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 \[c\text{ }=\text{ }3\text{ }\times \text{ }{{10}^{8}}\,m/s,\text{ }h=6.6\,\,\times \,\,{{10}^{-\,34}}J-s)\]

    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) \[3.86\text{ }\times \text{ }{{10}^{6}}\]

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  • 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? \[\left( c=3\text{ }\times \text{ }{{10}^{8}}\text{ }m{{s}^{-\,1}},\text{ }h\,\,=\,\,6.6\,\,\times \,\,{{10}^{-34}}\,J-s \right)\]

    A) \[6.82\text{ }eV\]

    B) \[8.52\text{ }eV\]

    C) \[12.5\text{ }eV\]

    D) \[7.55\text{ }eV\]

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  • 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:

    A) 6.0 m

    B) 9.6 m

    C) 2.9 m

    D) 4.8 m

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  • 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:

    A) 0.37     

    B) 0.57

    C) 0.77                 

    D) 0.17

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  • 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:

    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

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  • question_answer6) A carbon resistance has a following colour code. What is the value of the resistance?

    A) \[5.3\,M\,\Omega \,\,\pm \,\,5\,%\]

    B) \[530\,k\,\Omega \,\,\pm \,\,5%\]

    C) \[6.4\,k\,\Omega \,\,\pm \,10%\]

    D) \[6.4\,M\Omega \,\,\pm \,\,5%\]

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  • 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:

    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) \[3.39\text{ }\times \text{ }{{10}^{3}}\,J\]

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  • 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?

    A) 950 J

    B) 900 J

    C) 875 J

    D) 850 J

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  • 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:

    A) \[\frac{1}{N}\]

    B) N

    C) \[{{N}^{2}}\]

    D) \[\frac{1}{{{N}^{2}}}\]

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  • 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:

    A) 640                                          

    B) 641

    C) 320                  

    D) 321

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  • 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:

    A) 500K

    B) 300K

    C) 600 K

    D) 400 K

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  • 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-

    A) \[\frac{In\,2}{4}\]

    B) \[4\ln 2\]

    C) 2ln2

    D) \[\frac{In\,2}{2}\]

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  • 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:

    A) \[60{}^\circ \]

    B) \[75{}^\circ \]

    C) \[45{}^\circ \]

    D) \[90{}^\circ \]

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  • 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:

    A) \[550\text{ }\Omega \]

    B) \[450\text{ }\Omega \]

    C) \[230\,\,\Omega \]

    D) \[300\,\,\Omega \]

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  • 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:

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

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  • question_answer16) Expression for time in terms of G (universal gravitational constant), h (Planck constant) and c (speed of light) is proportional to:

    A) \[\sqrt{\frac{Gh}{{{c}^{5}}}}\]

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

    C) \[\sqrt{\frac{Gh}{{{c}^{3}}}}\]

    D) \[\sqrt{\frac{{{c}^{3}}}{Gh}}\]

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  • 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:

    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) \[\sqrt{2{{a}_{1}}{{a}_{2}}}\,\,t\]

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  • 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 \[\left( g=10\text{ }m{{s}^{-}}^{2} \right)\]

    A) 100 N

    B) 70 N

    C) 140 N

    D) 200 N

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  • 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:

    A) 5.725 mm

    B) 5.950 mm

    C) 5.755 mm

    D) 5.740 mm

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  • 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:

    A) 45 A

    B) 35 A

    C) 25 A

    D) 50 A

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  • 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]

    A) 10 kJ

    B) 0.9 KJ

    C) 14 kJ

    D) 6 kJ

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  • 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:

    A) \[a\omega \]

    B) \[\sqrt{3}\,a\omega \]

    C) \[\sqrt{2}\,a\omega \]

    D) \[2\,a\omega \]

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  • 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:

    A) \[\frac{A}{2\sqrt{2}}\]

    B) \[\frac{A}{\sqrt{2}}\]

    C) \[\frac{A}{2}\]

    D) A

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  • 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:

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

    B) \[1.6\times {{10}^{3}}km\]

    C) \[1.28\times {{10}^{4}}km\]

    D) \[6.4\times {{10}^{3}}km\]

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  • 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:

    A) 753 Hz

    B) 666 Hz

    C) 500 Hz

    D) 333 Hz

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  • 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 \[=1.6\,\times \,{{10}^{-19}}C\])

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

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

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

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

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  • 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 (\[g=10\text{ }m{{s}^{-2}}\])

    A) \[\sqrt{\frac{30}{2}}\]

    B) \[\frac{\sqrt{20}}{3}\]

    C) \[\frac{\sqrt{30}}{2}\]

    D) \[\sqrt{30}\]

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  • 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:

    A) \[{{U}_{E}}<{{U}_{B}}\]

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

    C) \[{{U}_{E}}={{U}_{B}}\]

    D) \[{{U}_{E}}>{{U}_{B}}\]

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  • 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\[\frac{1}{4\pi {{\in }_{0}}}\,\,=\,\,9\,\times {{10}^{9}}\,N{{m}^{2}}{{C}^{-}}^{2}\]]

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

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  • 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)

    A) 0.4 V

    B) 0.6 V

    C) 0.8 V

    D) 0.2 V

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  • 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.

    A) [B], [C]

    B) [A], [D]

    C) [A], [B]

    D) [A], [C]

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  • 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:

    A) 32

    B) 16

    C) 64

    D) 48

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  • question_answer33) For coagulation of arsenious sulphide sol which one of the following salt solution will be most effective?

    A) \[AlC{{l}_{3}}\]

    B) \[NaCl\]

    C) \[N{{a}_{3}}P{{O}_{4}}~~~~~~~~\]

    D) \[BaC{{l}_{2}}\]

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  • question_answer34) In which of the following processes, the bond order has increased and paramagnetic character has changed to diamagnetic?

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

    B) \[{{O}_{2}}\to {{O}_{{{2}^{+}}}}\]

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

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

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  • question_answer35) The complex that has highest crystal field splitting energy \[(\Delta )\], is:

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

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  • question_answer36) For the following reaction, the mass of water produced from 4.45 g of \[{{C}_{57}}{{H}_{110}}{{O}_{6}}\] is: \[2{{C}_{57}}{{H}_{110}}{{O}_{6}}(s)+163{{O}_{2}}(g)\to 114C{{O}_{2}}(g)+110{{H}_{2}}O(\ell )\]

    A) 445 g                                       

    B) 490 g

    C) 495g                

    D) 890 g

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  • 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 \[\left( R=8J{{K}^{-}}^{1}mo{{l}^{-1}},\text{ }F\,\,=\,\,96000\text{ }C\text{ }mo{{l}^{-1}} \right)\]

    A) \[{{e}^{160}}\]

    B) \[{{e}^{-160}}\]

    C) \[{{e}^{-80}}\]

    D) \[{{e}^{320}}\]

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  • 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), \[(log\text{ }273\,\,\,=\,\,2.436\], \[log\text{ }373=2.572,\text{ }log\text{ }383\,\,\text{=}\,\,2.583)\]

    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) \[8.49\text{ }kJ\text{ }k{{g}^{-1}}\text{ }{{K}^{-1}}\]

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  • 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?

    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.

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  • question_answer40) The major product obtained in the following reaction is:

    A)

    B)

    C)

    D)

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

    [a]
    [b]
    [c]
    [d]

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

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

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

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

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  • 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-

    A) \[{{L}_{3}}<{{L}_{2}}<{{L}_{1}}\]

    B) \[{{L}_{3}}<{{L}_{1}}<{{L}_{2}}\]

    C) \[{{L}_{1}}<{{L}_{2}}<{{L}_{3}}\]

    D) \[{{L}_{2}}<{{L}_{1}}<{{L}_{3}}\]

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  • 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:

    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

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  • 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:

    A) \[{{K}_{2}}={{K}_{1}}^{-3}\]

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

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

    D) \[{{K}_{2}}={{K}_{1}}^{3}\]

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  • question_answer45) Good reducing nature of \[{{H}_{3}}P{{O}_{2}}\] attributed to the presence of:

    A) One \[P-H\] bond

    B) Two \[P-OH\] bonds

    C) One \[P-OH\] bond

    D) Two \[P-H\]bonds

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  • 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-

    A)

    B)

    C)

    D)

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  • question_answer47) The pH rain water, is approximately:

    A) 5.6

    B) 6.5

    C) 7.5

    D) 7.0

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  • question_answer48) Which of the following compounds is not aromatic?

    A)

    B)

    C)

    D)

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  • question_answer49) The correct statement regarding the given Ellingham diagram is:

    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 \[ZnO\]

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  • question_answer50) The temporary hardness of water is due to:

    A) \[N{{a}_{2}}S{{O}_{4}}\]

    B) \[CaC{{l}_{2}}\]

    C) \[NaCI\]

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

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  • question_answer51) The major product of the following reaction is:

    A)

    B)

    C)

    D)

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  • question_answer52) The products formed in the reaction of cumene with \[{{O}_{2}}\] followed by treatment with dil. HCl are:

    A)

    B)

    C)

    D)

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  • 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 \[Cu\,\,=\,\,63.55\,u\]]

    A) \[\frac{422}{{{x}^{3}}}\]                   

    B) \[\frac{205}{{{x}^{3}}}\]

    C) \[\frac{211}{{{x}^{3}}}\]                               

    D) \[\frac{105}{{{x}^{3}}}\]

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  • question_answer54) The transition element that has lowest enthalpy of atomization, is:

    A) Zn

    B) Fe

    C) Cu

    D) V

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  • question_answer55) Which of the following conditions in drinking water causes methemoglobinemia?

    A) > 50 ppm of nitrate

    B) > 50 ppm of chloride

    C) > 50 ppm of lead

    D) > 100 ppm of sulphate

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  • question_answer56) The major product formed in the following reaction is:

    A)

    B)

    C)

    D)

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  • 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

    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)

    View Answer play_arrow
  • question_answer58) The metal that forms nitride by reacting directly with N2 of air, is:

    A) Li

    B) Cs

    C) K

    D) Rb

    View Answer play_arrow
  • question_answer59) The major product of the following reaction is:

    A)

    B)

    C)

    D)

    View Answer play_arrow
  • question_answer60) The correct sequence of amino acids present in the tripetide given below is:

    A) Val - Ser - Thr

    B) Thr - Ser - Vnl

    C) Thr - Ser - Leu

    D) Leu - Ser - Thr

    View Answer play_arrow
  • 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:

    A) \[\frac{\pi }{6}\,\]

    B) \[\frac{\pi }{3}\,\]

    C) 0

    D) \[\frac{\pi }{4}\,\]

    View Answer play_arrow
  • 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:

    A) 2

    B) 3

    C) 5

    D) 4

    View Answer play_arrow
  • question_answer63) The coefficient of \[{{t}^{4}}\] in the expansion of \[{{\left( \frac{1-{{t}^{6}}}{1-t} \right)}^{3}}\]

    A) 15

    B) 10

    C) 14

    D) 12

    View Answer play_arrow
  • 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:

    A) 4

    B) \[\sqrt{22}\]

    C) 6

    D) \[\sqrt{32}\]

    View Answer play_arrow
  • 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:

    A) \[-\frac{1}{2}\]

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

    C) \[\frac{1}{4}\]

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

    View Answer play_arrow
  • 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:

    A) \[\frac{3}{2\sqrt{2}}\]

    B) \[\frac{1}{6}\]

    C) \[\frac{1}{6\sqrt{2}}\]

    D) \[\frac{1}{3\sqrt{2}}\]

    View Answer play_arrow
  • 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:

    A) 7830

    B) 7520

    C) 7820

    D) 7510

    View Answer play_arrow
  • 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:

    A) \[\frac{7}{13}\]

    B) 2

    C) 4

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

    View Answer play_arrow
  • 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:

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

    B) \[\frac{2}{\sqrt{3}}\]

    C) 2

    D) \[\sqrt{3}\]

    View Answer play_arrow
  • 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:

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

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

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

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

    View Answer play_arrow
  • 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:

    A) 2

    B) 4

    C) 3

    D) 1

    View Answer play_arrow
  • 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

    A) 2

    B) 4

    C) 3

    D) 1

    View Answer play_arrow
  • question_answer73) If the tines \[x=ay+b,\]\[z=cy+d\]and \[x=a'z\,\,+b'\], \[y\,\,=\,\,c'z\,\,+d'\] are perpendicular then:

    A) \[cc'+a+a'=0\]

    B) \[aa'+c+c'=0\]

    C) \[bb'+cc'+1=0\]

    D) \[ab'+bc'+1=0\]

    View Answer play_arrow
  • 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 \[\frac{x}{3}=\frac{y}{4}=\frac{z}{2}\,\,and\,\,\frac{x}{4}=\frac{y}{2}=\frac{z}{3}\]

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

    B) \[x+2y-2z\,\,=\,\,0\]

    C) \[x-2y+z=0\]

    D) \[~5x+2y-4z=0\]

    View Answer play_arrow
  • 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:

    A) 2

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

    C) 0

    D) 1

    View Answer play_arrow
  • 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

    View Answer play_arrow
  • 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 :

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

    B) \[\frac{1}{3}\]

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

    D) 2

    View Answer play_arrow
  • 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

    A) \[r\,\,>\,\,11\]

    B) \[r\,\,=\,\,11\]

    C) \[1\,\,<\,\,r\,\,<\,\,11\]

    D) \[0\,\,<\,\,r\,\,<\,\,1\]

    View Answer play_arrow
  • 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:

    A) \[\frac{27}{49}\]

    B) \[\frac{26}{49}\]

    C) \[\frac{32}{49}\]

    D) \[\frac{21}{49}\]

    View Answer play_arrow
  • question_answer80) If then A is:

    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 \[t\text{ }\in \text{ }R\]

    View Answer play_arrow
  • 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:

    A) 372

    B) 375

    C) 250

    D) 374

    View Answer play_arrow
  • 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:

    A) 2

    B) 1

    C) 4

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

    View Answer play_arrow
  • 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:

    A) 4

    B) 2

    C) 5

    D) 3

    View Answer play_arrow
  • question_answer84) The logical statement \[[\tilde{\ }\left( \tilde{\ }p\vee q \right)\vee (p\wedge r)]\,\,\wedge \,(\sim q\wedge r)\,\] is equivalent to:

    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) \[\tilde{\ }p\wedge r\]

    View Answer play_arrow
  • question_answer85) If the system of linear equations

    \[x-4y+7z=g\]
    \[3y-5z=h\]
    \[-2x+5y-9z=k\]
    is consistent, then:

    A) \[g+2h+k=0\]

    B) \[g+h+2k=0\]

    C) \[g+h+k=0\]

    D) \[2g+h+k=0\]

    View Answer play_arrow
  • 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:

    A) (4, 5)

    B) (\[-5,\,\,-4\])

    C) (3, 4)

    D) (5, 6)

    View Answer play_arrow
  • question_answer87) If \[x=si{{n}^{-1}}\left( sin\text{ }10 \right)\] and \[y=co{{s}^{-1}}\,\,cos10)\], then \[y-x\] is equal to:

    A) 0

    B) \[7\,\pi \]

    C) \[\pi \]

    D) 10

    View Answer play_arrow
  • 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:

    A) not injective

    B) surjective but not injective

    C) injective but not surjective

    D) neither injective nor surjective

    View Answer play_arrow
  • question_answer89) For each\[x\text{ }\in \text{ }R\], let [x] be the greatest integer less than or equal to x. Then\[\underset{x\to {{0}^{-}}}{\mathop{\lim }}\,\,\frac{x([x]+\left| x \right|)\,sin\,[x]}{\left| x \right|}\]

    A) 1

    B) 0

    C) \[sin\text{ }1\]

    D) \[-sin\text{ }1\]

    View Answer play_arrow
  • 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:

    A) 32

    B) \[31\frac{3}{4}\]

    C) \[30\frac{1}{2}\]

    D) \[31\frac{1}{4}\]

    View Answer play_arrow

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