Solved papers for JEE Main & Advanced JEE Main Online Paper (Held On 12-Jan-2019 Evening)

done JEE Main Online Paper (Held On 12-Jan-2019 Evening)

  • question_answer1) A block kept on a rough inclined plane, as shown in the figure, remains at rest upto a maximum force 2 N down the inclined plane. The maximum external force up the inclined plane that does not move the block is 10 N. The coefficient of static friction between the block and the plane is [Take \[g=10\text{ }m/{{s}^{2}}\]]

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

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

    C) \[\frac{\sqrt{3}}{4}\]

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

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  • question_answer2) Formation of real image using a biconvex lens is shown below If the whole set up is immersed in water without disturbing the object and the screen positions what will one observe on the screen?

    A) Image disappears

    B) Magnified image

    C) Erect real image

    D) No change

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  • question_answer3) An alpha-particle of mass m suffers -dimensional elastic collision with a nucleus at rest of unknown mass. It is scattered directly backwards losing, 64% of its initial kinetic energy. The mass of the nucleus is

    A) 4 m

    B) 1.5 m

    C) 3.5 m

    D) 2 m

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  • question_answer4) A simple harmonic motion is represented by \[y=5(sin3\pi t+\sqrt{3}cos3\pi t)cm\] The amplitude and time period of the motion are

    A) \[5cm,\frac{3}{2}s\]

    B) \[10cm,\frac{2}{3}s\]

    C) \[5cm,\frac{2}{3}s\]

    D) \[10cm,\frac{3}{2}s\]

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  • question_answer5) A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is 5 cm and its rotational speed is 2 rotations per second, then the difference in the heights between the centre and the sides, in cm, will be

    A) 0.4

    B) 2.0

    C) 0.1

    D) 1.2

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  • question_answer6) A 10 m long horizontal wire extends from North East to South West. It is falling with a speed of 5.0 m \[{{s}^{-1}}\], at right angles to the horizontal component of the earths magnetic field of \[0.3\times {{10}^{-4}}Wb/{{m}^{2}}.\] The value of the induced emf in wire is

    A) \[0.3\times {{10}^{-3}}V\]

    B) \[2.5\times {{10}^{-3}}V\]

    C) \[1.5\times {{10}^{-3}}V\]

    D) \[1.1\times {{10}^{-3}}V\]

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  • question_answer7) A soap bubble, blown by a mechanical pump at the mouth of a tube, increases in volume, with time, at a constant rate. The graph that correctly depicts the time dependence of pressure inside the bubble is given by





    E) None of these

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  • question_answer8) In the given circuit, \[C=\frac{\sqrt{3}}{2}\mu F,{{R}_{2}}=20\Omega ,\]and\[{{R}_{1}}=10\Omega .\]Current in \[L-{{R}_{1}}\]path is \[{{I}_{1}}\]and in \[C-{{R}_{2}}\] path it is \[{{I}_{2}}.\]The voltage of A.C source is given by, \[V=200\sqrt{2}\sin (100t)\]volts. The phase difference between \[{{I}_{1}}\] and \[{{I}_{2}}\]is

    A) 0

    B) \[30{}^\circ \]

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

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

    E) None of these

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  • question_answer9) An ideal gas is enclosed in a cylinder at pressure of 2 atm and temperature, 300 K. The mean time between two successive collisions is \[6\times {{10}^{-8}}s.\]If the pressure is doubled and temperature is increased to 500 K, the mean time between two successive collisions will be close to

    A) \[4\times {{10}^{-8}}s\]

    B) \[3\times {{10}^{-6}}s\]

    C) \[0.5\times {{10}^{-8}}s\]

    D) \[2\times {{10}^{-7}}s\]

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  • question_answer10) In a Frank-Hertz experiment, an electron of energy 5.6 eV passes through mercury vapour and emerges with an energy 0.7 eV. The minimum wavelength of photons emitted by mercury atoms is close to

    A) 220 nm

    B) 1700 nm

    C) 250 nm

    D) 2020 nm

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  • question_answer11) A vertical closed cylinder is separated into two parts by a frictionless piston of mass m and negligible thickness. The piston is free to move along the length of the cylinder. The length of the cylinder above the piston is\[{{l}_{1}}\]and that below the piston is\[{{l}_{2}},\]such that \[{{l}_{1}}>{{l}_{2}}.\]Each part of the cylinder contains n moles of an ideal gas at equal temperature T. If the piston is stationary, its mass m, will be given by (R is universal gas constant and g is the acceleration due to gravity)

    A) \[\frac{RT}{ng}\left[ \frac{{{l}_{1}}-3{{l}_{2}}}{{{l}_{1}}{{l}_{2}}} \right]\]

    B) \[\frac{nRT}{g}\left[ \frac{1}{{{l}_{2}}}+\frac{1}{{{l}_{1}}} \right]\]

    C) \[\frac{RT}{g}\left[ \frac{2{{l}_{1}}+{{l}_{2}}}{{{l}_{1}}{{l}_{2}}} \right]\]

    D) \[\frac{nRT}{g}\left[ \frac{{{l}_{1}}-{{l}_{2}}}{{{l}_{1}}{{l}_{2}}} \right]\]

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  • question_answer12) A load of mass M kg is suspended from a steel wire of length 2 m and radius 1.0 mm in Searle's apparatus experiment. The increase in length produced in the wire is 4.0 mm. Now the load is fully immersed in a liquid of relative density 2. The relative density of the material of load is 8. The new value of increase in length of the steel wire is

    A) 4.0 mm                                    

    B) zero      

    C) 5.0 mm                        

    D)   3.0 mm.           

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  • question_answer13) A parallel plate capacitor with plates of area 1 m2 each, are at a separation of 0.1m. If the electric field between the plates is \[100\,\,N\,\,{{C}^{-1}},\]the magnitude of charge on each plate is \[\left( \text{Take}\,{{\varepsilon }_{0}}=8.85\times {{10}^{-12}}\frac{{{C}^{2}}}{N{{m}^{2}}} \right)\]

    A) \[8.85\times {{10}^{-10}}C\]

    B) \[7.85\times {{10}^{-10}}C\]

    C) \[9.85\times {{10}^{-10}}C\]

    D) \[6.85\times {{10}^{-10}}C\]

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  • question_answer14) The charge on a capacitor plate in a circuit, as a function of time, is shown in the figure, What is the value of current at t = 4 s?

    A) \[3\mu A\]

    B) zero

    C) \[1.5\mu A\]

    D) \[2\mu A\]

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  • question_answer15) In the circuit shown, find C if the effective capacitance of the whole circuit is to be \[0.5\,\,\mu F.\]All values in the circuit are in \[\mu F.\]

    A) \[\frac{6}{5}\mu F\]

    B) \[4\mu F\]

    C) \[\frac{7}{11}\mu F\]

    D) \[\frac{7}{10}\mu F\]

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  • question_answer16) Let \[l,\,\,r,\,\,c\] and \[v\] represent inductance, resistance, capacitance and voltage, respectively. The dimension of \[\frac{l}{rcv}\]in SI units will be

    A) \[[L{{A}^{-2}}]\]

    B) \[[L{{T}^{2}}]\]

    C) \[[{{A}^{-1}}]\]

    D) \[[LTA]\]

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  • question_answer17) Two satellites, A and B, have masses m and 2 m respectively. A is in a circular orbit of radius R, and B is in a circular orbit of radius 2R around the earth. The ratio of their kinetic energies, \[\frac{{{T}_{A}}}{{{T}_{B}}},\]is

    A) 1

    B) 2

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

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

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  • question_answer18) The mean intensity of radiation on the surface of the Sun is about \[{{10}^{8}}W/{{m}^{2}}\]. The rms value of the corresponding magnetic field is closest to

    A) \[{{10}^{-2}}T\]

    B) \[1T\]

    C) \[{{10}^{-4}}T\]

    D) \[{{10}^{2}}T\]

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  • question_answer19) A resonance tube is old and has jagged end. It is still used in the laboratory to determine velocity of sound in air. A tuning fork of frequency 512 Hz produces first resonance when the tube is filled with water to a mark 11 cm below a reference mark, near the open end of the tube. The experiment is repeated with another fork of frequency 256 Hz which produces first resonance when water reaches a mark 27 cm below the reference mark. The velocity of sound in air, obtained in the experiment, is close to

    A) \[335m\,{{s}^{-1}}\]

    B) \[322m\,{{s}^{-1}}\]

    C) \[328m\,{{s}^{-1}}\]

    D) \[341m\,{{s}^{-1}}\]

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  • question_answer20) In the figure, given that \[{{V}_{BB}}\]supply can vary from 0 to \[5.0V,\]\[{{V}_{CC}}=5V,{{\beta }_{dc}}=200,\]\[{{R}_{B}}=100k\Omega ,\]\[{{R}_{C}}=1\,k\Omega \]and\[{{V}_{BE}}=1.0\,V.\] The minimum base current and the input voltage at which the transistor will go to saturation, will be respectively

    A) \[20\mu A\]and 3.5 V

    B) \[25\mu A\]and 3.5V

    C) \[20\mu A\] and 2.8 V

    D) \[25\mu A\] and 2.8 V

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  • question_answer21) In the given circuit diagram, the currents, \[{{I}_{1}}=0.3A,{{I}_{4}}=0.8A\]and \[{{I}_{5}}=0.4A,\]are flowing as shown. The currents \[{{I}_{2}},{{I}_{3}}\]and \[{{I}_{6}},\]respectively, are

    A) \[1.1\text{ }A,\text{ }0.4\text{ }A,\text{ }0.4\text{ }A\]

    B) \[-0.4A,\,\,0.4A,\,\,1.1A\]

    C) \[1.1\text{ }A,\,\,-0.4\text{ }A,\,\,0.4\text{ }A\]

    D) \[0.4A,\,\,1.1A,\,\,0.4A\]

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  • question_answer22) When a certain photosensitive surface is illuminated with monochromatic light of frequency u, the stopping potential for the photo current is\[\frac{-{{V}_{0}}}{2}.\]When the surface is illuminated by monochromatic light of frequency\[\frac{\upsilon }{2},\]the stopping potential is\[-{{V}_{0}}.\] The threshold frequency for photoelectric emission is

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

    B) \[2\upsilon \]

    C) \[\frac{5\upsilon }{3}\]

    D) \[\frac{3\upsilon }{2}\]

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  • question_answer23) A paramagnetic material has\[{{10}^{28}}\,\,atoms/{{m}^{3}}\]. Its magnetic susceptibility at temperature 350 K is \[2.8\times {{10}^{-4}}.\] Its susceptibility at 300 K is

    A) \[3.267\times {{10}^{-4}}\]

    B) \[3.672\times {{10}^{-4}}\]

    C) \[2.672\times {{10}^{-4}}\]

    D) \[3.726\times {{10}^{-4}}\]

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  • question_answer24) A plano-convex lens (focal lengthy\[{{f}_{2}}\], refractive index \[{{\mu }_{2}},\]radius of curvature R) fits exactly into a plano-concave lens (focal length \[{{f}_{1}},\]refractive index \[{{\mu }_{1}},\]radius of curvature -R). Their plane surfaces are parallel to each other. Then, the focal length of the combination will be

    A) \[{{f}_{1}}+{{f}_{2}}\]

    B) \[\frac{R}{{{\mu }_{2}}-{{\mu }_{1}}}\]

    C) \[{{f}_{1}}-{{f}_{2}}\]

    D) \[\frac{2{{f}_{1}}{{f}_{2}}}{{{f}_{1}}+{{f}_{2}}}\]

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  • question_answer25) A galvanometer, whose resistance is 50 ohm, has 25 divisions in it. When a current of \[4\times {{10}^{-4}}\]A passes through it, its needle (pointer) deflects by one division. To use this galvanometer as a voltmeter of range 2.5 V, it should be connected to a resistance of

    A) 200 ohm

    B) 6250 ohm

    C) 6200 ohm

    D) 250 ohm

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  • question_answer26) Two particles A, B are moving on two concentric circles of radii \[{{R}_{1}}\]and \[{{R}_{2}}\]with equal angular speed\[\omega \]. At t = 0, their positions and direction of motion are shown in the figure. The relative velocity \[{{\vec{v}}_{A}}-{{\vec{v}}_{B}}\]at \[t=\frac{\pi }{2\omega }\]is given by

    A) \[-\omega ({{R}_{1}}+{{R}_{2}})\hat{i}\]

    B) \[\omega ({{R}_{1}}-{{R}_{2}})\hat{i}\]

    C) \[\omega ({{R}_{2}}-{{R}_{1}})\hat{i}\]

    D) \[-\omega ({{R}_{1}}+{{R}_{2}})\hat{i}\]

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  • question_answer27) The moment of inertia of a solid sphere, about an axis parallel to its diameter and at a distance of x from it, is I(x). Which one of the graphs represents the variation of I(x) with x correctly?





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  • question_answer28) To double the covering range, or' a TV transmission tower, its height should be multiplied by

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

    B) 2

    C) 4

    D) \[\sqrt{2}\]

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  • question_answer29) In a radioactive decay chain, the initial nucleus is \[_{90}^{232}Th.\]At the end there are \[6\alpha -\]particles and \[4\beta -\]particles which are emitted. it the end nucleus is \[_{Z}^{A}X,\] A and Z are given by

    A) \[A=202;\text{ }Z=80\]

    B) \[A=200;\text{ }Z=81\]

    C) \[A=208;\text{ }Z=80\]

    D) \[A=208;\text{ }Z=82\]

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  • question_answer30) A particle of mass 20 g is released with an initial velocity 5 m/s along the curve from the point A, as shown in the figure. The point A is at height h from point B. The particle slides along the frictionless surface. When the particle reaches point B, its angular momentum about O will be (Take\[g=10m/{{s}^{2}}\])

    A) \[6kg-{{m}^{2}}/s\]

    B) \[8kg-{{m}^{2}}s\]

    C) \[3kg-{{m}^{2}}s\]

    D) \[2kg-{{m}^{2}}/s\]

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  • question_answer31) The pair that does not require calcination is

    A) \[ZnO\]and\[F{{e}_{2}}{{O}_{3}}.x{{H}_{2}}O\]

    B) \[ZnC{{O}_{3}}\]and\[CaO\]

    C) \[ZnO\]and\[MgO\]

    D) \[F{{e}_{2}}{{O}_{3}}\]and\[CaC{{O}_{3}}.MgC{{O}_{3}}\]

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  • question_answer32) The two monomers for the synthesis of Nylon 6,6 are

    A) \[HOOC{{(C{{H}_{2}})}_{6}}COOH,{{H}_{2}}N{{(C{{H}_{2}})}_{6}}N{{H}_{2}}\]

    B) \[HOOC{{(C{{H}_{2}})}_{6}}COOH,{{H}_{2}}N{{(C{{H}_{2}})}_{4}}N{{H}_{2}}\]

    C) \[HOOC{{(C{{H}_{2}})}_{4}}COOH,{{H}_{2}}N{{(C{{H}_{2}})}_{6}}N{{H}_{2}}\]

    D) \[HOOC{{(C{{H}_{2}})}_{4}}COOH,{{H}_{2}}N{{(C{{H}_{2}})}_{4}}N{{H}_{2}}\]

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  • question_answer33) 8 g of NaOH is dissolved in 18 g of \[{{H}_{2}}O.\] Mole fraction of \[NaOH\]in solution and molality (in \[mol\,k{{g}^{-1}}\]) of the solution respectively are

    A) 0.167, 22.20

    B) 0.167, 11.11

    C) 0.2, 22.20

    D) 0.2, 11.11

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  • question_answer34) The correct statement(s) among I to III with respect to potassium ions that are abundant within the cell fluids is/are

    I. They activate many enzymes.
    II. They participate in the oxidation of glucose to produce ATP.
    III. Along with sodium ions, they are responsible for the transmission of nerve signals.

    A) III only

    B) I and II only

    C) I, II and III

    D) I and III only

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  • question_answer35) The magnetic moment of an octahedral homoleptic Mn(II) complex is 5.9 B.M. The suitable ligand for this complex is

    A) \[NC{{S}^{-}}\]

    B) \[C{{N}^{-}}\]

    C) CO

    D) ethylenediamine

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  • question_answer36) Among the following, the false statement is

    A) it is possible to cause artificial rain by throwing electrified sand carrying charge opposite to the one on clouds from an aeroplane

    B) lyophilic sol can be coagulated by adding an electrolyte

    C) Tyndall effect can be used to distinguish between a colloidal solution and a true solution

    D) latex is a colloidal solution of rubber particles which are positively charged.

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  • question_answer37) The element that shows greater ability to form \[p\pi -p\pi \] multiple bonds is

    A) C

    B) Ge

    C) Sn

    D) Si

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  • question_answer38) The aldehydes which will not form Grignard product with one equivalent Grignard reagent are

    A) (C, D)

    B) (B, D)

    C) (B, C, D)

    D) (B, C)

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  • question_answer39) The correct structure of histidine in a strongly acidic solution (pH = 2) is





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  • question_answer40) The major product of the following reaction is





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  • question_answer41) The major product of the following reaction is \[C{{H}_{3}}C{{H}_{2}}\underset{\begin{smallmatrix} | \\ Br \end{smallmatrix}}{\mathop{CH}}\,-\underset{\begin{smallmatrix} | \\ Br \end{smallmatrix}}{\mathop{C{{H}_{2}}}}\,\xrightarrow[(ii)\,\,NaN{{H}_{2}}in\,liq.N{{H}_{3}}]{(i)\,KOH\,alc.}\]

    A) \[C{{H}_{3}}CH=C=C{{H}_{2}}\]

    B) \[C{{H}_{3}}C{{H}_{2}}C\equiv CH\]

    C) \[C{{H}_{3}}C{{H}_{2}}\underset{\begin{smallmatrix} | \\ N{{H}_{2}} \end{smallmatrix}}{\mathop{CH}}\,-\underset{\begin{smallmatrix} | \\ N{{H}_{2}} \end{smallmatrix}}{\mathop{C{{H}_{2}}}}\,\]

    D) \[C{{H}_{3}}CH=CHC{{H}_{2}}N{{H}_{2}}\]

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  • question_answer42) Chlorine on reaction with hot and concentrated sodium hydroxide gives

    A) \[C{{l}^{-}}\,\text{and}\,ClO_{3}^{-}\]

    B) \[C{{l}^{-}}\,\text{and}\,ClO_{2}^{-}\]

    C) \[C{{l}^{-}}\,\text{and}\,ClO_{{}}^{-}\]

    D) \[ClO_{3}^{-}\,\text{and}\,ClO_{2}^{-}\]

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  • question_answer43) The combination of plots which does not represent isothermal expansion of an ideal gas is

    A) B and D

    B) A and D

    C) B and C

    D) A and C

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  • question_answer44) The major product of the following reaction is





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  • question_answer45) Given:

    (i)\[{{C}_{(graphite)}}+{{O}_{2(g)}}\to C{{O}_{2(g)}};{{\Delta }_{r}}{{H}^{o}}=xkJ\,mo{{l}^{-1}}\]
    (ii)\[{{C}_{(graphite)}}+\frac{1}{2}{{O}_{2(g)}}\to C{{O}_{(g)}};\]\[{{\Delta }_{r}}{{H}^{o}}=y\,\,kJ\,\,mo{{l}^{-1}}\]
    (iii)\[C{{O}_{(g)}}+\frac{1}{2}{{O}_{2(g)}}\to C{{O}_{2}}_{(g)};{{\Delta }_{r}}{{H}^{o}}=z\,\,kJ\,\,mo{{l}^{-1}}\]
    Based on the above thermochemical equations, find out which one of the following algebraic relationships is correct?

    A) \[z=x+y\]

    B) \[x=y-z\]

    C) \[x=y+z\]

    D) \[y=2zx\]

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  • question_answer46) The major product of the following reaction is





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  • question_answer47) The volume strength of \[1M\,{{H}_{2}}{{O}_{2}}\]is (molar mass of \[\,{{H}_{2}}{{O}_{2}}=34g\,mo{{l}^{-1}}\])

    A) 22.4

    B) 16.8

    C) 5.6

    D) 11.35

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  • question_answer48) The upper stratosphere consisting of the ozone layer protects us from the suns radiation that falls in the wavelength region of

    A) 400-550 nm

    B) 600-750 nm

    C) 200-315 nm

    D) 0.8-1.5 nm

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  • question_answer49) For a reaction, consider the plot of In k versus 1/r given in the figure. If the rate constant of this reaction at 400 K is \[{{10}^{-5}}{{s}^{-1}},\]then the rate constant at 500 K

    A) \[{{10}^{-4}}{{s}^{-1}}\]

    B) \[4\times {{10}^{-4}}{{s}^{-1}}\]

    C) \[{{10}^{-6}}{{s}^{-1}}\]

    D) \[2\times {{10}^{-4}}{{s}^{-1}}\]

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  • question_answer50) An open vessel \[27{}^\circ C\] at is heated until two fifth of the air (assumed as an ideal gas) in it has escaped from the vessel. Assuming that the volume of the vessel remains constant, the temperature at which the vessel has been heated is

    A) 750 K

    B) \[750{}^\circ C\]

    C) \[500{}^\circ C\]

    D) 500 K

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  • question_answer51) The element that does not show catenation is

    A) Sn

    B) Ge

    C) Si

    D) Pb

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  • question_answer52) The increasing order of the reactivity of the following with \[LiAl{{H}_{4}}\]is


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

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

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

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

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  • question_answer53) Molecules of benzoic acid \[({{C}_{6}}{{H}_{5}}COOH)\]dimerise in benzene. V g of the acid dissolved in 30 g of benzene shows a depression in freezing point equal to 2 K. If the percentage association of the acid to form dimer in the solution is 80, then w is (Given that \[{{K}_{f}}=5\,K\,kg\,mo{{l}^{-1}},\]Molar mass of benzoic acid \[=122g\,mo{{l}^{-1}}\])

    A) 2.4 g

    B) 1.8 g

    C) 1.0 g

    D) 1.5 g

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  • question_answer54) The major product of the following reaction is





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  • question_answer55) If the de Broglie wavelength of the electron in \[{{n}^{th}}\] Bohr orbit in a hydrogenic atom is equal to \[1.5\pi {{a}_{0}}\](\[{{a}_{0}}\]is Bohr radius), then the value of n/z is

    A) 1.0

    B) 1.50

    C) 0.75

    D) 0.40

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  • question_answer56) \[\Lambda {{{}^\circ }_{m}}\] for \[NaCl,HCl\]and NaA are 126.4, 425.9 and \[100.5\,S\,c{{m}^{2}}\,mo{{l}^{-1}},\]respectively. If the conductivity of 0.001 M HA is \[5\times {{10}^{-5}}S\,c{{m}^{-1}},\]degree of dissociation of HA is

    A) 0.75

    B) 0.25

    C) 0.125

    D) 0.50

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  • question_answer57) If \[{{K}_{sp}}\]of \[A{{g}_{2}}C{{O}_{3}}\]is \[8\times {{10}^{-12}},\]the molar solubility of \[A{{g}_{2}}C{{O}_{3}}\]in \[0.1\,M\,AgN{{O}_{3}}\]is

    A) \[8\times {{10}^{-11}}M\]

    B) \[8\times {{10}^{-10}}M\]

    C) \[8\times {{10}^{-13}}M\]

    D) \[8\times {{10}^{-12}}M\]

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  • question_answer58) The compound that is not a common component of photochemical smog is

    A) \[{{H}_{3}}C-\underset{\begin{smallmatrix} || \\ O \end{smallmatrix}}{\mathop{C}}\,-OON{{O}_{2}}\]

    B) \[C{{H}_{2}}=CHCHO\]

    C) \[C{{F}_{2}}C{{l}_{2}}\]

    D) \[{{O}_{3}}\]

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  • question_answer59) The correct order of atomic radii is

    A) \[Ce>Eu>Ho>N\]

    B) \[Ho>N>Eu>Ce\]

    C) \[Eu>Ce>Ho>N\]

    D) \[N>Ce>Eu>Ho\]

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  • question_answer60) The major product in the following conversion is





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  • question_answer61) Let s and \[S'\] be the foci of an ellipse and B be any one of the extremities of its minor axis. If \[\Delta S'BS\]is a right angled triangle with right angle at B and area \[(\Delta S'BS)=8sq.\]units, then the length of altos rectum of the ellipse is

    A) 2

    B) 4

    C) \[4\sqrt{2}\]

    D) \[2\sqrt{2}\]

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  • question_answer62) The expression\[\tilde{\ }(\tilde{\ }p\to q)\]is logically equivalent to

    A) \[p\wedge q\]

    B) \[\tilde{\ }p\wedge q\]

    C) \[\tilde{\ }p\wedge \tilde{\ }q\]

    D) \[p\wedge \tilde{\ }q\]

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  • question_answer63) If the sum of the first 15 terms of the series \[{{\left( \frac{3}{4} \right)}^{3}}+{{\left( 1\frac{1}{2} \right)}^{3}}+{{\left( 2\frac{1}{4} \right)}^{3}}+{{3}^{3}}+{{\left( 3\frac{3}{4} \right)}^{3}}+.....\]is equal to 225 k, then k is equal to

    A) 27

    B) 9

    C) 108

    D) 54

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  • question_answer64) If \[{{\sin }^{4}}\alpha +4{{\cos }^{4}}\beta +2=4\sqrt{2}\sin \alpha \cos \beta ;\]\[\alpha ,\beta \in [0,\pi ],\]then \[\cos (\alpha +\beta )-\cos (\alpha -\beta )\]is equal to

    A) \[-1\]

    B) 0

    C) \[\sqrt{2}\]

    D) \[-\sqrt{2}\]

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  • question_answer65) In a game, a man wins Rs. 100 if he gets 5 or 6 on a throw of a fair die and lose Rs. 50 for getting any other number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three throws, then his expected gain/loss (in rupees) is

    A) \[\frac{400}{9}loss\]

    B) \[\frac{400}{3}gain\]

    C) 0

    D) \[\frac{400}{3}loss\]

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  • question_answer66) Let S be the set of all real values of \[\lambda \] such that a plane passing through the points \[(-{{\lambda }^{2}},1,1),\]\[(1,-{{\lambda }^{2}},1)\]and \[(1,1,-{{\lambda }^{2}})\]also passes through the point (\[-1,\text{ }-1,1\]). Then S is equal to

    A) \[\{1,-1\}\]

    B) \[\{3,-3\}\]

    C) \[\{\sqrt{3}\}\]

    D) \[\{\sqrt{3},-\sqrt{3}\}\]

    View Answer play_arrow
  • question_answer67) The tangent to the curve \[y={{x}^{2}}-\text{5}x+5,\]parallel to the line \[2y=4x+1,\]also passes through the point

    A) \[\left( \frac{7}{2},\frac{1}{4} \right)\]

    B) \[\left( \frac{1}{4},\frac{7}{2} \right)\]

    C) \[\left( -\frac{1}{8},7 \right)\]

    D) \[\left( \frac{1}{8},-7 \right)\]

    View Answer play_arrow
  • question_answer68) The total number of irrational terms in the binomial expansion \[{{({{7}^{1/5}}-{{3}^{1/10}})}^{60}}\]is

    A) 55

    B) 54

    C) 48

    D) 49

    View Answer play_arrow
  • question_answer69) If a straight line passing through the point \[P\left( -3,\text{ }4 \right)\] is such that its intercepted portion between the coordinate axes is bisected at P, then its equation is

    A) \[4x+3y=0\]

    B) \[4x-3y+24=0\]

    C) \[3x-4y+25=0\]

    D) \[x-y+7=0\]

    View Answer play_arrow
  • question_answer70) \[\underset{x\to {{1}^{-}}}{\mathop{\lim }}\,\frac{\sqrt{\pi }-\sqrt{2{{\sin }^{-1}}x}}{\sqrt{1-x}}\]is equal to

    A) \[\sqrt{\pi }\]

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

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

    D) \[\sqrt{\frac{2}{\pi }}\]

    View Answer play_arrow
  • question_answer71) If\[^{n}{{C}_{4}},{{\,}^{n}}{{C}_{5}}\]and \[{{\,}^{n}}{{C}_{6}}\]are in A.R, then n can be

    A) 12

    B) 14

    C) 9

    D) 11

    View Answer play_arrow
  • question_answer72) Let f be a differentiable function such that \[f(1)=2\] and \[f'(x)=f(x)\]for all \[x\in R.\]If \[h(x)=f(f(x)),\]then \[h'(1)\] is equal to

    A) \[2{{e}^{2}}\]

    B) 4e

    C) 2e

    D) \[4{{e}^{2}}\]

    View Answer play_arrow
  • question_answer73) The set of all values of\[\lambda \]for which the system of linear equations

    \[x-2y-2z=\lambda x\]
    \[x+2y+z=\lambda y\]
    \[-x-y=\lambda z\]
    has a non-trivial solution

    A) is an empty set

    B) contains exactly two elements

    C) is a singleton

    D) contains more than two elements

    View Answer play_arrow
  • question_answer74) The number of integral values of m for which the quadratic expression, \[(1+2m){{x}^{2}}-2\]\[(1+3m)x+4(1+m),x\in R,\]is always positive is

    A) 8

    B) 7

    C) 3

    D) 6

    View Answer play_arrow
  • question_answer75) The mean and the variance of five observations are 4 and 5.20, respectively. If three of the observations are 3, 4 and 4; then the absolute value of the difference of the other two observations is

    A) 3

    B) 1

    C) 7

    D) 5

    View Answer play_arrow
  • question_answer76) Let \[\vec{a},\vec{b}\]and \[\vec{c}\]be three unit vectors, out of which vectors \[\vec{b}\]and \[\vec{c}\]are non-parallel. If \[\alpha \]and \[\beta \]are the angles which vector a makes with \[\vec{a}\]vectors \[\vec{b}\] and \[\vec{c}\]respectively and \[\vec{a}\times (\vec{b}\times \vec{c})=\frac{1}{2}\vec{b},\]then\[|\alpha -\beta |\]is equal to

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

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

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

    D) \[30{}^\circ \]

    View Answer play_arrow
  • question_answer77) If the function f given by \[f(x)={{x}^{3}}-3(a-2){{x}^{2}}+3ax+7,\]for some \[a\in R\]is increasing in (0, 1] and decreasing in [1, 5), then a root of the equation, \[\frac{f(x)-14}{{{(x-1)}^{2}}}=0(x\ne 1)\]is

    A) 7

    B) \[-7\]

    C) 5

    D) 6

    View Answer play_arrow
  • question_answer78) The integral \[\int_{{}}^{{}}{\frac{3{{x}^{13}}+2{{x}^{11}}}{{{(2{{x}^{4}}+3{{x}^{2}}+1)}^{4}}}}dx\]is equal to (where C is a constant of integration)

    A) \[\frac{{{x}^{4}}}{6{{(2{{x}^{4}}+3{{x}^{2}}+1)}^{3}}}+C\]

    B) \[\frac{{{x}^{4}}}{{{(2{{x}^{4}}+3{{x}^{2}}+1)}^{3}}}+C\]

    C) \[\frac{{{x}^{12}}}{6{{(2{{x}^{4}}+3{{x}^{2}}+1)}^{3}}}+C\]

    D) \[\frac{{{x}^{12}}}{{{(2{{x}^{4}}+3{{x}^{2}}+1)}^{3}}}+C\]

    View Answer play_arrow
  • question_answer79) The integral \[\int\limits_{1}^{e}{\left\{ {{\left( \frac{x}{e} \right)}^{2x}}-{{\left( \frac{e}{x} \right)}^{x}} \right\}}{{\log }_{e}}xdx\]equal to

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

    B) \[-\frac{1}{2}+\frac{1}{e}-\frac{1}{2{{e}^{2}}}\]

    C) \[\frac{3}{2}-e-\frac{1}{2{{e}^{2}}}\]

    D) \[\frac{3}{2}-\frac{1}{e}-\frac{1}{2{{e}^{2}}}\]

    View Answer play_arrow
  • question_answer80) If a curve passes through the point (\[1,\text{ }-2\]) and has slope of the tangent at any point \[(x,y)\]on it as\[\frac{{{x}^{2}}-2y}{x},\]then the curve also passes through the point

    A) \[(-\sqrt{2},1)\]

    B) \[(-1,2)\]

    C) \[(\sqrt{3},0)\]

    D) \[(3,0)\]

    View Answer play_arrow
  • question_answer81) There are m men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by 84, then the value of m is

    A) 11

    B) 9

    C) 12

    D) 7

    View Answer play_arrow
  • question_answer82) If the angle of elevation of a cloud from a point P which is 25 m above a lake be \[30{}^\circ \] and the angle of depression of reflection of the cloud in the lake from P be \[60{}^\circ \], then the height of the cloud (in metres) from the surface of the lake is

    A) 50

    B) 45

    C) 60

    D) 42

    View Answer play_arrow
  • question_answer83) \[\underset{n\to \infty }{\mathop{\lim }}\,\left( \frac{n}{{{n}^{2}}+{{1}^{2}}}+\frac{n}{{{n}^{2}}+{{2}^{2}}}+\frac{n}{{{n}^{2}}+{{3}^{2}}}+....+\frac{1}{5n} \right)\]is equal to

    A) \[{{\tan }^{-1}}(2)\]

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

    C) \[{{\tan }^{-1}}(3)\]

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

    View Answer play_arrow
  • question_answer84) If a circle of radius R passes through the origin and intersects the coordinate axes at A and B, then the locus of the foot of perpendicular from 0 on AB is

    A) \[{{({{x}^{2}}+{{y}^{2}})}^{3}}=4{{R}^{2}}{{x}^{2}}{{y}^{2}}\]

    B) \[{{({{x}^{2}}+{{y}^{2}})}^{2}}=4R{{x}^{2}}{{y}^{2}}\]

    C) \[({{x}^{2}}+{{y}^{2}})(x+y)={{R}^{2}}xy\]

    D) \[{{({{x}^{2}}+{{y}^{2}})}^{2}}=4{{R}^{2}}{{x}^{2}}{{y}^{2}}\]

    View Answer play_arrow
  • question_answer85) If an angle between the line, \[\frac{x+1}{2}=\frac{y-2}{1}=\frac{z-3}{-2}\]and the plane, \[x-2y-kz=3\]is \[{{\cos }^{-1}}\left( \frac{2\sqrt{2}}{3} \right),\] then a value of k is

    A) \[\sqrt{\frac{5}{3}}\]

    B) \[-\frac{3}{5}\]

    C) \[\sqrt{\frac{3}{5}}\]

    D) \[-\frac{5}{3}\]

    View Answer play_arrow
  • question_answer86) The equation of a tangent to the parabola, \[{{x}^{2}}=8y,\]which makes an angle \[\theta \] with the positive direction of x-axis is

    A) \[x=y\cot \theta -2\tan \theta \]

    B) \[y=x\tan \theta -2\cot \theta \]

    C) \[x=y\cot \theta +2\tan \theta \]

    D) \[y=x\tan \theta +2\cot \theta \]

    View Answer play_arrow
  • question_answer87) In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 opted for both NCC and NSS. If one of these students is selected at random, then the probability that the student selected has opted neither for NCC nor for NSS is

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

    B) \[\frac{5}{6}\]

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

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

    View Answer play_arrow
  • question_answer88) Let \[{{z}_{1}}\] and \[{{z}_{2}}\]be two complex numbers satisfying \[|{{z}_{1}}|=9\] and \[|{{z}_{2}}-3-4i|=4\].Then the minimum value of \[|{{z}_{1}}-{{z}_{2}}|\]is

    A) \[\sqrt{2}\]

    B) 2

    C) 0

    D) 1

    View Answer play_arrow
  • question_answer89) If \[a=\left[ \begin{matrix} 1 & \sin \theta & 1 \\ -\sin \theta & 1 & \sin \theta \\ -1 & -\sin \theta & 1 \\ \end{matrix} \right];\]then for all \[\theta \in \left( \frac{3\pi }{4},\frac{5\pi }{4} \right),\]det lies in the interval

    A) \[\left( \frac{3}{2},3 \right]\]

    B) \[\left[ \frac{5}{2},4 \right)\]

    C) \[\left( 1,\frac{5}{2} \right]\]

    D) \[\left( 0,\frac{3}{2} \right]\]

    View Answer play_arrow
  • question_answer90) Let Z be the set of integers. If \[A=\{x\in Z:{{2}^{(x+2)({{x}^{2}}-5x+6)}}=1\}\]and \[B=\{x\in Z:-3<2x-1<9\}\]then the number of subsets of the set \[A\times B\]is

    A) \[{{2}^{18}}\]

    B) \[{{2}^{12}}\]

    C) \[{{2}^{15}}\]

    D) \[{{2}^{10}}\]

    View Answer play_arrow

Study Package

JEE Main Online Paper (Held On 12-Jan-2019 Evening)
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