# Solved papers for JEE Main & Advanced JEE Main Online Paper (Held On 10-Jan-2019 Evening)

### done JEE Main Online Paper (Held On 10-Jan-2019 Evening)

• question_answer1) Four equal point charges Q each are placed in the xy plane at$\left( 0,\text{ }2 \right),\text{ }\left( 4,\text{ }2 \right),\text{ }\left( 4,\,-2 \right)\text{ }and\text{ }\left( 0,-\,2 \right)$. The work required to put a fifth charge Q at the origin of the coordinate system will be- [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) $\frac{{{Q}^{2}}}{4\pi {{\varepsilon }_{0}}}$

B) $\frac{{{Q}^{2}}}{2\sqrt{2}\pi {{\varepsilon }_{0}}}$

C) $\frac{{{Q}^{2}}}{4\pi {{\varepsilon }_{0}}}\left( 1+\frac{1}{\sqrt{3}} \right)$

D)                  $\frac{{{Q}^{2}}}{4\pi {{\varepsilon }_{0}}}\left( 1+\frac{1}{\sqrt{5}} \right)$

• question_answer2)             A rigid massless rod of length 3l has two masses attached at each end as shown in the figure. The rod is pivoted at point P on the horizontal axis (see figure).  When released  from initial horizontal position, its instantaneous angular acceleration will be- [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) $\frac{g}{13l}$

B) $\frac{g}{2l}$

C) $\frac{g}{3l}$

D)                  $\frac{7g}{3l}$

• question_answer3) A closed organ pipe has a fundamental frequency of 1.5 kHz. The number of overtones that can be distinctly heard by a person with this organ pipe will be (Assume that the highest frequency a person can hear is 20,000 Hz) [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) 4

B) 7

C) 6

D)                  5

• question_answer4) Consider the nuclear fission $N{{e}^{20}}\to 2H{{e}^{4}}+{{C}^{\text{12}}}$ Given that the binding energy/nucleon of$N{{e}^{20}}$, $H{{e}^{4}}$ and ${{C}^{12}}$ are respectively, 8.03 MeV, 7.07 MeV and 7.86 MeV, identify the correct statement- [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) 8.3 MeV energy will be released

B) energy of 11.9 MeV has to be supplied

C) energy of 12.4 MeV will be supplied

D) energy of 3.6 MeV will be released

• question_answer5) A metal plate of area $1\times {{10}^{-}}^{4}\,{{m}^{2}}$ is illuminated by a radiation of intensity$16\text{ }mW/{{m}^{2}}$. The work function of the metal is 5 eV. The energy of the incident photons is 10 eV and only $10%$ of it produces photo electrons. The number of  emitted photoelectrons per second and their maximum energy, respectively, will be- [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) ${{10}^{14}}$ and 10 eV

B) ${{10}^{12}}$ and 5 Ev

C) ${{10}^{11}}$ and 5 eV

D)                  ${{10}^{10}}$and 5 eV

• question_answer6) For the circuit shown below, the current through the Zener diode is- [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) 5 mA

B) zero

C) 14 mA

D)                  9 mA

• question_answer7) Two vectors  $\overrightarrow{A}\text{ }and\text{ }\overrightarrow{B}$ have equal magnitudes. The magnitude of $\left( \overrightarrow{A}+\text{ }\overrightarrow{B} \right)$ is 'n' times the magnitude of$\left( \overrightarrow{A}-\overrightarrow{B} \right)$. The angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ is- [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) ${{\sin }^{-1}}\,\left[ \frac{n-1}{n+1} \right]$

B) ${{\sin }^{-1}}\,\left[ \frac{{{n}^{2}}-1}{{{n}^{2}}+1} \right]$

C) ${{\cos }^{-1}}\,\left[ \frac{{{n}^{2}}-1}{{{n}^{2}}+1} \right]$

D) ${{\cos }^{-1}}\,\left[ \frac{n-1}{n+1} \right]$

• question_answer8) The diameter and height of a cylinder are measured by a meter scale to be $12.6\,\,\pm \,\,0.1$ cm and $34.2\,\,\pm \,0.1$ cm, respectively. What will be the value of its volume in appropriate significant figures? [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) $4264.4\,\,\pm \,\,81.0\text{ }c{{m}^{3}}$

B) $4264\,\,\pm \,\,81c{{m}^{3}}$

C) $4300\,\,\pm \,\,80\text{ }c{{m}^{3}}$

D)                  $4260\,\,\pm \,\,80\text{ }c{{m}^{3}}$

• question_answer9) A current of 2 mA was passed through an unknown resistor which dissipated a power of 4.4 W. Dissipated power when an ideal power supply of 11 V is connected across it is- [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) $11\times {{10}^{-5}}\text{ }W$

B) $11\times {{10}^{-3}}\text{ }W$

C) $11\times {{10}^{5}}\text{ }W$

D)                  $11\times {{10}^{-}}^{4}W$

• question_answer10) Two stars of masses $3\times {{10}^{31}}$ kg each, and at distance $2\times {{10}^{11}}$ m rotate in a plane about their common centre of mass 0. A meteorite passes through 0 moving perpendicular to the star/s rotation plane. In order to escape from the gravitational field of this double star, the minimum speed that meteorite should have at 0 is-  (Take       Gravitational      constant;             $G=6.67\times {{10}^{-11}}\,N{{m}^{2}}k{{g}^{-}}^{2})$ [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) $2.4\times {{10}^{4}}m/s$

B) $1.4\times {{10}^{5}}m/s$

C) $3.8\times {{10}^{4}}m/s$

D) $2.8\times {{10}^{5}}m/s$

• question_answer11) Consider a Young's double slit experiment as shown in figure. What should be the slit separation d in terms of wavelength $\lambda$ such that the first minima occurs directly in front of the slit$\left( {{S}_{1}} \right)$? [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) $\frac{\lambda }{2(5-\sqrt{2})}$

B) $\frac{\lambda }{2(\sqrt{5}-2)}$

C) $\frac{\lambda }{(5-\sqrt{2})}$

D) $\frac{\lambda }{(\sqrt{5}-2)}$

• question_answer12) At some location on earth the horizontal component of earth's magnetic field$18\times {{10}^{-}}^{6}T$. At this location, magnetic needle of length 0.12 m and pole strength 1.8 Am is suspended from its mid-point using a thread, it makes $45{}^\circ$ angle with horizontal in equilibrium. To keep this needle horizontal, the vertical force that should be applied at one of its ends is- [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) $3.6\times {{10}^{-5}}\,N$

B) $1.8\times {{10}^{-5}}\text{ }N$

C) $1.3\times {{10}^{-5}}\,N$

D) $6.5\times {{10}^{-5}}\,N$

• question_answer13) Charges -q and +q located at A and B. respectively, constitute an electric dipole. Distance $AB=2a$, 0 is the mid-point of the dipole and OP is perpendicular to AB. A charge Q is placed at P where $OP=y$ and $y\,\,>\,\,>\,\,2a$. The charge Q experiences an electrostatic force F. If Q is now moved along the equatorial line to P? such that $OP'=\left( \frac{y}{3} \right)$,  the force on Q will be close to- $\left( \frac{y}{3}>>2a \right)$ [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) 9F

B) 3F

C) F/3

D)                  27F

• question_answer14) The self-induced emf of a coil is 25 volts. When the current in it is changed at uniform rate from 10 A to 25 A in 1s, the change in the energy of the inductance is- [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) 740 J

B) 637.5 J

C) 540 J

D)                  437.5 J

• question_answer15) Half mole of an ideal monoatomic gas is heated at constant pressure of 1 atm from$20{}^\circ C\text{ }to\text{ }90{}^\circ C$. Work done by gas is close to -(Gas constant $R=8.31\text{ }J$ /mol. K) [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) 581 J

B) 73 J

C) 146 J

D)                  291 J

• question_answer16) Two kg of a monoatomic gas is at a pressure of $4\times {{10}^{4}}N/{{m}^{2}}$. The density of the gas is $8\text{ }kg/{{m}^{3}}$. What is the order of energy of the gas due to its thermal motion? [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) ${{10}^{4}}$ J

B) ${{10}^{3}}J$

C) ${{10}^{5}}\text{ }J$

D)                  ${{10}^{6}}J$

• question_answer17) The modulation frequency of an AM radio station is 250 kHz, which is 10% of the carrier wave. If another AM station approaches you for license what broadcast frequency will you allot? [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) 2900 kHz

B) 2750 kHz

C) 2250 kHz

D)                  2000 kz

• question_answer18) The electric field of a plane polarized electromagnetic wave in free space at time  $t=0$ is given by an expression $\overrightarrow{E}\left( x,y \right)=10\widehat{j}\text{ }cos\left[ \left( 6x+8z \right) \right]$. The magnetic field $\overrightarrow{B}\left( x,\text{ }z,\text{ }t \right)$ is given by - (c is the velocity of light) [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) $\frac{1}{c}(6\widehat{k}+8\widehat{i})\,cos[(6x+8z-10ct)]$

B) $\frac{1}{c}(6\widehat{k}-8\widehat{i})\,cos[(6x+8z-10ct)]$

C) $\frac{1}{c}(6\widehat{k}+8\widehat{i})\,cos[(6x-8z+10ct)]$

D) $\frac{1}{c}(6\widehat{k}-8\widehat{i})\,cos[(6x+8z+10ct)]$

• question_answer19) A particle starts from the origin at time $t=0$ and moves along the positive x-axis. The graph of velocity with respect to time is shown in figure. What is the position of the particle at time$t=5s$? [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) 3 m

B) 9 m

C) 10 m

D)                  6 m

• question_answer20) Two forces P and Q, of magnitude 2F and 3F, respectively; are at an angle 9 with each other. If the force Q is doubled, then their resultant also gets doubled. Then, the angle $\theta$ is- [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) $90{}^\circ$

B) $60{}^\circ ~$

C) $30{}^\circ ~~$

D)                  $120{}^\circ$

• question_answer21) The eye can be regarded as a single refracting surface. The radius of curvature of this surface is equal to that of cornea (7.8 mm). This surface separateds two media of refractive indices 1 and 1.34. Calculate the distance from the refracting surface at which a parallel beam of light will come to focus- [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) 2 cm

B) 3.1 cm

C) 4.0 cm

D)                  1 cm

• question_answer22) A cylindrical plastic bottle of negligible mass is filled with 310 ml of water and left floating in a pond with still water. If pressed downward slightly and released, it starts performing simple harmonic motion at angular frequency co. If the radius of the bottle is 2.5 cm then co is close to - (density of water$={{10}^{3}}kg/{{m}^{3}}$). [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) $2.50\text{ }rad\text{ }{{s}^{-}}^{1}$

B) $3.75\text{ }rad\text{ }{{s}^{-1}}$

C) $5.00\text{ }rad\text{ }{{s}^{-1}}$

D)                  $1.25\text{ }rad\text{ }{{s}^{-1}}$

E)                  None of these

• question_answer23) A hope and a solid cylinder of same mass and radius are made of a permanent magnetic material with their magnetic moment parallel to their respective axes. But the magnetic moment of hoop is twice of solid cylinder. They are placed in a uniform magnetic field in such a manner angle with the field. If the oscillation periods of hoop and cylinder are ${{T}_{h}}\text{ }and\text{ }{{T}_{c}}$ respectively, then- [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) ${{T}_{h}}=1.5\text{ }{{T}_{c}}$

B) ${{T}_{h}}={{T}_{c}}$

C) ${{T}_{h}}=2{{T}_{c}}$

D)                  ${{T}_{h}}=0.5{{T}_{c}}$

• question_answer24) The Wheatstone bridge shown in figure, here, gets balanced when the carbon resistor used as ${{R}_{1}}$ has the colour code (Orange, Red, Brown).  he resistors ${{R}_{2}}\text{ }and\text{ }{{R}_{4}}\text{ }are\text{ }80\Omega \,\,and\text{ }40\Omega$ , respectively. Assuming that the colour code for the carbon resistors gives their accurate values, the colour code for the carbon resistor, used as Rs, would be- [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) Brown, Blue, Brown

B) Grey, Black, Brown

C) Red, Green, Brown

D) Brown, Blue, Black

• question_answer25) The actual value of resistance R, shown in the figure is $30\,\Omega$. This is measured in an experiment as shown using the standard formula $R=\frac{V}{I}$ where V and I are the readings of the voltmeter and ammeter, respectively. If the measured value of R is $5%$ less, then the internal resistance of the voltmeter is- [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) 570 $\Omega$

B) 600 $\Omega$

C) 350 $\Omega$

D)                  35 $\Omega$

• question_answer26) An unknown metal of mass 192 g heated to a temperature of $100{}^\circ C$ was immersed into a brass calorimeter of mass 128 g containing 240 g of water at a temperature of $8.4{}^\circ \,C$. Calculate the specific heat of the unknown metal if water temperature stabilizes at $21.5{}^\circ C$. (Specific heat of brass is $394\text{ }J\text{ }k{{g}^{-1}}{{K}^{-1}}$) [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) 458 J $394\text{ }J\text{ }k{{g}^{-1}}{{K}^{-1}}$

B) 1232 J $394\text{ }J\text{ }k{{g}^{-1}}{{K}^{-1}}$

C) 654 J $394\text{ }J\text{ }k{{g}^{-1}}{{K}^{-1}}$

D)                  916 J $394\text{ }J\text{ }k{{g}^{-1}}{{K}^{-1}}$

• question_answer27) A particle which is experiencing a force, given by $\overrightarrow{F}=3\overrightarrow{i}-12\overrightarrow{j}$, undergoes a displacement of $\overrightarrow{d}=4\overrightarrow{i}$ . If particle had a kinetic energy of 3 J at the beginning of the displacement what is its kinetic energy at the end of the displacement? [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) 9 J

B) 10 J

C) 12 J

D)                  15 J

• question_answer28) A particle executes simple harmonic motion with an amplitude of 5 cm. When the particle is at 4 cm from the mean position, the magnitude of its velocity in SI units is equal to that of its acceleration. Then, its periodic time in seconds is- [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) $\frac{4\pi }{3}$

B) $\frac{3\,}{8}\pi$

C) $\frac{7\,}{3}\pi$

D)                  $\frac{8\,\pi }{3}$

• question_answer29) Two identical spherical balls of mass M and radius R each are stuck on two ends of a rod of length 2R and mass M (see figure). The moment of inertia of the system about the axis passing perpendicularly through the centre of the rod is: [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) $\frac{17}{15}M{{R}^{2}}$

B) $\frac{137}{15}M{{R}^{2}}$

C) $\frac{209}{15}M{{R}^{2}}$

D)                  $\frac{152}{15}M{{R}^{2}}$

• question_answer30) A   parallel   plate   capacitor   having capacitance 12 pF is charged by a battery to a potential difference of 10 V between its plates. The charging battery is now disconnected and a porcelain slab of dielectric constant 6.5 is slipped between the plates. The work done by the capacitor on the slab is: [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) 508 pJ

B) 692 pJ

C) 560 pJ

D)                  600 pJ

• question_answer31) A reaction of cobalt (III) chloride and ethylenediamine in a 1 : 2 mole ratio generates two isomeric products A (violet coloured) and B (green coloured). A can show optical activity, but B is optically inactive. What type of isomers does A and B represent? [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) Ionisation isomers

C) Coordination isomers

D) Geometrical isomers

• question_answer32) The pair that contains two $P-H$ bonds in each of the oxoacids is: [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) ${{H}_{3}}P{{O}_{2}}\text{ }and\text{ }{{H}_{4}}{{P}_{2}}{{O}_{5}}$

B) ${{H}_{4}}{{P}_{2}}{{O}_{5}}\text{ }and\text{ }{{H}_{4}}{{P}_{2}}{{O}_{6}}$

C) ${{H}_{4}}{{P}_{2}}{{O}_{5}}\,and\,{{H}_{3}}P{{O}_{3}}$

D) ${{H}_{3}}P{{O}_{3}}$ and ${{H}_{3}}P{{O}_{2}}$

• question_answer33) In  the  reaction   of  oxalate  with permanganate in acidic medium, the number of electrons involved in producing one molecule of $C{{O}_{2}}$ is: [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) 10

B) 2

C) 1

D)                  5

• question_answer34) The reaction that is NOT involved in the ozone layer depletion mechanism in the stratosphere is: [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) $Cl\overset{\bullet }{\mathop{O}}\,(g)+O(g)\,\,\to \,\,\overset{\bullet }{\mathop{Cl}}\,(g)+{{O}_{2}}(g)$

B) $C{{F}_{2}}C{{l}_{2}}(g)\,\,\,\xrightarrow{uv}\,\,\overset{\bullet }{\mathop{Cl}}\,(g)+\overset{\bullet }{\mathop{C}}\,{{F}_{2}}Cl(g)$

C) $\,C{{H}_{4}}+2{{O}_{3}}\to 3C{{H}_{2}}=O+3\,\,{{H}_{2}}O$

D) $HOCl(g)\xrightarrow{hv}\,\,\overset{\bullet }{\mathop{OH}}\,\,(g)+\overset{\bullet }{\mathop{Cl\,}}\,(g)$

• question_answer35) An aromatic compound 'A' having molecular formula ${{C}_{7}}{{H}_{6}}{{O}_{2}}$ on treating with aqueous ammonia and heating forms compound 'B'. The compound 'B' on reaction with molecular bromine and potassium hydroxide provides compound 'C' having molecular formula${{C}_{6}}{{H}_{7}}N$. The structure of 'A' is: [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) B) C) D) • question_answer36) For an elementary chemical reaction; ${{A}_{2}}\,\,2{{A}_{1}}$, the expression for $\frac{d[A]}{dt}$ is [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) $2{{K}_{1}}\left[ {{A}_{2}} \right]-{{K}_{-1}}{{[A]}^{2}}$

B) ${{K}_{1}}\left[ {{A}_{2}} \right]-{{K}_{-1}}{{[A]}^{2}}$

C) ${{K}_{1}}\left[ {{A}_{2}} \right]+{{K}_{-1}}{{[A]}^{2}}$

D)                  $2{{K}_{1}}\left[ {{A}_{2}} \right]-2{{K}_{-1}}{{[A]}^{2}}$

• question_answer37) The electrolytes usually used in the electroplating   of gold and silver, respectively are: [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) ${{\left[ Au{{\left( CN \right)}_{2}} \right]}^{-}}and\text{ }{{\left[ Ag{{\left( CN \right)}_{2}} \right]}^{-}}$

B) ${{\left[ Au{{\left( CN \right)}_{2}} \right]}^{-}}and\text{ }{{\left[ Ag{{\left( Cl \right)}_{2}} \right]}^{-}}$

C) ${{\left[ Au{{\left( OH \right)}_{4}} \right]}^{-}}and\text{ }{{\left[ Ag{{\left( OH \right)}_{2}} \right]}^{-}}$

D) ${{[Au{{(N{{H}_{3}})}_{2}}]}^{+}}\,and\,\,{{[Ag{{(CN)}_{2}}]}^{-}}$

• question_answer38) Among the following reactions of hydrogen with halogens, the one that requires a catalyst is [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) ${{H}_{2}}+B{{r}_{2}}\to 2HBr$

B) ${{H}_{2}}+C{{l}_{2}}\to 2HCl$

C) ${{H}_{2}}+{{F}_{2}}\to 2HF$

D) ${{H}_{2}}+{{I}_{2}}\to 2HI$

• question_answer39) The major product of the following reaction is [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) B) C) D) • question_answer40) What is the IUPAC name of the following compound? [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) 4-Bromo-3-methylpent-2-ene

B) 3-Bromo 1, 2-dimethylbut-1-ene

C) 3-Bromo-3-methyl-1, 2-dimethylprop-1-ene

D) 2-Bromo-3-methylpent-3-ene

• question_answer41) A compound of formula ${{A}_{2}}{{B}_{3}}$ has the hcp lattice. Which atom forms the hcp lattice and what fraction of tetrahedral voids is occupied by the other atoms: [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) hcp lattice - A, $\frac{1}{3}$ Tetrahedral voids - B

B) hcp lattice - B, $\frac{1}{3}$ Tetrahedral voids - A

C) hcp lattice - A, $\frac{2}{3}$ Tetrahedral voids - B

D) hcp lattice -B, $\frac{2}{3}$ Tetrahedral voids - A

• question_answer42) Sodium metal on dissolution in liquid ammonia gives a deep blue solution due to the formation of: [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) ammoniated electrons

B) sodamide

C) sodium-ammonia complex

D) sodium ion-ammonia complex

• question_answer43) Which of the following- test cannot be used for identifying amino acids? [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) Ninhydrin test

B) Barfoed lest

C) Xanthoproteic test

D) Biuret test

• question_answer44) What will be the major product in the following mononitration reaction? [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) B) C) D) • question_answer45) The difference in the number of unpaired electrons of a metal ion in its high spin and low-spin octahedral complexes is two. The metal ion is [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) $M{{n}^{2+}}$

B) $N{{i}^{2}}^{+}$

C) $C{{o}^{2+}}$

D)                  $F{{e}^{2}}^{+}$

• question_answer46) The ground state energy of hydrogen atom is- 13.6 eV. The energy of second excited state of $H{{e}^{+}}$ ion in eV is: [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) - 6.04

B)                              - 54.4

C) - 27.2

D)                  - 3.4

• question_answer47) The 71st electron of an element X with an atomic  number of 71 enters into the orbital; [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) 4f

B) 6s

C) 6p

D)                  5d

• question_answer48) The major product of the following reaction [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) B) C) D) • question_answer49) The major product obtained in the following reaction is: [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) B) C) D) • question_answer50)   In the cell $Pt\left| \,\left( s \right)\, \right|{{H}_{2}}$(g, 1 bar) $\left| \text{ }HCl\left( aq \right)\text{ } \right|$ $AgCl\left| \,\left( s \right)\, \right|\,Ag\left( s \right)|Pt\left( s \right)$ the cell potential is 0.92 V when a ${{10}^{-}}^{6}$ molal HCl solution is used. The standard electrode potential of $\left( AgCl/Ag,C{{l}^{-}} \right)$ electrode is: {Given, $\frac{2.303RT}{F}\,=\,0.06V\,at\,\,298\,K$ [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) 0.94 V

B) 0.40V

C) 0.76 V

D)                  0.20 V

• question_answer51) Which is the most suitable reagent for the following transformation? [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) alkaline$KMn{{O}_{4}}$

B) Tollen's neagent

C) ${{I}_{2}}/NaOH$

D) $Cr{{O}_{2}}C{{l}_{2}}/C{{S}_{2}}$

• question_answer52) The process with negative entropy change is [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) Dissociation of$CaS{{O}_{4}}$, (s) to CaO(s) and $S{{O}_{3}}$(g)

B) Dissolution of iodine in water

C) Synthesis of ammonia from N2 and H2

D) Sublimation of dry ice

• question_answer53) Elevation in the boiling point for 1 molar solution of glucose is 2 K. The depression in the freezing point for 2 molar solution of glucose in the same solvent is 2 K. The relation between ${{K}_{b}}$ and ${{K}_{f}}$ is: [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) ${{K}_{b}}={{K}_{f}}$

B) ${{K}_{b}}\,=0.5\,\,{{K}_{f}}$

C) ${{K}_{b}}\,=\,1.5\,{{K}_{f}}$

D)                  ${{K}_{b}}=2\,\,{{K}_{f}}$

• question_answer54) The amount of sugar $\left( {{C}_{12}}{{H}_{22}}{{O}_{11}} \right)$ required to prepare 2L of its 0.1 M aqueous solution is: [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) 17.1 g

B) 34.2 g

C) 68.4 g

D)                  136.8 g

• question_answer55) The correct match between item - I and item - II is:

 Item - I (compound) Item - II (reagent) (A) Lysine (P) 1-naphthol (B) Furfural (Q) ninhydrin (C) Benzylalcohol (R) $KMn{{O}_{4}}$ (D) Styrene (S) Ceric ammonium nitate
[JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) [A] $\to$ (Q); [B] $\to$ (R); [C] $\to$ (S); [D] $\to$ (P)

B) [A] $\to$ (Q); [B] $\to$ (P); [C] $\to$ (S); [D] $\to$ (R)

C) [A] $\to$  (R); [B] $\to$ (P); [C] $\to$ (Q); [D] $\to$ (S)

D) [A] $\to$ (Q); [B] $\to$ (P); [C] $\to$ (R); [D] $\to$ (S)

• question_answer56) An ideal gas undergoes isothermal compression from $5{{m}^{3}}$ to $1\text{ }{{m}^{3}}$ against a constant external pressure of $4\text{ }N{{m}^{-}}^{2}$. Heat released in this process is used to increase the temperature of 1 mole of Al. If molar heat capacity of Al is 24 J $mo{{l}^{-1}}\text{ }{{K}^{-1}}$, the temperature of Al increases by: [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) $\frac{2}{3}$K

B) $\frac{3}{2}$K

C) 1 K

D)                  2 K

• question_answer57) The major product of the following reaction is: [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) B) C) D) • question_answer58) The number of 2-centre-2-electron and 3- centre   -2-electron bonds in ${{B}_{2}}{{H}_{6}}$, respectively are: [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) 2 and 2

B) 2 and 1

C) 2 and 4

D)                  4 and 2

• question_answer59) Haemoglobin and gold sol are examples of: [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) positively charged sols

B) negatively charged sols

C) Positively and negatively charged sols, respectively

D) negatively and positively charged sols, respectively

• question_answer60) 5.1 g $N{{H}_{4}}SH$ is introduced in 3.0 L evacuated flask at $327{}^\circ C$. 30% of the solid $N{{H}_{4}}SH$ decomposed to $N{{H}_{3}}$ and ${{H}_{2}}S$ as gases. The ${{K}_{p}}$ of the reaction at $327{}^\circ C$ is ($R=0.082$ L atm $mo{{l}^{-1}}\text{ }{{K}^{-}}^{1}$, Molar mass of $S=32$ g $mo{{l}^{-}}^{1}$ molar mass of $N=14\,g\text{ }mo{{l}^{-1}}$) [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) $0.242\times {{10}^{-4}}\text{ }at{{m}^{2}}$

B) $1\times {{10}^{-4}}\text{ }at{{m}^{2}}$

C) $4.9\times {{10}^{-3}}\text{ }at{{m}^{2}}$

D)                  $0.242\text{ }at{{m}^{2}}$

• question_answer61) The length of the chord of the parabola ${{x}^{2}}=4y$ having equation $x-\sqrt{2}y+4\sqrt{2}=0$ is- [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) $8\sqrt{2}$

B)                              $6\sqrt{3}$

C) $3\sqrt{2}$

D)                  $2\sqrt{11}$

• question_answer62) Let N be the set of natural numbers and two functions f and g be defined as $f,\text{ }g\text{ }:\text{ }N\to N$ such that $f(n)\,=\,\left\{ \begin{matrix} \frac{n+1}{2} \\ \frac{n}{2} \\ \end{matrix} \right.\,\,\,\begin{matrix} ;\,\,\,\,if\,\,n\,\,is\,\,odd \\ ;\,\,if\,\,n\,\,is\,\,given \\ \end{matrix}\,\,\,\,;\,\,and$$g\left( n \right)=n-{{\left( -1 \right)}^{n}}$ . Then fog is [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) neither one-one nor onto

B) onto but not one-one

C) both one-one and onto

D) one-one but not onto

• question_answer63) Two sides of a parallelogram are along the lines,$x+y=3\,\,\,\And \,\,x-y+3=0$. If its diagonals intersect at (2, 4), then one of its vertex is- [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) (2, 1)

B) (2, 6)

C) (3, 5)

D)                  (3, 6)

• question_answer64) If mean and standard deviation of 5 observations ${{x}_{1}},\text{ }{{x}_{2}},\text{ }{{x}_{3}},\text{ }{{x}_{4}},\text{ }{{x}_{5}}$ are 10 and 3 respectively, then the variance of 6 observations ${{x}_{1}},\text{ }{{x}_{2}},\text{ }......\text{ }{{x}_{5}}$ and - 50 is equal to [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) 582.5

B) 507.5

C) 586.5

D)                  509.5

• question_answer65) The value of cot $\left( \sum\limits_{n\,=\,1}^{19}{{{\cot }^{-1}}}\left( 1+\sum\limits_{p\,=\,1}^{n}{2\,p} \right) \right)$is - [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) $\frac{22}{23}$

B) $\frac{23}{22}$

C) $\frac{21}{19}$

D)                  $\frac{19}{21}$

• question_answer66) The value of$cos\frac{\pi }{{{2}^{2}}}.\,cos\frac{\pi }{{{2}^{3}}}\,\,......\,cos\,\frac{\pi }{{{2}^{10}}}.\,sin\,\frac{\pi }{{{2}^{10}}}$ is- [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) $\frac{1}{256}$

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

C) $\frac{1}{1024}$

D)                  $\frac{1}{512}$

• question_answer67) If $\sum\limits_{r\,=\,0}^{25}{{{\{}^{50}}{{C}_{r}}{{.}^{50\,-\,r}}{{C}_{25\,-\,r}}\}\,=\,K{{(}^{50}}{{C}_{25}})}$ then K is equal to [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) ${{2}^{24}}$

B) ${{2}^{25}}-1$

C) ${{2}^{25}}$

D)                  ${{\left( 25 \right)}^{2}}$

• question_answer68) Let ${{a}_{1}},\text{ }{{a}_{2}},{{a}_{3}},.....\text{ }{{a}_{10}}$ be in G.P. with ${{a}_{i}}>0$ for $i=1,\text{ }2,\text{ }......10$ and S be the set of pairs (r, k), r, k e N (the set of natural numbers) for which

 $\left| \begin{matrix} {{\log }_{e}}\,{{a}_{1}}{{\,}^{r}}{{a}_{2}}^{k} & {{\log }_{e}}\,{{a}_{2}}{{\,}^{r}}{{a}_{3}}^{k} & {{\log }_{e}}\,{{a}_{3}}{{\,}^{r}}{{a}_{4}}^{k} \\ {{\log }_{e}}\,{{a}_{4}}{{\,}^{r}}{{a}_{5}}^{k} & {{\log }_{e}}\,{{a}_{5}}{{\,}^{r}}{{a}_{6}}^{k} & {{\log }_{e}}\,{{a}_{6}}{{\,}^{r}}{{a}_{7}}^{k} \\ {{\log }_{e}}\,{{a}_{7}}{{\,}^{r}}{{a}_{8}}^{k} & {{\log }_{e}}\,{{a}_{8}}{{\,}^{r}}{{a}_{9}}^{k} & {{\log }_{e}}\,{{a}_{9}}{{\,}^{r}}{{a}_{10}}^{k} \\ \end{matrix} \right|=0$ Then the number of elements in S, is -
[JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) 10

B) 4

C) 2

D)                  infinitely many

• question_answer69) Two vertices of a triangle are (0, 2) and (4, 3). If its orthocenter is at the origin,  then its third vertex lies in which quadrant- [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) third

B) fourth

C) second

D)                  first

• question_answer70) If the probability of hitting a target by a shooter, in any shot, is $\frac{1}{3}$, then the minimum number of independent shots at the target required by him so that the probability of hitting the target at least once is greater than $\frac{5}{6}$, is- [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) 4

B) 6

C) 5

D)                  3

• question_answer71) The tangent to the curve, $y=x{{e}^{{{x}^{2}}}}$passing through the point (1, e) also passes through the point

A) $\left( \frac{4}{3},\,\,\,2e \right)$

B) $\left( 3,\,\,\,6e \right)$

C) $\left( 2,\,\,3e \right)$

D) $\left( \frac{5}{3},\,\,2e \right)$

• question_answer72) The value of $\int\limits_{-\pi /2}^{\pi /2}{\frac{dx}{[x]+[sin\,x]+4}}$ where [t] denotes the greatest integer less than or equal to t, is- [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) $\frac{1}{12}(7\pi -5)$

B) $\frac{1}{12}(7\pi +5)$

C) $\frac{3}{10}(4\pi -3)$

D)                  $\frac{3}{20}(4\pi -3)$

• question_answer73) Let $S=\,\left\{ (x,\,\,y)\,\in \,\,{{R}^{2}}:\frac{{{y}^{2}}}{1+r}-\frac{{{x}^{2}}}{1-r}=1 \right\};\,r\ne \pm 1$Then S represents [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) an ellipse whose eccentricity is $\frac{1}{\sqrt{r}+1}$ where $r>1$

B) a hyperbola whose eccentricity is $\frac{2}{\sqrt{r+1}}$, when $0<r<1$

C) a hyperbola whose eccentricity is $\frac{2}{\sqrt{1-r}}$when $0<r<1$

D) an ellipse whose eccentricity is $\sqrt{\frac{2}{r+1}}$ when  $r>1$

• question_answer74) If $\int\limits_{0}^{x}{f(t)\,dt\,\,=\,\,{{x}^{2}}+}\int\limits_{x}^{1}{{{t}^{2}}f(t)\,\,dt\,\,then\,\,f\,\,'\left( \frac{1}{2} \right)}$ is- [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) $\frac{18}{25}$

B) $\frac{6}{25}$

C) $\frac{24}{25}$

D)                  $\frac{4}{5}$

• question_answer75) Let $A=\left[ \begin{matrix} 2 & b & 1 \\ b & {{b}^{2}}+1 & b \\ 1 & b & 2 \\ \end{matrix} \right]$ where$b>0$. Then the minimum value of $\frac{\det (A)}{b}$is- [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) $\sqrt{3}$

B) $-2\sqrt{3}$

C) $-\sqrt{3}$

D)                  $2\sqrt{3}$

• question_answer76) With the usual notation, in $\Delta \,ABC$, if $\angle A+\angle B=120{}^\circ$, $a=\sqrt{3}+1\,\,and\,\,b=\sqrt{3}-1$, then the ratio $\angle A:\angle B$, is- [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) 9 : 7

B) 7 : 1

C) 5 : 3

D)                  3 : 1

• question_answer77) The value of $\lambda$. such that sum of the squares of the roots of the quadratic equation, ${{x}^{2}}+(3-\lambda )x+2=\lambda$ has the least value is- [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) 1

B) 2

C) $\frac{15}{8}$

D)                  $\frac{4}{9}$

• question_answer78) On which of the following lines lies the point  of intersection of the line, $\frac{x-4}{2}=\frac{y-5}{2}=\frac{z-3}{1}$ and the plane,$x+y+z=2$? [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) $\frac{x-4}{1}=\frac{y-5}{1}=\frac{z-5}{-1}$

B) $\frac{x-2}{2}=\frac{y-3}{2}=\frac{z+3}{3}$

C) $\frac{x-1}{1}=\frac{y-3}{2}=\frac{z+4}{-5}$

D) $\frac{x+3}{3}=\frac{4-y}{3}=\frac{z+1}{-\,2}$

• question_answer79) The positive value of $\lambda$ for which the co-efficient of ${{x}^{2}}$ in the expression ${{x}^{2}}{{\left( \sqrt{x}+\frac{\lambda }{{{x}^{2}}} \right)}^{10}}$is 720, is- [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) 4

B) $2\sqrt{2}$

C) 3

D)                  $\sqrt{5}$

• question_answer80) Let $z={{\left( \frac{\sqrt{3}}{2}+\frac{i}{2} \right)}^{5}}\,+\,{{\left( \frac{\sqrt{3}}{2}-\frac{i}{2} \right)}^{5}}$. If R(z) and I(z) respectively denote the real and imaginary parts of z, then- [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) $R\left( z \right)=-3$

B) $R\left( z \right)<0\text{ }and\text{ }I\left( z \right)>0$

C) $I\left( z \right)=0$

D) $R\left( z \right)>0\text{ }and\text{ }I\left( z \right)>0$

• question_answer81) The number of values of $\theta \,\in (0,\,\,\,\pi )$ for which the system of linear equations

 $x+3y+7z=0$ $-x+4y+7z=0$ $\left( sin3\theta \right)x+\left( cos2\theta \right)y+2z=0$ has a non-trivial solution, is-
[JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) two

B) one

C) four

D)      three

• question_answer82) The curve amongst the family of curves represented by the differential equation, $({{x}^{2}}-{{y}^{2}})dx+2xy\,\,\,dy=0$ which passes through (1, 1) is [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) a circle with centre on the y-axis

B) an ellipse with major axis along the y-axis

C) a circle with centre on the x-axis

D) a hyperbola with transverse axis along the x-axis

• question_answer83) Let $f:\left( -1,\text{ }\,1 \right)\to R$ be a function defined by$f(x)=max\left\{ -|x|-\sqrt{1-{{x}^{2}}} \right\}$. If K be the set of all points at which f is not differentiable then K has exactly- [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) one element

B) three elements

C) five elements

D)                  two elements

• question_answer84) Consider the following three statements:

 P : 5 is a prime number Q : 7  is a factor of 192 R : L.C.M. of 5 and 7 is 35
Then the truth value of which one of the following statements is true? [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) $(P\wedge Q)\vee (\sim R)$

B) $P\vee (\sim Q\wedge R)$

C) $(\sim P)\wedge (\sim Q\wedge R)$

D)                  $\left( \sim P \right)\vee \left( Q\wedge R \right)$

• question_answer85) Let f be a differentiable function such that $f'(x)\,=\,7-\frac{3}{4}\,\frac{f(x)}{x},\,\,(x>0)$ and$f(1)\,\ne \,4$. Then $\underset{x\to {{0}^{+}}}{\mathop{\lim }}\,\,xf\left( \frac{1}{x} \right)\,$ [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) does not exist

B) exists and equals $\frac{4}{7}$

C) exists and equals 4

D) exists and equals 0

• question_answer86) If $\overrightarrow{\alpha }=(\lambda -2)\overrightarrow{a}+\overrightarrow{b}\,\,and\,\,\overrightarrow{\beta }=(4\lambda -2)\overrightarrow{a}+3\overrightarrow{b}$ be two given vectors where vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ are non-collinear. The value of $\lambda$ which vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ are collinear, is- [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) 4

B) 3

C) - 3

D)                  - 4

• question_answer87) The plane which bisects the line segment joining the points (-3, -3, 4) and (3, 7, 6) at right angles, passes through which one of the following points? [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) (2, 1, 3)

B) (4, -1, 2)

C) (4, 1, -2)

D)                  (-2, 3, 5)

• question_answer88) If the area of an equilateral triangle inscribed in the circle ${{x}^{2}}+{{y}^{2}}+10x+12y+c=0$ is $27\sqrt{3}$ sq units then c is equal to [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) 20

B) 25

C) -25

D)                  13

• question_answer89) If $\int{{{x}^{5}}.\,{{e}^{-}}^{4{{x}^{3}}}dx=\frac{1}{48}{{e}^{-4{{x}^{3}}}}\,f(x)+C}$, where C is a constant of integration, then f(x) is equal to- [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) $-2{{x}^{3}}-1$

B) $-\text{ }2{{x}^{3}}+1$

C) $4{{x}^{3}}+1$

D)                  $-\,4{{x}^{3}}-1$

• question_answer90) A helicopter is flying along the curve given by$y-{{x}^{3/2}}\,=7,\,\,(x\ge 0)\,$.   A soldier positioned at the point $\left( \frac{1}{2},\,\,7 \right)$wants to shoot down the helicopter when it is nearest to him. Then this nearest distance is: [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) $\frac{1}{6}\,\sqrt{\frac{7}{3}}$

B) $\frac{\sqrt{5}}{6}$

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

D)                  $\frac{1}{3}\,\sqrt{\frac{7}{3}}$

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