-3}}$

D)
${{M}_{A}}=10\times {{10}^{-3}}$and ${{M}_{B}}=5\times {{10}^{-3}}$

• question_answer32) The major product of the following addition reaction is : ${{H}_{3}}C-CH=C{{H}_{2}}\xrightarrow[{}]{C{{l}_{2}}/{{H}_{2}}O}$              [JEE Main Held on 12-4-2019 Morning]

A)

B)

C)

D)

• question_answer33)           What is the molar solubility of $Al{{(OH)}_{3}}$in 0.2 M NaOH solution? Given that, solubility product of $Al{{(OH)}_{3}}=2.4\times {{10}^{-24}}$:                               [JEE Main Held on 12-4-2019 Morning]

A)
$12\times {{10}^{-23}}$

B)
$12\times {{10}^{-21}}$

C)
$3\times {{10}^{-19}}$

D)
$3\times {{10}^{-22}}$

• question_answer34) But-2-ene on reaction with alkaline $KMn{{O}_{4}}$at elevated temperature followed by acidification will give: [JEE Main Held on 12-4-2019 Morning]

A)
one molecule of $C{{H}_{3}}CHO$and one molecule of $C{{H}_{3}}CHOOH$

B)

C)
2 molecules of $C{{H}_{3}}COOH$

D)
2 molecules of $C{{H}_{3}}CHO$

• question_answer35) The correct sequence of thermal stability of the following carbonates is           [JEE Main Held on 12-4-2019 Morning]

A)
$BaC{{O}_{3}}<CaC{{O}_{3}}<SrC{{O}_{3}}<MgC{{O}_{3}}$

B)
$MgC{{O}_{3}}<CaC{{O}_{3}}<SrC{{O}_{3}}<BaC{{O}_{3}}$

C)
$BaC{{O}_{3}}<SrC{{O}_{3}}<CaC{{O}_{3}}<MgC{{O}_{3}}$

D)
$MgC{{O}_{3}}<SrC{{O}_{3}}<CaC{{O}_{3}}<BaC{{O}_{3}}$

• question_answer36) The correct statement among the following is              [JEE Main Held on 12-4-2019 Morning]

A)
${{(Si{{H}_{3}})}_{3}}N$is pyramidal and more basic than ${{(C{{H}_{3}})}_{3}}N$

B)
${{(Si{{H}_{3}})}_{3}}N$ is planar and more basic than${{(C{{H}_{3}})}_{3}}N$

C)
${{(Si{{H}_{3}})}_{3}}N$is pyramidal and less basic than${{(C{{H}_{3}})}_{3}}N$

D)
${{(Si{{H}_{3}})}_{3}}N$ is planar and less basic than${{(C{{H}_{3}})}_{3}}N$

• question_answer37) Peptization is a :                                                          [JEE Main Held on 12-4-2019 Morning]

A)
process of converting a colloidal solution into precipitate

B)
process of converting precipitate into colloidal solution

C)
process of converting soluble particles to form colloidal solution

D)
process of bringing colloidal molecule into solution

• question_answer38) Given : $C{{o}^{3+}}+{{e}^{-}}\to C{{o}^{2+}};{{E}^{o}}=+1.81V$ $P{{o}^{3+}}+{{e}^{-}}\to C{{o}^{2+}};{{E}^{o}}=+1.81\,V$ $C{{e}^{4+}}+{{e}^{-}}\to C{{e}^{3+}};{{E}^{o}}=+1.61\,V$ $B{{i}^{3+}}+3{{e}^{-}}\to Bi\,;{{E}^{o}}=+\,0.20\,V$ Oxidizing power of the species will increase in the order :       [JEE Main Held on 12-4-2019 Morning]

A)
$C{{e}^{4+}}<P{{b}^{4+}}<B{{i}^{3+}}<C{{o}^{3+}}$

B)
$C{{o}^{3+}}<P{{b}^{4+}}<C{{e}^{4+}}<B{{i}^{3+}}$

C)
$B{{i}^{3+}}<C{{e}^{4+}}<P{{b}^{4+}}<C{{o}^{3+}}$

D)
$B{{i}^{3+}}<C{{e}^{4+}}<P{{b}^{4+}}<C{{o}^{3+}}$

• question_answer39) The metal that gives hydrogen gas upon treatment with both acid as well as base is : [JEE Main Held on 12-4-2019 Morning]

A)
zinc

B)
iron

C)
magnesium

D)
mercury

• question_answer40) The group number, number of valence electrons, and valency of an element with atomic number 15, respectively, are                                                       [JEE Main Held on 12-4-2019 Morning]

A)
16, 5 and 2

B)
16, 6 and 3

C)
15, 5 and 3

D)
15, 6 and 2

• question_answer41) The complex ion that will lose its crystal field stabilization energy upon oxidation of its metal to +3 state is                                                                           [JEE Main Held on 12-4-2019 Morning]

A)
${{[Fe{{(phen)}_{3}}]}^{2+}}$

B)
${{[Zn{{(phen)}_{3}}]}^{2+}}$

C)
${{[Ni{{(phen)}_{3}}]}^{2+}}$

D)
${{[Co{{(phen)}_{3}}]}^{2+}}$

• question_answer42) Complete removal of both the axial ligands (along the z-axis) from an octahedral complex leads to which of the following splitting patterns? (relative orbital energies not on scale). [JEE Main Held on 12-4-2019 Morning]

A)

B)

C)

D)

• question_answer43) The major product(s) obtained in the following reaction is/are :                                                  [JEE Main Held on 12-4-2019 Morning]

A)

B)

C)

D)

• question_answer44) An element has a face-centred cubic (fcc) structure with a cell edge of a. The distance between the centres of two nearest tetrahedral voids in the lattice is:         [JEE Main Held on 12-4-2019 Morning]

A)
$\frac{a}{2}$

B)
$a$

C)
$\frac{3}{2}a$

D)
$\sqrt{2}a$

• question_answer45) The major products of the following reaction are:        [JEE Main Held on 12-4-2019 Morning]

A)

B)

C)

D)

• question_answer46) The increasing order of the $p{{K}_{b}}$of the following compound is: [JEE Main Held on 12-4-2019 Morning] [a] [b] [c] [d] Options :

A)
$\left( A \right)<\left( C \right)<\left( D \right)<\left( B \right)$

B)
$\left( B \right)<\left( D \right)<\left( A \right)<\left( C \right)$

C)
$\left( C \right)<\left( A \right)<\left( D \right)<\left( B \right)$

D)
$\left( B \right)<\left( D \right)<\left( C \right)<\left( A \right)$

• question_answer47) Which of the following statements is not true about RNA? [JEE Main Held on 12-4-2019 Morning]

A)
It has always double stranded a-helix structure

B)
It usually does not replicate

C)
It is present in the nucleus of the cell

D)
It controls the synthesis of protein

• question_answer48) In the following reaction; $xA\to yB$                           [JEE Main Held on 12-4-2019 Morning] ${{\log }_{10}}\left[ -\frac{d[A]}{dt} \right]={{\log }_{10}}\left[ \frac{d[B]}{dt} \right]+0.3010$ 'A' and 'B' respectively can be :

A)
n-Butane and Iso-butane

B)
${{C}_{2}}{{H}_{4}}$and ${{C}_{4}}{{H}_{8}}$

C)
${{N}_{2}}{{O}_{4}}$and$N{{O}_{2}}$

D)
${{C}_{2}}{{H}_{2}}$and ${{C}_{6}}{{H}_{6}}$

• question_answer49) Glucose and Galactose are having identical configuration in all the positions except position. [JEE Main Held on 12-4-2019 Morning]

A)
C-3

B)
C-2

C)
C-4

D)
C-5

• question_answer50) An ideal gas is allowed to expand from 1 L to 10 L against a constant external pressure of 1bar. The work done in kJ is :                                                               [JEE Main Held on 12-4-2019 Morning]

A)
-9.0

B)
+10.0

C)
-0.9

D)
-2.0

• question_answer51) Which of the following is a thermosetting polymer?     [JEE Main Held on 12-4-2019 Morning]

A)
Buna-N

B)
PVC

C)
Bakelite

D)
Nylon 6

• question_answer52) The idea of froth floatation method came from a person X and this method is related to the process Y of ores. X and Y, respectively, are:                                   [JEE Main Held on 12-4-2019 Morning]

A)
fisher woman and concentration

B)
washer man and reduction

C)
washer woman and concentration

D)
fisher man and reduction

• question_answer53) An example of a disproportionation reaction is:          [JEE Main Held on 12-4-2019 Morning]

A)
$2KMn{{O}_{4}}\to {{K}_{2}}Mn{{O}_{4}}+Mn{{O}_{2}}+{{O}_{2}}$

B)
$2MnO_{4}^{-}+10{{I}^{-}}+16{{H}^{+}}\to 2M{{n}^{2+}}+5{{I}_{2}}+8{{H}_{2}}O$

C)
$2CuBr\to CuB{{r}_{2}}+Cu$

D)
$2NaBr+C{{l}_{2}}\to 2NaCl+B{{r}_{2}}$

• question_answer54) The correct set of species responsible for the photochemical smog is: [JEE Main Held on 12-4-2019 Morning]

A)
$NO,N{{O}_{2}},{{O}_{3}}$and hydrocarbons

B)
${{N}_{2}},{{O}_{2}},{{O}_{3}}$and hydrocarbons

C)
${{N}_{2}},N{{O}_{2}}$ and hydrocarbons

D)
$C{{O}_{2}},N{{O}_{2}},S{{O}_{2}}$and hydrocarbons

• question_answer55) The electrons are more likely to be found:                    [JEE Main Held on 12-4-2019 Morning]

A)
in the region a and b

B)
in the region a and c

C)
only in the region c

D)
only in the region a

• question_answer56) The basic structural unit of feldspar, zeolites, mica, and asbestos is:   [JEE Main Held on 12-4-2019 Morning]

A)
${{(Si{{O}_{3}})}^{2-}}$

B)
$Si{{O}_{2}}$

C)
${{(Si{{O}_{4}})}^{4-}}$

D)

• question_answer57) An organic compound 'A' is oxidized with $N{{a}_{2}}{{O}_{2}}$followed by boiling with $HN{{O}_{3}}.$he resultant solution is then treated with ammonium molybdate to yield a yellow precipitate. Based on above observation, the element present in the given compound is:                                                                                     [JEE Main Held on 12-4-2019 Morning]

A)
Sulphur

B)
Nitrogen

C)
Fluorine

D)
Phosphorus

• question_answer58) Enthalpy of sublimation of iodine is $24\,ca\operatorname{l}\,{{g}^{-1}}$ at $200{}^\circ C.$If specific heat of ${{I}_{2}}(s)$and ${{I}_{2}}(vap)$ are 0.055 and 0.031 $cal\,{{g}^{-1}}{{K}^{-1}}$respectively, then enthalpy of sublimation of iodine at $250{}^\circ C$ in $cal\,{{g}^{-1}}$is : [JEE Main Held on 12-4-2019 Morning]

A)
2.85

B)
11.4

C)
5.7

D)
22.8

• question_answer59) The major product of the following reaction                [JEE Main Held on 12-4-2019 Morning]

A)

B)

C)

D)

• question_answer60) The mole fraction of a solvent in aqueous solution of a solute is 0.8. The molality (in $\text{mol}\,\text{k}{{\text{g}}^{-1}}$) of the aqueous solution is                                                            [JEE Main Held on 12-4-2019 Morning]

A)
$13.88\times {{10}^{1}}$

B)
$13.88\times {{10}^{2}}$

C)
$13.88$

D)
$13.88\times {{10}^{3}}$

• question_answer61) If m is the minimum value of k for which the function $f(x)=x\sqrt{kx-{{x}^{2}}}$is increasing in the interval$\left[ 0,3 \right]$and M is the maximum value of f in$\left[ 0,3 \right]$when $k=m,$then the ordered pair (m, M) is equal to: [JEE Main Held on 12-4-2019 Morning]

A)
$(4,3\sqrt{2})$

B)
$(4,3\sqrt{3})$

C)
$(3,3\sqrt{3})$

D)
$(5,3\sqrt{6})$

• question_answer62) The equation$|z-i|=|z-1|,i=\sqrt{-1},$represents:              [JEE Main Held on 12-4-2019 Morning]

A)
the line through the origin with slope -1.

B)

C)
a circle of radius$\frac{1}{2}.$

D)
the line through the origin with slope 1.

• question_answer63) For$x\in \left( 0,\frac{3}{2} \right),let\,f(x)=\sqrt{x},g(x)=tanx$and$h(x)=\frac{1-{{x}^{2}}}{1+{{x}^{2}}}.$If $\phi (x)=((h\,of)og)(x),$then$\phi =\left( \frac{\pi }{3} \right)$is equal to: [JEE Main Held on 12-4-2019 Morning]

A)
$\tan \frac{\pi }{12}$

B)
$\tan \frac{7\pi }{12}$

C)
$\tan \frac{11\pi }{12}$

D)
$\tan \frac{5\pi }{12}$

• question_answer64) If three of the six vertices of a regular hexagon are chosen at random, then the probability that the triangle formed with these chosen vertices is equilateral is:      [JEE Main Held on 12-4-2019 Morning]

A)
$\frac{3}{10}$

B)
$\frac{1}{10}$

C)
$\frac{3}{20}$

D)
$\frac{1}{5}$

• question_answer65) If the normal to the ellipse $3{{x}^{2}}+4{{y}^{2}}=12$ at a point P on it is parallel to the line, $2x+y=4$ and the tangent to the ellipse at P passes through Q(4, 4) then PQ is equal to:            [JEE Main Held on 12-4-2019 Morning]

A)
$\frac{\sqrt{221}}{2}$

B)
$\frac{\sqrt{157}}{2}$

C)
$\frac{\sqrt{61}}{2}$

D)
$\frac{5\sqrt{5}}{2}$

• question_answer66) If${{e}^{y}}+xy=e,$the ordered pair$\left( \frac{dy}{dx},\frac{{{d}^{2}}y}{d{{x}^{2}}} \right)$at x = 0 is equal to: [JEE Main Held on 12-4-2019 Morning]

A)
$\left( -\frac{1}{e},\frac{1}{{{e}^{2}}} \right)$

B)
$\left( \frac{1}{e},\frac{1}{{{e}^{2}}} \right)$

C)
$\left( \frac{1}{e},-\frac{1}{{{e}^{2}}} \right)$

D)
$\left( -\frac{1}{e},-\frac{1}{{{e}^{2}}} \right)$

• question_answer67) If the line$\frac{x-2}{3}=\frac{y+1}{2}=\frac{z-1}{-1}$intersects the palne $2x+3yz+13=0$at a point P and the plane $3x+y+4z=16$at a point Q, then PQ is equal to:       [JEE Main Held on 12-4-2019 Morning]

A)
$2\sqrt{14}$

B)
$\sqrt{14}$

C)
$2\sqrt{7}$

D)
$14$

• question_answer68) The value of ${{\sin }^{-1}}\left( \frac{12}{13} \right)-{{\sin }^{-1}}\left( \frac{3}{5} \right)$is equal to:                        [JEE Main Held on 12-4-2019 Morning]

A)
$\pi -{{\sin }^{-1}}\left( \frac{63}{65} \right)$

B)
$\pi -{{\cos }^{-1}}\left( \frac{33}{65} \right)$

C)
$\frac{\pi }{2}-{{\sin }^{-1}}\left( \frac{56}{65} \right)$

D)
$\frac{\pi }{2}-{{\cos }^{-1}}\left( \frac{9}{65} \right)$

• question_answer69) If$\alpha$and $\beta$are the roots of the equation $375{{x}^{2}}25x2=0,$then[JEE Main Held on 12-4-2019 Morning] $\underset{n\to \infty }{\mathop{\lim }}\,\sum\limits_{r=1}^{n}{{{\alpha }^{r}}}+\underset{n\to \infty }{\mathop{\lim }}\,\sum\limits_{r=1}^{n}{{{\beta }^{r}}}$is equal to:

A)
$\frac{21}{346}$

B)
$\frac{29}{358}$

C)
$\frac{1}{12}$

D)
$\frac{7}{116}$

• question_answer70) If$\int\limits_{0}^{\frac{\pi }{2}}{\frac{\cot x}{\cot x+\cos ecx}}dx=m(\pi +n),$then m. n is equal to: [JEE Main Held on 12-4-2019 Morning]

A)
$-1$

B)
$1$

C)
$\frac{1}{2}$

D)
$-\frac{1}{2}$

• question_answer71) The number of ways of choosing 10 objects out of 31 objects of which 10 are identical and the remaining 21 are distinct, is:                                                       [JEE Main Held on 12-4-2019 Morning]

A)
${{2}^{20}}$

B)
${{2}^{20}}-1$

C)
${{2}^{20}}+1$

D)
${{2}^{21}}$

• question_answer72) If the data ${{x}_{1}},{{x}_{2}},....,{{x}_{10}}$is such that the mean of first four of these is 11, the mean of the remaining six is 16 and the sum of squares of all of these is 2,000; then the standard deviation of this data is : [JEE Main Held on 12-4-2019 Morning]

A)
$4$

B)
$2$

C)
$\sqrt{2}$

D)
$2\sqrt{2}$

• question_answer73) The number of solutions of the equation $1+{{\sin }^{4}}x={{\cos }^{2}}3x,x\in \left[ -\frac{5\pi }{2},\frac{5\pi }{2} \right]$is: [JEE Main Held on 12-4-2019 Morning]

A)
5

B)
4

C)
7

D)
3

• question_answer74) Let ${{S}_{n}}$denote the sum of the first n terms of an A.P. If ${{S}_{4}}=16$and ${{S}_{6}}=-48,$then${{S}_{10}}$is equal to: [JEE Main Held on 12-4-2019 Morning]

A)
-320

B)
-260

C)
-380

D)
-410

• question_answer75) If$B=\left[ \begin{matrix} 5 & 2\alpha & 1 \\ 0 & 2 & 1 \\ \alpha & 3 & -1 \\ \end{matrix} \right]$is the inverse of a $3\times 3$matrix A, then the sum of all values of$\alpha$for which det + 1 = 0, is :                                                                [JEE Main Held on 12-4-2019 Morning]

A)
0

B)
2

C)
1

D)
-1

• question_answer76) Let a random variable X have a binomial distribution with mean 8 and variance 4. If $P(x\le 2)=\frac{k}{{{2}^{16}}},$then k is equal to:                 [JEE Main Held on 12-4-2019 Morning]

A)
17

B)
1

C)
121

D)
137

• question_answer77) If the truth value of the statement $P\to (\tilde{\ }p\vee r)$is false(F), then the truth values of the statements p, q, r are respectively :                                                                      [JEE Main Held on 12-4-2019 Morning]

A)
F, T, T

B)
T, F, F

C)
T, T, F

D)
T, F, T

• question_answer78) Consider the differential equation,${{y}^{2}}dx+\left( x-\frac{1}{y} \right)dy=0.$If value of y is 1 when $x=1,$ the value of x for which $y=2,$is :                [JEE Main Held on 12-4-2019 Morning]

A)
$\frac{1}{2}+\frac{1}{\sqrt{e}}$

B)
$\frac{3}{2}-\sqrt{e}$

C)
$\frac{5}{2}+\frac{1}{\sqrt{e}}$

D)
$\frac{3}{2}-\frac{1}{\sqrt{e}}$

• question_answer79) Let $f:R\to R$be a continuously differentiable function wuch that $f\left( 2 \right)=6$ and $f\left( 2 \right)=\frac{1}{48}.$ If $\int_{6}^{f(x)}{4{{t}^{3}}}dt=(x-2)g(x),$then$\underset{x\to 2}{\mathop{\lim }}\,g(x)$is equal to:                         [JEE Main Held on 12-4-2019 Morning]

A)
24

B)
36

C)
12

D)
18

• question_answer80) The coefficient of ${{x}^{18}}$in the product $(1+x){{(1-x)}^{10}}{{(1+x+{{x}^{2}})}^{9}}$is : [JEE Main Held on 12-4-2019 Morning]

A)
-84

B)
84

C)
126

D)
-126

• question_answer81) For $x\in R,$let [x] denote the greatest integer $\le x,$ then the sum of the series $\left[ -\frac{1}{3} \right]+\left[ -\frac{1}{3}-\frac{1}{100} \right]+\left[ -\frac{1}{3}-\frac{2}{100} \right]+.....+\left[ -\frac{1}{3}-\frac{99}{100} \right]$is                  [JEE Main Held on 12-4-2019 Morning]

A)
-153

B)
-133

C)
-131

D)
-135

• question_answer82) The equation $y=\text{sin}x\text{sin}\left( x+2 \right)\text{si}{{\text{n}}^{2}}\left( x+1 \right)$represents a straight line lying in : [JEE Main Held on 12-4-2019 Morning]

A)

B)

C)

D)

• question_answer83) Let P be the point of intersection of the common tangents to the parabola ${{y}^{2}}=12x$ and the hyperbola $8{{x}^{2}}{{y}^{2}}=8.$If S and S' denote the foci of the hyperbola where S lies on the positive x-axis then P divides SS' in a ratio:                                                                [JEE Main Held on 12-4-2019 Morning]

A)
5:4

B)
14:13

C)
2:1

D)
13:11

• question_answer84) If the volume of parallel piped formed by the vectors $\hat{i}+\lambda \hat{j}+\hat{k},\hat{j}+\lambda \hat{k}$and $\lambda \hat{i}+\hat{k}$is minimum, then $\lambda$is equal to:                                                                           [JEE Main Held on 12-4-2019 Morning]

A)
$\sqrt{3}$

B)
$-\frac{1}{\sqrt{3}}$

C)
$\frac{1}{\sqrt{3}}$

D)
$-\sqrt{3}$

• question_answer85) A 2 m ladder leans against a vertical wall. If the top of the ladder begins to slide down the wall at the rate 25 cm/ sec., then the rate (in cm/sec.) at which the bottom of the ladder slides away from the wall on the horizontal ground when the top of the ladder is 1 m above the ground is: [JEE Main Held on 12-4-2019 Morning]

A)
$25\sqrt{3}$

B)
$25$

C)
$\frac{25}{\sqrt{3}}$

D)
$\frac{25}{3}$

• question_answer86) If a is A symmetric matrix and B is a skewsymmetrix matrix such that $A+B=\left[ \begin{matrix} 2 & 3 \\ 5 & -1 \\ \end{matrix} \right],$then AB is equal to :                              [JEE Main Held on 12-4-2019 Morning]

A)
$\left[ \begin{matrix} -4 & 2 \\ 1 & 4 \\ \end{matrix} \right]$

B)
$\left[ \begin{matrix} -4 & -2 \\ -1 & 4 \\ \end{matrix} \right]$

C)
$\left[ \begin{matrix} 4 & -2 \\ -1 & -4 \\ \end{matrix} \right]$

D)
$\left[ \begin{matrix} 4 & -2 \\ 1 & -4 \\ \end{matrix} \right]$

• question_answer87) Let $\vec{a}=3\hat{i}+2\hat{j}+2\hat{k}$and $\vec{b}=\hat{i}+2\hat{j}-2\hat{k}$be two vectors. If a vector perpendicular to both the vectors $\vec{a}+\vec{b}$and $\vec{a}-\vec{b}$ has the magnitude 12 then one such vector is[JEE Main Held on 12-4-2019 Morning]

A)
$4(2\hat{i}+2\hat{j}-\hat{k})$

B)
$4(-2\hat{i}-2\hat{j}+\hat{k})$

C)
$4(2\hat{i}-2\hat{j}-\hat{k})$

D)
$4(2\hat{i}+2\hat{j}+\hat{k})$

• question_answer88) The integral$\int_{{}}^{{}}{\frac{2{{x}^{3}}-1}{{{x}^{4}}+x}}dx$ is equal to: (Here C is a constant of integration)                            [JEE Main Held on 12-4-2019 Morning]

A)
${{\log }_{e}}\left| \frac{{{x}^{3}}+1}{x} \right|+C$

B)
$\frac{1}{2}{{\log }_{e}}\frac{{{({{x}^{3}}+1)}^{2}}}{|{{x}^{3}}|}+C$

C)
$\frac{1}{2}{{\log }_{e}}\frac{|{{x}^{3}}+1|}{{{x}^{2}}}+C$

D)
${{\log }_{e}}\frac{|{{x}^{3}}+1|}{{{x}^{2}}}+C$

• question_answer89) If the angle of intersection at a point where the two circles with radii 5 cm and 12 cm intersect is$90{}^\circ ,$then the length (in cm) of their common chord is:                 [JEE Main Held on 12-4-2019 Morning]

A)
$\frac{60}{13}$

B)
$\frac{120}{13}$

C)
$\frac{13}{2}$

D)
$\frac{13}{5}$

• question_answer90) If the area (in sq. units) of the region $\{(x,y):{{y}^{2}}\le 4x,x+y\le 1,x\ge 0,y\ge O\}$$a\sqrt{2}+b,$is then $ab$is equal to : [JEE Main Held on 12-4-2019 Morning]

A)
$\frac{8}{3}$

B)
$\frac{10}{3}$

C)
$6$

D)
$-\frac{2}{3}$