# Solved papers for JEE Main & Advanced JEE Main Online Paper (Held On 09-Jan-2019 Evening)

### done JEE Main Online Paper (Held On 09-Jan-2019 Evening)

• question_answer1) In a communication system operating at wavelength 800 nm, only one percent of source frequency is available as signal bandwidth. The number of channels accommodated for transmitting TV signals of band width 6 MHz are (Take velocity of light $c\text{ }=\text{ }3\text{ }\times \text{ }{{10}^{8}}\,m/s,\text{ }h=6.6\,\,\times \,\,{{10}^{-\,34}}J-s)$ [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) $3.75\text{ }\times \text{ }{{10}^{6}}$

B)               $4.87\text{ }\times \text{ }{{10}^{5}}$

C) $6.25\text{ }\times \text{ }{{10}^{5}}$

D)               $3.86\text{ }\times \text{ }{{10}^{6}}$

• question_answer2) The magnetic field associated with a light wave is given, at the origin, by $B\text{ }=\text{ }{{B}_{0}}$ $[sin(3.14\,\times \,\,{{10}^{7}})ct+sin(6.28\,\,\times \,{{10}^{6}})ct]$ If this light falls on a silver plate having a work function of 4.7 eV, what will be the maximum kinetic energy of the photo electrons? $\left( c=3\text{ }\times \text{ }{{10}^{8}}\text{ }m{{s}^{-\,1}},\text{ }h\,\,=\,\,6.6\,\,\times \,\,{{10}^{-34}}\,J-s \right)$ [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) $6.82\text{ }eV$

B)               $8.52\text{ }eV$

C) $12.5\text{ }eV$

D)               $7.55\text{ }eV$

• question_answer3)      The top of a water tank is open to air and its water level maintained. It is giving out $0.74\text{ }{{m}^{3}}$ water per minute through a circular opening of 2 cm radius is its wall. The depth of the centre of the opening from the level of water in the tank is close to: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) 6.0 m

B)                                       9.6 m

C) 2.9 m

D)               4.8 m

• question_answer4) A rod of mass 'M' and length '2L' is suspended at its middle by a wire. It exhibits torsional oscillations; If two masses each of 'm' are attached at distance 'L/2' from its centre on both sides, it reduces the oscillation frequency by $20%$ The value of ratio m/M is close to: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) 0.37

B) 0.57

C) 0.77

D) 0.17

• question_answer5) A parallel plate capacitor with square plates is filled with four dielectrics of dielectric constants ${{K}_{1}},\text{ }{{K}_{2}},\text{ }{{K}_{3}},\text{ }{{K}_{4}}$ arranged as shown in the figure. The effective dielectric constant K will be: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) $K\,\,=\,\,\frac{({{K}_{1}}+{{K}_{2}})({{K}_{2}}+{{K}_{4}})}{{{K}_{1}}+{{K}_{2}}+{{K}_{3}}+{{K}_{4}}}$

B) $K\,\,=\,\,\frac{({{K}_{1}}+{{K}_{2}})({{K}_{2}}+{{K}_{4}})}{2({{K}_{1}}+{{K}_{2}}+{{K}_{3}}+{{K}_{4}})}$

C) $K\,\,=\,\,\frac{({{K}_{1}}+{{K}_{2}})({{K}_{3}}+{{K}_{4}})}{({{K}_{1}}+{{K}_{2}}+{{K}_{3}}+{{K}_{4}})}$

D) $K\,\,=\,\,\frac{({{K}_{1}}+{{K}_{4}})({{K}_{2}}+{{K}_{3}})}{2({{K}_{1}}+{{K}_{2}}+{{K}_{3}}+{{K}_{4}})}$

E) None of these

• question_answer6) A carbon resistance has a following colour code. What is the value of the resistance? [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) $5.3\,M\,\Omega \,\,\pm \,\,5\,%$

B)                           $530\,k\,\Omega \,\,\pm \,\,5%$

C) $6.4\,k\,\Omega \,\,\pm \,10%$

D)               $6.4\,M\Omega \,\,\pm \,\,5%$

• question_answer7) A series AC circuit containing an inductor$\left( 20\text{ }mH \right)$, a capacitor $\left( 120\text{ }\mu F \right)$ and a resistor $\left( 60\text{ }\Omega \right)$ is driven by an AC source of$24\text{ }V/50\text{ }Hz$. The energy dissipated in the circuit in 60 s is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) $5.65\text{ }\times \text{ }{{10}^{2}}J$

B) $2.26\text{ }\times {{10}^{3}}J$

C) $5.17\text{ }\times \text{ }{{10}^{2}}\,J~$

D)               $3.39\text{ }\times \text{ }{{10}^{3}}\,J$

• question_answer8) A force acts on a 2 kg object so that its position is given as a function of time as$x=3{{t}^{2}}+5$. What is the work done by this force in first 5 seconds? [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) 950 J

B) 900 J

C) 875 J

D)               850 J

• question_answer9)             One of the two identical conducting wires of length L is bent in the form of a circular   loop and the other one into a circular coil. If the same current is passed in both, the ratio of the magnetic field at the central of the loop $({{B}_{L}}),\,\,\,\,i.e.\,\,\,\frac{{{B}_{L}}}{{{B}_{C}}}$will be: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

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

B) N

C) ${{N}^{2}}$

D)               $\frac{1}{{{N}^{2}}}$

• question_answer10) In a young's double slit experiment, the slits are placed 0.320 mm apart. Light of wavelength $\lambda \text{ }=\text{ }500\text{ }nm$ is incident on the slits. The total number of bright fringes that are observed in the angular range $-30{}^\circ \le \,\theta \le 30{}^\circ$ is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) 640

B) 641

C) 320

D) 321

• question_answer11) Two Carnot engines A and B are operated in series. The first one, A, receives heat at ${{T}_{1}}\left( =600\text{ }K \right)$ and rejects to a reservoir at temperature Ta. The second engine B receives heat rejected by the first engine and, in turn, rejects to a heat reservoir at${{T}_{3}}(=400\text{ }K)$. Calculate the temperature ${{T}_{2}}$ if the work outputs of the engines are equal: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) 500K

B) 300K

C) 600 K

D)               400 K

• question_answer12) At a given instant, say$t=0$, two radioactive substances A and B have equal activities. The ratio $\frac{{{R}_{B}}}{{{R}_{A}}}$ of their activities after time t itself decays with time t as ${{e}^{-3t}}$. If the half-life of A is ln2, the half-life of B is- [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) $\frac{In\,2}{4}$

B) $4\ln 2$

C) 2ln2

D)               $\frac{In\,2}{2}$

• question_answer13) Two plane mirrors are inclined to each other such that a ray of light incident on the first mirror $\left( {{M}_{1}} \right)$ and parallel to the second mirror $({{M}_{2}})$ is finally reflected from the second mirror $({{M}_{2}})$ parallel to the first mirror$\left( {{M}_{1}} \right)$. The angle between the two mirrors will be:   [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) $60{}^\circ$

B) $75{}^\circ$

C) $45{}^\circ$

D)               $90{}^\circ$

• question_answer14)             [a]   In the given circuit the internal resistance of the 18 V cell is negligible. If ${{R}_{1}}\,\,=\,\,400\,\Omega$,  ${{R}_{3}}=100\text{ }\Omega$ and ${{R}_{4}}=500\Omega$and the reading of an ideal voltmeter across ${{R}_{4}}$ is 5 V, then the value of ${{R}_{2}}$ will be: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) $550\text{ }\Omega$

B) $450\text{ }\Omega$

C) $230\,\,\Omega$

D)               $300\,\,\Omega$

• question_answer15) Charge is distributed within a sphere of radius R with a volume charge density$\rho (r)=\frac{A}{{{r}^{2}}}{{e}^{{}^{-2r}/{}_{a}}}$, where A and a are constants. If Q is the total charge of this charge distribution, the radius R is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) $\frac{a}{2}\,\log \,\left( 1-\frac{Q}{2\,\pi \,a\,A} \right)$

B) $\frac{a}{2}\,\log \,\left( 1-\frac{1}{\frac{Q}{2\,\pi \,a\,A}} \right)$

C) $a\,\,\log \,\,\left( \frac{1}{1-\frac{Q}{2\,\pi \,a\,A}} \right)$

D) $a\,\,\log \,\,\left( 1-\frac{Q}{2\,\pi \,a\,A} \right)$

• question_answer16) Expression for time in terms of G (universal gravitational constant), h (Planck constant) and c (speed of light) is proportional to: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) $\sqrt{\frac{Gh}{{{c}^{5}}}}$

B)               $\sqrt{\frac{h{{c}^{5}}}{G}}$

C) $\sqrt{\frac{Gh}{{{c}^{3}}}}$

D)               $\sqrt{\frac{{{c}^{3}}}{Gh}}$

• question_answer17) In a car race on straight road, car A takes a time t less than car B at the finish and passes finishing point with a speed 'v' more than that of car B. Both the cars start, from rest and travel with constant acceleration ${{a}_{1}}\text{ }and\text{ }{{a}_{2}}$ respectively. Then 'v' is equal to: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) $\sqrt{{{a}_{1}}\,{{a}_{2}}}\,\,t$

B) $\frac{2{{a}_{1}}{{a}_{2}}}{{{a}_{1}}+{{a}_{2}}}\,\,t$

C) $\frac{{{a}_{1}}+{{a}_{2}}}{2}\,\,t$

D) $\sqrt{2{{a}_{1}}{{a}_{2}}}\,\,t$

• question_answer18) A mass of 10 kg is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point, the rope deviated at an angle of $45{}^\circ$ at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is $\left( g=10\text{ }m{{s}^{-}}^{2} \right)$ [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) 100 N

B) 70 N

C) 140 N

D)               200 N

• question_answer19) The pitch and the number of divisions, on the circular scale, for a given screw gauge are 0.5 mm and 100 respectively. When the screw gauge is fully tightened without any object, the zero of its circular scale lies 3 divisions below the mean line. The readings of the main scale and the circular scale, for a thin sheet, are 5.5 mm and 48 respectively, the thickness of this sheet is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) 5.725 mm

B) 5.950 mm

C) 5.755 mm

D)               5.740 mm

• question_answer20) A power transmission line feeds input power at 2300 V to a step down transformer with its primary windings having 4000 turns. The output power is delivered at 230 V by the transformer. If the current in the primary of the transformer is 5A and its efficiency is $90%$, the output current would be: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) 45 A

B) 35 A

C) 25 A

D)               50 A

• question_answer21) A 15 g mass of nitrogen gas is enclosed in a vessel at a temperature$27{}^\circ C$. Amount of heat transferred to the gas, so that rms velocity of molecules is doubled, is about: [Take$\,R=8.3$ J/K mole] [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) 10 kJ

B)                                       0.9 KJ

C) 14 kJ

D)               6 kJ

• question_answer22) The position co-ordinates of a particle moving in a 3-D coordinate system is given by             $~x=a\text{ }cos\omega t$             $y=a\text{ }sin\omega t$       and $z=a\omega t$ The speed of the particle is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) $a\omega$

B)                           $\sqrt{3}\,a\omega$

C) $\sqrt{2}\,a\omega$

D)               $2\,a\omega$

• question_answer23) A particle is executing simple harmonic motion (SHM) of amplitude A, along the x-axis, about$x=0$. When its potential Energy (PE) equals kinetic energy (KE), the position of the particle will be: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

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

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

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

D)               A

• question_answer24) The energy required to take a satellite to a height 'h' above Earth surface (radius of Earth $=6.4\times {{10}^{3}}km$) is ${{E}_{1}}$ and kinetic energy required for the satellite to be in a circular orbit at this height is ${{E}_{2}}$. The value of h for which ${{E}_{1}}$ and ${{E}_{2}}$ are equal, is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) $3.2\times {{10}^{3}}\text{ }km$

B) $1.6\times {{10}^{3}}km$

C) $1.28\times {{10}^{4}}km$

D) $6.4\times {{10}^{3}}km$

• question_answer25) A musician using an open flute of length 50 cm produces second harmonic sound waves. A person runs towards the musician from another end of a hall at n speed of 10 km/h. If the wave speed is 330 m/s, the frequency heard by the running person shall be close to: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) 753 Hz

B) 666 Hz

C) 500 Hz

D)               333 Hz

• question_answer26) A particle having the same charge as of electron moves in a circular path of radius 0.5 cm under the influence of a magnetic field of 0.5 T. If an electric field of 100 V/m makes it to move in a straight path, then the mass of the particle is (Given charge of electron $=1.6\,\times \,{{10}^{-19}}C$) [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) $1.6\times {{10}^{-19}}kg$

B) $1.6\times {{10}^{-27}}\text{ }kg$

C) $9.1\times {{10}^{-}}^{31}kg$

D)               $2.0\times {{10}^{-}}^{24}kg$

• question_answer27) A rod of length 50 cm is pivoted at one end. It is raised such that if makes an angle of $30{}^\circ$from the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in rad ${{s}^{-1}}$) will be ($g=10\text{ }m{{s}^{-2}}$) [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) $\sqrt{\frac{30}{2}}$

B) $\frac{\sqrt{20}}{3}$

C) $\frac{\sqrt{30}}{2}$

D)               $\sqrt{30}$

• question_answer28) The energy associated with electric field is (${{U}_{E}}$) and with magnetic field is (${{U}_{B}}$) for an electromagnetic wave in free space. Then: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) ${{U}_{E}}<{{U}_{B}}$

B) ${{U}_{E}}=\,\frac{{{U}_{B}}}{2}$

C) ${{U}_{E}}={{U}_{B}}$

D)               ${{U}_{E}}>{{U}_{B}}$

• question_answer29) Two point charges ${{q}_{1}}\,(\sqrt{10}\,\mu C)$and ${{q}_{2}}(-25\,\,\mu C)$ are placed on the x-axis at $x=1\,m$ and $x=4\,m$respectively. The electric field (in V/m) at a point $y=3$m on y-axis is, [take$\frac{1}{4\pi {{\in }_{0}}}\,\,=\,\,9\,\times {{10}^{9}}\,N{{m}^{2}}{{C}^{-}}^{2}$] [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) $(-81\widehat{i}\,\,+\,\,81\widehat{j})\,\,\times \,{{10}^{2}}$

B) $(81\widehat{i}-81\widehat{j})\times {{10}^{2}}$

C) $(63\widehat{i}\,\,-\,\,27\widehat{j})\,\,\times \,{{10}^{2}}$

D) $(-63\widehat{i}+27\widehat{j})\times {{10}^{2}}$

• question_answer30) Ge and Si diodes start conducting at 0.3 V and 0.7 V respectively. In the following figure if Ge diode connection are reversed, the value of ${{V}_{0}}$ changes by: (assume that the Ge diode has large breakdown voltage)   [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) 0.4 V

B)                                       0.6 V

C) 0.8 V

D)               0.2 V

• question_answer31) Which of the following combination of statements is true regarding the interpretation of the atomic orbitals?

 [A] An electron in an orbital of high angular momentum stays away from the nucleus than an electron in the orbital of lower angular momentum. [B] For a given value of the principal quantum number, the size of the orbit is inversely proportional to the azimuthal quantum number. [C] According to wave mechanics, the ground state angular momentum is equal to$\frac{h}{2\pi }$. [D] The plot of $\psi \,Vs\,\,r$for various azimuthal quantum numbers, shows peak shifting towards higher r value.
[JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) [B], [C]

B)                           [A], [D]

C) [A], [B]

D)               [A], [C]

• question_answer32) A solution containing 62 g ethylene glycol in 250 g water is cooled to$-10{}^\circ C$. If ${{K}_{f}}$ for water is $1.86\text{ }K\text{ }kg\text{ }mo{{l}^{-1}}$, the amount of water (in g) separated as ice is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) 32

B)   16

C) 64

D)   48

• question_answer33) For coagulation of arsenious sulphide sol which one of the following salt solution will be most effective? [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) $AlC{{l}_{3}}$

B) $NaCl$

C) $N{{a}_{3}}P{{O}_{4}}~~~~~~~~$

D)               $BaC{{l}_{2}}$

• question_answer34)             In which of the following processes, the bond order has increased and paramagnetic character has changed to diamagnetic? [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) $NO\,\,\to \,\,N{{O}^{+}}$

B)               ${{O}_{2}}\to {{O}_{{{2}^{+}}}}$

C) ${{N}_{2}}\,\,\to \,\,{{N}_{{{2}^{+}}}}$

D)               ${{O}_{2}}\,\,\to \,\,{{O}_{{{2}^{2-}}}}$

• question_answer35) The complex that has highest crystal field splitting energy $(\Delta )$, is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) ${{K}_{3}}\left[ Co{{\left( CN \right)}_{6}} \right]$

B) ${{K}_{2}}\left[ CoC{{l}_{4}} \right]$

C) $\left[ Co{{\left( N{{H}_{3}} \right)}_{5}}Cl \right]\text{ }C{{l}_{2}}$

D) $\left[ Co{{\left( N{{H}_{3}} \right)}_{5}}\left( {{H}_{2}}O \right)C{{l}_{3}} \right]$

• question_answer36) For the following reaction, the mass of water produced from 4.45 g of ${{C}_{57}}{{H}_{110}}{{O}_{6}}$ is: $2{{C}_{57}}{{H}_{110}}{{O}_{6}}(s)+163{{O}_{2}}(g)\to 114C{{O}_{2}}(g)+110{{H}_{2}}O(\ell )$ [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) 445 g

B) 490 g

C) 495g

D) 890 g

• question_answer37) If the standard electrode potential for a cell is 2 V at 300 K, the equilibrium constant (K) for the reaction $Zn(s)+C{{u}^{2+}}(aq)\,\,\,\rightleftharpoons \,\,Z{{n}^{2+}}(aq)+Cu\,(s)$ At 300 K is approximately $\left( R=8J{{K}^{-}}^{1}mo{{l}^{-1}},\text{ }F\,\,=\,\,96000\text{ }C\text{ }mo{{l}^{-1}} \right)$ [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) ${{e}^{160}}$

B) ${{e}^{-160}}$

C) ${{e}^{-80}}$

D)               ${{e}^{320}}$

• question_answer38) The entropy change associated with the conversion of 1 kg of ice at 273 K to water vapours at 383 K is: (Specific heat of water liquid and water vapour are $4.2\text{ }kJ\text{ }{{K}^{-1}}\,k{{g}^{-}}^{1}$ and $2.0\text{ }kJ\text{ }{{K}^{-1}}\,k{{g}^{-}}^{1}$heat of liquid fusion and vapourisation of water are $334\text{ }kJ\text{ }k{{g}^{-1}}$ and $2491\text{ }kJ\text{ }k{{g}^{-1}}$, respectively), $(log\text{ }273\,\,\,=\,\,2.436$, $log\text{ }373=2.572,\text{ }log\text{ }383\,\,\text{=}\,\,2.583)$ [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) $2.64\text{ }kJ\text{ }k{{g}^{-1}}\text{ }{{K}^{-1}}$

B) $9.26\text{ }kJ\text{ }k{{g}^{-1}}\text{ }{{K}^{-1}}$

C) $7.90\text{ }kJ\text{ }k{{g}^{-1}}\text{ }{{K}^{-1}}~$

D)             $8.49\text{ }kJ\text{ }k{{g}^{-1}}\text{ }{{K}^{-1}}$

• question_answer39) For the reaction, $2A\,\,+\,\,B\,\,\to$ products, when the concentrations of A and B both were doubled, the rate of the reaction increased from $0.3\text{ }mol\text{ }{{L}^{-1}}{{s}^{-}}^{1}$ to$2.4\text{ }mol\text{ }{{L}^{-1}}{{s}^{-}}^{1}$. When the concentration of A alone is doubled, the rate increased from $0.3\text{ }mol\text{ }{{L}^{-}}^{1}\,{{s}^{-}}^{1}$ to$0.6\text{ }mol\,\,L{{\,}^{-}}^{1}s{{\,}^{-1}}$. Which one of the following statements is correct? [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) Order of the reaction with respect to A is 2.

B) Total order of the reaction is 4.

C) Order of the reaction with respect to B is 1.

D) Order of the reaction with respect to B is 2.

• question_answer40) The major product obtained in the following reaction is:   [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

B)

C)

D)

• question_answer41) The increasing basicity order of the following compounds is:

 [a] [b] [c] [d]
[JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) [a] <[b] < [c] < [d]

B) [d] < [c] < [b] < [a]

C) [d] < [c] < [a] < [b]

D) [a] < [b] < [d] < [c]

• question_answer42) Homoleptic octahedral complexes of a metal ion ${{M}^{3+}}$ with three monodentate ligands ${{L}_{1}},\text{ }{{L}_{2}}and\text{ }{{L}_{3}}$ absorb wavelengths in the region of green, blue and red respectively. The increasing order of the ligand strength is- [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) ${{L}_{3}}<{{L}_{2}}<{{L}_{1}}$

B) ${{L}_{3}}<{{L}_{1}}<{{L}_{2}}$

C) ${{L}_{1}}<{{L}_{2}}<{{L}_{3}}$

D) ${{L}_{2}}<{{L}_{1}}<{{L}_{3}}$

• question_answer43) When the first electron gain enthalpy $\left( {{\Delta }_{eg}}H \right)$ of oxygen is $-141\text{ }kJ/mol$, Its second electron gain enthalpy is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) a positive value

B) a more negative value than the first

C) almost the same as that of the first

D) negative, but less negative than the first

• question_answer44) Consider the following reversible chemical reactions:

 ${{A}_{2}}(g)\,\,+\,\,{{B}_{2}}\,(g)\,\,\,\,\,2AB\,(g)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,.......\,(1)$ $6AB\,(g)\,\,\,\,\,3{{A}_{2}}\,(g)\,\,+3{{B}_{2}}\,(g)\,\,\,\,\,\,\,\,\,\,\,\,\,.......\,\,(2)$
The relation between ${{K}_{1}}\,\,\,and\,\,\,{{K}_{2}}$ is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) ${{K}_{2}}={{K}_{1}}^{-3}$

B) ${{K}_{1}}{{K}_{2}}\,\,=\,\,\frac{1}{3}$

C) ${{K}_{1}}{{K}_{2}}\,\,=\,\,3$

D)               ${{K}_{2}}={{K}_{1}}^{3}$

• question_answer45) Good reducing nature of ${{H}_{3}}P{{O}_{2}}$ attributed to the presence of: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) One $P-H$ bond

B)   Two $P-OH$ bonds

C) One $P-OH$ bond

D) Two $P-H$bonds

• question_answer46) The tests performed on compound X and their inferences are:

 Test Inference [A] 2, 4-DNP test Coloured Precipitate [B] Iodoform test Yellow Precipitate [C] Azo-dye test No dye precipitate
Compound ?X? is- [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

B)

C)

D)

• question_answer47) The pH rain water, is approximately: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) 5.6

B) 6.5

C) 7.5

D)               7.0

• question_answer48) Which of the following compounds is not aromatic? [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

B)

C)

D)

• question_answer49) The correct statement regarding the given Ellingham diagram is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) Coke cannot be used for the extraction of Cu from $C{{u}_{2}}O$

B) At$500{}^\circ C$, coke can be used for the extraction of Zn from $ZnO$

C) At$1400{}^\circ C$, Al can be used for the extraction of Zn from $ZnO$

D) At $800{}^\circ C$ Cu can be used for the extraction of Zn from $ZnO$

• question_answer50) The temporary hardness of water is due to: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) $N{{a}_{2}}S{{O}_{4}}$

B) $CaC{{l}_{2}}$

C) $NaCI$

D)               $Ca{{\left( HC{{O}_{3}} \right)}_{2}}_{~}~~~~~~~~~$

• question_answer51) The major product of the following reaction is:   [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

B)

C)

D)

• question_answer52) The products formed in the reaction of cumene  with ${{O}_{2}}$ followed by treatment with dil. HCl are: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

B)

C)

D)

• question_answer53) At$100{}^\circ C$, copper (Cu) has FCC unit cell structure with cell edge length of x $\overset{o}{\mathop{A}}\,$. What is the approximate density of Cu (in$g\text{ }c{{m}^{-}}^{3}$) at this temperature? [Atomic Mass of $Cu\,\,=\,\,63.55\,u$] [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) $\frac{422}{{{x}^{3}}}$

B) $\frac{205}{{{x}^{3}}}$

C) $\frac{211}{{{x}^{3}}}$

D) $\frac{105}{{{x}^{3}}}$

• question_answer54) The transition element that has lowest enthalpy of atomization, is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) Zn

B) Fe

C) Cu

D)               V

• question_answer55) Which of the following conditions in drinking water causes methemoglobinemia? [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) > 50 ppm of nitrate

B) > 50 ppm of chloride

C) > 50 ppm of lead

D) > 100 ppm of sulphate

• question_answer56) The major product formed in the following reaction is:   [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

B)

C)

D)

• question_answer57) The correct match between Item-I and Item-II is:

 Item-I Item-II [A] Benzaldehyde (P) Mobile phase [B] Alumina (Q) Adorbent [C] Acetonitrile (R) Adsorbate
[JEE Main Online Paper (Held On 09-Jan-2019 Evening]

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

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

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

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

• question_answer58) The metal that forms nitride by reacting directly with N2 of air, is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) Li

B) Cs

C) K

D)               Rb

• question_answer59)             The major product of the following reaction is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A)

B)

C)

D)

• question_answer60) The correct sequence of amino acids present in the tripetide given below is:   [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) Val - Ser - Thr

B) Thr - Ser - Vnl

C) Thr - Ser - Leu

D)               Leu - Ser - Thr

• question_answer61) Let ${{z}_{0}}$ be a root of the quadratic equation, ${{x}^{2}}+x+1=0$. If $z=3+6i\,{{z}_{0}}^{81}-\,3i\,{{z}_{0}}^{93}$, then arg z is equal to: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) $\frac{\pi }{6}\,$

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

C)               0

D)               $\frac{\pi }{4}\,$

• question_answer62) Let f: $\left[ 0,\text{ }1 \right]\,\,\to \,\,R$ be such that$f\left( xy \right)=f\left( x \right).f\left( y \right)$, for all $x,\,\,y\,\,\in \,\,\,[0,\,\,\,1]$ and$f(0)\,\,\ne \,\,0$. If $y\,\,=\,\,y(x)$satisfies the differential equation, $\frac{dy}{dx}\,\,=\,\,f(x)\,$with $y\left( 0 \right)\,\,=\,\,1$, then $y\left( \frac{1}{4} \right)+y\left( \frac{3}{4} \right)$is equal to: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) 2

B)                           3

C)               5

D)               4

• question_answer63) The coefficient of ${{t}^{4}}$ in the expansion of ${{\left( \frac{1-{{t}^{6}}}{1-t} \right)}^{3}}$ [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) 15

B)               10

C)               14

D)               12

• question_answer64) Let $\overrightarrow{a}=\widehat{i}+\widehat{j}\,\,+\sqrt{2}\widehat{k},\,\,\,\overrightarrow{b}={{b}_{1}}\widehat{i}\,\,+\,{{b}_{2}}\widehat{j}\,\,+\,\,\sqrt{2}\widehat{k}$and $\overrightarrow{c}=5\widehat{i}\,\,+\,\,\widehat{j}\,\,+\,\,\sqrt{2}\widehat{k}$ be three vectors such that the projection vector of $\overrightarrow{b}$ on $\overrightarrow{a}$ is $\overrightarrow{a}$. If $\overrightarrow{a}\,\,+\,\,\overrightarrow{b}$ is perpendicular to $\overrightarrow{c}$, then $\left| \overrightarrow{b} \right|$ is equal to: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) 4

B)               $\sqrt{22}$

C)               6

D)               $\sqrt{32}$

• question_answer65) If $f\left( x \right)\,\,=\,\int{\frac{5{{x}^{8}}+7{{x}^{6}}}{{{({{x}^{2}}+1+2{{x}^{7}})}^{2}}}}\,\,dx\,,\,\,\,(x\,\,\ge \,\,0)\,$, and $f\left( 0 \right)\,\,\,=\,\,0$, then the value of f(1) is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

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

B)               $-\frac{1}{4}$

C)               $\frac{1}{4}$

D)               $\frac{1}{2}$

• question_answer66) If $x\,\,=\,\,3\text{ }tan\text{ }t$ and $y\,\,=\,\,3\text{ }sec\text{ }t$, then the value of $\frac{{{d}^{2}}y}{d{{x}^{2}}}$ at $t=\frac{\pi }{4}$is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

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

B)               $\frac{1}{6}$

C)               $\frac{1}{6\sqrt{2}}$

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

• question_answer67) The sum of the following series $1+6+\frac{9({{1}^{2}}+{{2}^{2}}+{{3}^{2}})}{7}\,\,+\,\,\frac{12({{1}^{2}}+{{2}^{2}}+{{3}^{2}}+{{4}^{2}})}{9}+$ $\frac{15({{1}^{2}}+{{2}^{2}}+......\,\,+{{5}^{2}})}{11}\,+\,.....$up to 15 terms, is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) 7830

B)               7520

C)               7820

D)               7510

• question_answer68) Let a, b and c be the${{7}^{th}}$, ${{11}^{th}}$ and ${{13}^{th}}$ terms respectively of a non-constant A.P. If these are also the three consecutive terms of a G.P., then $\frac{a}{c}$ is equal to: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) $\frac{7}{13}$

B)               2

C)               4

D)               $\frac{1}{2}$

• question_answer69) A hyperbola has its centre at the origin, passes through the point $\left( 4,\text{ }2 \right)$ and has transverse axis of length 4 along the x-axis. Then the eccentricity of the hyperbola is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

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

B)               $\frac{2}{\sqrt{3}}$

C)               2

D)               $\sqrt{3}$

• question_answer70) Let the equations of two sides of a triangle be $3x-2y+6=0$ and$4x+5y-20=0$. If the orthocentre of this triangle is at $\left( 1,\text{ }1 \right)$, then the equation of its third side is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) $26x\,-\,122y\,-\,1675\,=\,0$

B)               $26x\,+61y\,+\,1675\,=\,0$

C)               $122y\,-\,\,26x\,-\,1675\,=\,0$

D)               $122y\,+\,\,26x\,+\,1675\,=\,0$

• question_answer71) A data consists of n observations: ${{x}_{1}},\,\,{{x}_{2}},\,\,\,....,\,\,{{x}_{n}},$. If $\sum\limits_{i\,=\,1}^{n}{{{({{x}_{i}}+1)}^{2}}\,\,=\,\,9n}$ and $\sum\limits_{i\,=\,1}^{n}{{{({{x}_{i}}-1)}^{2}}=5n}$then the standard deviation of this data is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) 2

B)               4

C)               3

D)               1

• question_answer72) If $0\,\,\le \,\,x\,<\,\,\frac{\pi }{2}$ , then the number of values of x for which $\sin \,\,x-sin\text{ 2}x+sin\text{ }3x=0$ is [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) 2

B)               4

C)               3

D)               1

• question_answer73) If the tines $x=ay+b,$$z=cy+d$and $x=a'z\,\,+b'$, $y\,\,=\,\,c'z\,\,+d'$ are perpendicular then: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) $cc'+a+a'=0$

B)               $aa'+c+c'=0$

C)               $bb'+cc'+1=0$

D)               $ab'+bc'+1=0$

• question_answer74) The equation of the plane containing the straight line $\frac{x}{2}\,\,=\,\,\frac{y}{3}\,\,=\,\,\frac{z}{4}$and perpendicular to the plane containing the straight lines $\frac{x}{3}=\frac{y}{4}=\frac{z}{2}\,\,and\,\,\frac{x}{4}=\frac{y}{2}=\frac{z}{3}$ [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) $3x+2y-3z\,\,=\,\,0$

B)               $x+2y-2z\,\,=\,\,0$

C)               $x-2y+z=0$

D)               $~5x+2y-4z=0$

• question_answer75) Let f be a differentiable function from, R to R such that$\left| f(x)-f(y) \right|\,\,\le \,\,2\,\,{{\left| x-y \right|}^{3/2}}$, for all$x,\,\,y\,\,\in \,\,\,R.\,$. If $f\left( 0 \right)=1$ then $\int\limits_{0}^{1}{{{f}^{2}}\left( x \right)dx}$ is equal to: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) 2

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

C)               0

D)               1

• question_answer76) Let S be the set of all triangles in the xy-plane, each having one vertex at the origin and the other two vertices lie on coordinate axes with integral coordinates. If each triangle in S has area 50 sq. units, then the number of elements in the set S is:

A) 32

B) 36

C) 9

D) 18

• question_answer77) The area of the region $A=\{(x,\,\,y):0\,\,\le \,\,y\,\,\le \,\,x|x|+1\,\,and\,\,-\,1\le x\le 1\}$in sq. units, is : [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

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

B)               $\frac{1}{3}$

C)               $\frac{2}{3}$

D)               2

• question_answer78) If the circles ${{x}^{2}}+{{y}^{2}}-16x-20y+164={{r}^{2}}$and ${{\left( x-4 \right)}^{2}}+{{\left( y-7 \right)}^{2}}=36$ intersect at two distinct points, then [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) $r\,\,>\,\,11$

B)               $r\,\,=\,\,11$

C)               $1\,\,<\,\,r\,\,<\,\,11$

D)               $0\,\,<\,\,r\,\,<\,\,1$

• question_answer79) An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) $\frac{27}{49}$

B)               $\frac{26}{49}$

C)               $\frac{32}{49}$

D)               $\frac{21}{49}$

• question_answer80) If then A is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) invertible only if $t=n$

B)               invertible for all $t\,\,\in \,\,R$

C)               invertible only if $t=\frac{\pi }{2}$

D)               not invertible for any $t\text{ }\in \text{ }R$

• question_answer81) The number of natural numbers less than 7,000 which can be formed by using the digits 0, 1, 3, 7, 9 (repetition of digits allowed) is equal to: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) 372

B)               375

C)               250

D)               374

• question_answer82) If $\int\limits_{0}^{\pi /3}{\frac{\tan \,\theta }{\sqrt{2\,k\,\,\sec \,\theta }}}\,d\,\theta \,\,=\,\,1-\frac{1}{\sqrt{2}}\,,\text{ }\left( k\,\,>\,\,0 \right)$, then the value of k is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) 2

B)               1

C)               4

D)               $\frac{1}{2}$

• question_answer83)               The number of all possible positive integral values of a for which the roots of the quadratic equation, $6{{x}^{2}}-11x+\alpha =0$ are rational numbers is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) 4

B)               2

C)               5

D)               3

• question_answer84) The logical statement $[\tilde{\ }\left( \tilde{\ }p\vee q \right)\vee (p\wedge r)]\,\,\wedge \,(\sim q\wedge r)\,$ is equivalent to: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) $(\sim p\wedge \sim q)\wedge r$

B)               $(p\wedge \sim q)\vee r$

C)               $\left( p\wedge r \right)\,\,\wedge \tilde{\ }\,q$

D)               $\tilde{\ }p\wedge r$

• question_answer85) If the system of linear equations

 $x-4y+7z=g$ $3y-5z=h$ $-2x+5y-9z=k$
is consistent, then: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) $g+2h+k=0$

B)               $g+h+2k=0$

C)               $g+h+k=0$

D)               $2g+h+k=0$

• question_answer86) If both the roots of the quadratic equation ${{x}^{2}}-mx+4=0$ are real and distinct and they lie in the interval $\left[ 1,\text{ }5 \right]$, then m lies in the interval: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) (4, 5)

B)               ($-5,\,\,-4$)

C)               (3, 4)

D)               (5, 6)

• question_answer87) If $x=si{{n}^{-1}}\left( sin\text{ }10 \right)$ and $y=co{{s}^{-1}}\,\,cos10)$, then $y-x$ is equal to: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) 0

B)               $7\,\pi$

C)               $\pi$

D)               10

• question_answer88) Let $A=\{x\text{ }\in \text{ }R:x$ is not a positive integer}. Define a function $f:A\to R$ as $f(x)\,\,=\,\,\frac{2x}{x-1}$, then f is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) not injective

B)               surjective but not injective

C)               injective but not surjective

D)               neither injective nor surjective

• question_answer89) For each$x\text{ }\in \text{ }R$, let [x] be the greatest integer less than or equal to x. Then$\underset{x\to {{0}^{-}}}{\mathop{\lim }}\,\,\frac{x([x]+\left| x \right|)\,sin\,[x]}{\left| x \right|}$ [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) 1

B)               0

C)               $sin\text{ }1$

D)               $-sin\text{ }1$

• question_answer90) Let A($4,\text{ }-4$) and B(9, 6) be points on the parabola, ${{y}^{2}}=4x$. Let C be chosen on the arc AOB of the parabola, where 0 is the origin, such that the area of $\Delta \,ACB$ is maximum. Then, the area (in sq. units) of $\Delta \,ACB$, is: [JEE Main Online Paper (Held On 09-Jan-2019 Evening]

A) 32

B)               $31\frac{3}{4}$

C)               $30\frac{1}{2}$

D)               $31\frac{1}{4}$

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