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

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

  • question_answer1) Two guns A and B can fire bullets at speeds 1 km/s and 2 km/s respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bullets fired by the two guns, on the ground is -

    A) 1 : 16

    B) 1 : 8

    C) 1 : 2

    D) 1 : 4

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  • question_answer2) A heat source at \[T={{10}^{3}}\] K is connected to another heat reservoir at \[T={{10}^{2}}\] K by a copper slab which is 1 m thick. Given that the thermal conductivity of copper is 0.1 \[W{{K}^{-}}^{1}{{m}^{-}}^{1}\], the energy flux through it in the steady state is -

    A) 200 \[W{{m}^{-}}^{2}\]

    B) 65 \[W{{m}^{-}}^{2}\]

    C) 120 \[W{{m}^{-}}^{2}\]

    D) 90 \[W{{m}^{-}}^{2}\]

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  • question_answer3) A satellite is moving with a constant speed v in circular orbit around the earth. An object of mass 'm' is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of ejection, the kinetic energy of the object is -

    A) \[m{{v}^{2}}\]                                               

    B) \[\frac{1}{2}m{{v}^{2}}\]

    C) \[\frac{3}{2}m{{v}^{2}}\]                  

    D)   \[2\,m{{v}^{2}}\]

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  • question_answer4) A TV transmission tower has a height of 140 m and the height of the receiving antenna is 40 m. What is the maximum distance upto which signals can be broadcasted from this tower is LOS (Line of Sight) mode? (Given: radius of earth \[=\text{ }6.4\times {{10}^{6}}m)\].

    A) 40 km

    B) 65 km

    C) 48 km

    D) 80 km

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  • question_answer5) A train moves towards a stationary observer with speed 34 m/s. The train sounds a whistle and its frequency registered by the observer is\[{{f}_{1}}\]. If the speed of the train is reduced to 17 m/s, the frequency registered is\[{{f}_{2}}\]. If speed of sound is 340 m/s, then the ratio \[{{f}_{1}}/{{f}_{2}}\] is -

    A) 19/18

    B) 20/19

    C) 21/20

    D) 18/17

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  • question_answer6) In the cube of side 'a' shown in the figure, the vector from the central point of the face ABOD to the central point of the face BEFO will be -  

    A) \[\frac{1}{2}a\,(\widehat{k}-\widehat{i})\]                                   

    B) \[\frac{1}{2}a\,(\widehat{j}-\widehat{i})\]

    C) \[\frac{1}{2}a\,(\widehat{j}-\widehat{k})\]                       

    D) \[\frac{1}{2}a\,(\widehat{i}-\widehat{k})\]

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  • question_answer7) A parallel plate capacitor is of area \[6\text{ }c{{m}^{2}}\] and a separation 3 mm. The gap is filled with three dielectric materials of equal thickness (see figure) with dielectric constants \[{{K}_{1}}=10,\text{ }{{K}_{2}}=12\] and\[{{K}_{3}}=14\]. The dielectric constant of a material which when fully inserted in above capacitor, gives same capacitance would be -

    A) 12

    B) 36

    C) 14

    D) 4

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  • question_answer8) To mop-clean a floor, a cleaning machine presses a circular mop of radius R vertically down with a total force F and rotates it with a constant angular speed about its axis. If the force F is distributed uniformly over the mop and if coefficient of friction between the mop and the floor is u, the torque, applied by the machine on the mop is -

    A) \[\mu \,FR/2\]

    B) \[\mu \,FR/3\]

    C) \[\mu \,FR/6\]

    D) \[\frac{2}{3}\mu \,FR\]

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  • question_answer9) A block of mass m is kept on a platform which starts from rest with constant acceleration \[g/2\] acceleration \[g/2\] upward, as shown in figure. Work done by normal reaction on block in time is-

    A) \[\frac{m{{g}^{2}}{{t}^{2}}}{8}\]

    B) \[\frac{3\,m{{g}^{2}}{{t}^{2}}}{8}\]

    C) \[-\frac{\,m{{g}^{2}}{{t}^{2}}}{8}\]

    D) 0

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  • question_answer10) Water flows into a large tank with flat bottom at the rate of\[{{10}^{-}}^{4}{{m}^{3}}{{s}^{-1}}\]. Water is also leaking out of a hole of area \[1\,c{{m}^{2}}\] at its bottom. If the height of the water in the tank remains steady, then this height is

    A) 2.9 cm

    B) 5.1 cm

    C) 4 cm

    D) 1.7 cm

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  • question_answer11) A magnet of total magnetic moment \[{{10}^{-}}^{2}\widehat{i}\,A-{{m}^{2}}\] is placed in a time varying magnetic field, \[B\widehat{i}\left( cos\text{ }\omega t \right)\] where \[B=1\] Tesla and\[\omega =0.125\text{ }rad/s\]. The work done for reversing the direction of the magnetic moment at \[t=1\] second, is-

    A) 0.014 J

    B) 0.028 J

    C) 0.01 J

    D) 0.007 J

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  • question_answer12) Two electric dipoles, A, B with respective dipole moments \[{{\overrightarrow{d}}_{A}}=-4qa\widehat{i}\] and \[{{\overrightarrow{d}}_{B}}=-2qa\widehat{i}\] are placed on the x-axis with a separation R, as shown in the figure. The distance from A at which both of them produce the same potential is -

    A) \[\frac{\sqrt{2}\,R}{\sqrt{2}+1}\]

    B) \[\frac{\,R}{\sqrt{2}+1}\]

    C) \[\frac{\,\sqrt{2}\,R}{\sqrt{2}-1}\]

    D) \[\frac{\,\,R}{\sqrt{2}-1}\]

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  • question_answer13) To get output 'I' at R, for the given logic gate circuit the input values must be-

    A) \[X=0,\text{ }Y=0\]               

    B) \[X=1,\text{ }Y=0\]

    C) \[X=0,\text{ }Y=1\]                  

    D)   \[X=1,\text{ }Y=1\]

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  • question_answer14) A solid metal cube of edge length 2 cm is moving in a positive y-direction at a constant speed of 6 m/s. There it?, a uniform magnetic field of 0.1 T in the positive z- direction. The potential difference between the two faces of the cube perpendicular to the x-axis, is -

    A) 2 mV

    B) 12 mV

    C) 6 mV

    D) 1 mV

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  • question_answer15) In a Young's double slit experiment with slit separation 0.1 mm, one observes a bright fringe at angle \[\frac{1}{40}\] rad by using light of wavelength\[{{\lambda }_{1}}\]. When the light of wavelength \[{{\lambda }_{2}}\] is used a bright fringe is seen at the same angle in the same set up. Given that \[{{\lambda }_{1}}\] and \[{{\lambda }_{2}}\] are in visible range (380 nm to 740 nm), their values are -

    A) 400 nm, 500 nm                        

    B) 625 nm, 500 nm

    C) 380 nm, 500 nm            

    D)   380 nm, 525 nm

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  • question_answer16) The density of a material in SI units is 128 \[kg\text{ }{{m}^{-}}^{3}\]. In certain units in which the unit of length is 25 cm and the unit of mass is 50 g, the numerical value of density of the material is-

    A) 40

    B) 640

    C) 16

    D) 410

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  • question_answer17) Using a nuclear counter the count rate of emitted particles from a radioactive source is measured. At \[t=0\] it was 1600 counts per second and \[t=8\] seconds it was 100 counts per second. The count rate observed, as counts per second, at \[t=6\] seconds is close to-

    A) 200

    B) 150

    C) 400

    D) 360

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  • question_answer18) A uniform metallic wire has a resistance of \[18\,\Omega \] and is bent into an equilateral triangle. Then, the resistance between any two vertices of the triangle is-

    A) \[12\,\Omega \]

    B) \[2\,\Omega \]

    C) \[4\,\Omega \]

    D) \[8\,\Omega \]

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  • question_answer19) An insulating thin rad of length l has a linear charge density \[\rho (x)\,\,=\,\,{{\rho }_{0}}\,\frac{x}{l}\]on it. The rod is rotated about an axis passing through the origin \[(x\,\,=\,\,0)\]and perpendicular to the rod. If the rod makes n rotations per second, then the time averaged magnetic moment of the rod is-

    A) \[\frac{\pi }{3}\,n\,\,\rho {{l}^{3}}\]

    B) \[\frac{\pi }{4}\,n\,\,\rho {{l}^{3}}\]

    C) \[n\,\,\rho {{l}^{3}}\]

    D) \[\pi n\,\,\rho {{l}^{3}}\]

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  • question_answer20) A plano convex lens of refractive index \[{{\mu }_{1}}\] and focal, length \[{{f}_{1}}\] is kept in contact with another piano concave lens of refractive index \[{{\mu }_{2}}\]and focal length\[{{f}_{2}}\]. If the radius of curvature of their spherical faces is R each and \[{{f}_{1}}\,=\,2{{f}_{2}}\], then \[{{\mu }_{1}}\,and\,\,{{\mu }_{2}}\] are related as-

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

    B) \[{{\mu }_{1}}+{{\mu }_{2}}=3\]

    C) \[2{{\mu }_{1}}-{{\mu }_{2}}=1\]

    D) \[2{{\mu }_{2}}-{{\mu }_{1}}=1\]

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  • question_answer21) In an electron microscope, the resolution that can be achieved is of the order of the wavelength of electrons used. To resolve a width of \[7.5\times {{10}^{-}}^{12}\] m, the minimum electron required is close to-

    A) 25 ke V

    B) 500 ke V

    C) 100 ke V

    D) 1 ke V

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  • question_answer22) A homogeneous solid cylindrical roller of radius R and mass M is pulled on a cricket pitch by a horizontal force. Assuming rolling without slipping, angular acceleration of the cylinder is-

    A) \[\frac{F}{2mR}\]

    B) \[\frac{2\,F}{3mR}\]

    C) \[\frac{3\,F}{2mR}\]

    D) \[\frac{F}{3mR}\]

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  • question_answer23) A string of length 1 m and mass 5 g is fixed at both ends. The tension in the string is 8.0 N. The string is set into vibration using an external vibrator of frequency 100 Hz. The separation between successive nodes on the string is close to-

    A) 16.6 cm

    B) 10.0 cm

    C) 20.0 cm

    D) 33.3 cm

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  • question_answer24) A 2 W carbon resistor is color coded with green, black, red and brown respectively. The maximum current which can be passed through this resistor is-

    A) 0.4 mA

    B) 20 mA

    C) 63 mA

    D) 100 mA

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  • question_answer25) If the magnetic field of a plane electromagnetic wave is given by (the speed of light \[=~\,3~\times ~{{10}^{8}}m/s)\] \[B\,=\,100\times {{10}^{-6}}\,\sin \,\left[ 2\pi \times 2\times {{10}^{15}}\left( t-\frac{x}{c} \right) \right]\]then the maximum electric field associated with it is -

    A) \[4.5\times {{10}^{4}}\,N/C\]

    B) \[4\times {{10}^{4}}\,N/C\]

    C) \[6\times {{10}^{4}}\,N/C\]

    D) \[3\times {{10}^{4}}\,N/C\]

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  • question_answer26) In the given circuit the cells have zero internal resistance. The currents (in Amperes) passing through resistance \[{{R}_{1}}and\text{ }{{R}_{2}}\] respectively, are-

    A) 0.5, 0

    B) 0, 1

    C) 1, 2

    D) 2, 2

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  • question_answer27) Three Carnot engines operate in series between a heat source at a temperature \[{{T}_{1}}\] and a heat sink at temperature \[{{T}_{4}}\] (see figure). There are two other reservoirs at temperature\[{{T}_{2}}and\text{ }{{T}_{3}}\], as shown, with\[{{T}_{1}}>{{T}_{2}}>{{T}_{3}}>{{T}_{4}}\]. The three engines are equally efficient if -

    A) \[{{T}_{2}}=\,\,{{({{T}_{1}}^{3}{{T}_{4}})}^{1/4}};\,\,=\,\,{{T}_{3}}\,\,=\,\,{{({{T}_{1}}{{T}_{4}}^{3})}^{1/4}}\]

    B) \[{{T}_{2}}=\,\,{{({{T}_{1}}{{T}_{4}})}^{1/2}};\,\,\,{{T}_{3}}\,\,=\,\,{{({{T}_{1}}^{2}{{T}_{4}})}^{1/3}}\]

    C) \[{{T}_{2}}=\,\,{{({{T}_{1}}{{T}_{4}}^{2})}^{1/3}};\,\,{{T}_{3}}\,\,=\,\,{{({{T}_{1}}^{2}{{T}_{4}})}^{1/3}}\]

    D) \[{{T}_{2}}=\,\,{{({{T}_{1}}^{2}{{T}_{4}})}^{1/3}};\,\,\,\,{{T}_{3}}\,\,=\,\,{{({{T}_{1}}{{T}_{4}}^{2})}^{1/3}}\]

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  • question_answer28) A potentiometer wire AB having length L and resistance 12 r is joined to a cell D of emf \[\varepsilon \] and internal resistance r. A cell C having emf \[\varepsilon /2\] and internal resistance 3r is connected. The length AJ at which the galvanometer as shown in figure shows no deflection is-

    A) \[\frac{11}{12}\,L\]

    B) \[\frac{13}{24}\,L\]

    C) \[\frac{5}{12}\,L\]

    D) \[\frac{11}{24}\,L\]

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  • question_answer29) A charge Q is distributed over three concentric spherical shells of radii a, b, c \[\left( a<b<c \right)\] such that their surface charge densities are equal to one another. The total potential at a point at distance r from their common centre, where \[r<a\], would be

    A) \[\frac{Q({{a}^{2}}+{{b}^{2}}+{{c}^{2}})}{{{4}_{\pi {{\varepsilon }_{0}}}}({{a}^{3}}+{{b}^{3}}+{{c}^{3}})}\]

    B) \[\frac{Q}{{{4}_{\pi {{\varepsilon }_{0}}}}(a+b+c)}\]

    C) \[\frac{Q}{{{12}_{\pi \varepsilon {{\,}_{0}}}}}\,\,\frac{ab+bc+ca}{abc}\]

    D) \[\frac{Q(a+b+c)}{{{4}_{\pi \varepsilon {{\,}_{0}}}}({{a}^{2}}+{{b}^{2}}+{{c}^{2}})}\]

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  • question_answer30) A piece of wood of mass 0.03 kg is dropped from the top of a 100 m height building. At the same time, a bullet of mass 0.02 kg is fired vertically upward, with a velocity \[100\text{ }m{{s}^{-1}}\]from the ground. The bullet gets embedded in the wood. Then the maximum height to which the combined system reaches above the top of the building before falling below is - \[(g=10\,m{{s}^{-2}})\]

    A) 30 m

    B) 40 m

    C) 20 m

    D) 10 m

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  • question_answer31) The type of hybridisation and number of lone pair (s) of electrons of Xe in \[XeO{{F}_{4}}\] respectively, are:

    A) \[s{{p}^{3}}d\] and 2

    B) \[s{{p}^{3}}{{d}^{2}}\] and 2

    C) \[s{{p}^{3}}d\] and 1

    D) \[s{{p}^{3}}{{d}^{2}}\] and 1

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  • question_answer32) Which of the following is not an example of heterogeneous catalytic reaction?

    A) Ostwald's process

    B) Combustion of coal

    C) Hydrogenation of vegetable oils

    D) Haber?s process

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  • question_answer33) Which hydrogen in compound `is easily replaceable during bromination reaction in presence of light?

    A) \[\beta hydrogen\]

    B) \[\alpha hydrogen\]

    C) \[\gamma hydrogen\]

    D) \[\delta hydrogen\]

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  • question_answer34) The total number of isotopes of hydrogen and number of radioactive isotopes among them, respectively, are:

    A) 3 and 2

    B) 2 and 1

    C) 2 and 0

    D) 3 and 1

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  • question_answer35) A process has \[\Delta H=200\text{ }J\text{ }mo{{l}^{-1}}\] and\[\Delta \,S=40\text{ }J{{K}^{-1}}\,mo{{l}^{-1}}\]. Out of the values given below, choose the minimum temperature above which the process will be spontaneous:

    A) 4 K

    B) 20 K

    C) 5 K

    D) 12 K

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  • question_answer36) A mixture of 100 m mol of \[Ca{{\left( OH \right)}_{2}}\], and 2 g of sodium sulphate was dissolved in water and the volume was made up to 100 mL. The mass of calcium sulphate formed and the concentration of \[O{{H}^{-}}\]in resulting solution, respectively, are: (Molar mass \[Ca{{\left( OH \right)}_{2}}\], \[N{{a}_{2}}S{{O}_{4}}\], and \[CaS{{O}_{4}}\] are 74, 143 and \[136\text{ }g\text{ }mo{{l}^{-1}}\], respectively; \[{{K}_{sp}}\]of \[Ca{{\left( OH \right)}_{2}}\]is \[5.5\,\times \,{{10}^{-6}}\])

    A) \[13.6g,\text{ }0.28\text{ }mol\text{ }{{L}^{-1}}\]

    B) \[13.6\,g,\text{ }0.14\,mol\,{{L}^{-\,1}}\]

    C) \[1.9\,g,\text{ }0.28\text{ }mol\text{ }{{L}^{-1}}\]

    D) \[1.9\,g,\text{ }0.14\text{ }mol\,{{L}^{-1}}\]

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  • question_answer37) The increasing order of the pKa values of the following compounds is:

    A) \[B<C<D<A\]

    B) \[B<C<A<D\]

    C) \[D<A<C<B\]

    D) \[C<B<A<D\]

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  • question_answer38) Hall- Heroult's process is given by:

    A) \[C{{u}^{2}}^{+}\left( aq \right)+{{H}_{2}}\left( g \right)\to Cu\left( s \right)+2{{H}^{+}}\left( aq \right)\]

    B) \[C{{r}_{2}}{{O}_{3}}+2Al\to A{{l}_{2}}{{O}_{3}}+2\,Cr\]

    C) \[2A{{l}_{2}}{{O}_{3}}+3C\to 4Al+3\text{ }C{{O}_{2}}\]

    D) \[ZnO+C\xrightarrow{Coke,\,1673\,K}\,\,Zn+CO\]

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  • question_answer39) The electronegativity of aluminium is similar to:

    A) Beryllium

    B) Carbon

    C) Boron

    D) Lithium

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  • question_answer40) The metal used for marking X-ray tube window is:

    A) Ca

    B) Na

    C) Mg

    D) Be

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  • question_answer41) Which premitive unit cell has unequal edge lengths \[(a\ne b\ne c)\] and all axial angles different from \[90{}^\circ \]?

    A) Hexagonal

    B) Tetragonal

    C) Triclinic

    D) Monoclinic

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  • question_answer42) Which of the graphs shown below does not represent the relationship between incident light and the electron ejected from metal surface?

    A)

    B)

    C)

    D)

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  • question_answer43) The major product formed in the reaction given below will be:

    A)

    B)

    C)

    D)

    E) None of these

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  • question_answer44) The values of \[{{K}_{p}}/{{K}_{c}}\] for the following reactions at. 300 K are, respectively: (At 300 K, \[RT=24.62\text{ }d{{m}^{3}}\] atm \[mo{{l}^{-1}}\])

    \[{{N}_{2}}\left( g \right)+{{O}_{2}}\left( g \right)\rightleftharpoons 2\text{ }NO\left( g \right)\]
    \[{{N}_{2}}{{O}_{4}}(g)\,\,\rightleftharpoons \,\,2NO\,(g)\]
    \[{{N}_{2}}(g)+3{{H}_{2}}(g)\rightleftharpoons 2N{{H}_{3}}(g)\]

    A) 24.62 \[d{{m}^{3}}\] atm \[mo{{l}^{-1}}\], 606.0 \[d{{m}^{6}}\] \[at{{m}^{2}}\]\[mo{{l}^{-2}}\] \[1.65\times {{10}^{-3}}d{{m}^{-}}^{6}at{{m}^{-}}^{2}mo{{l}^{2}}\]

    B) \[1,4.1\times {{10}^{-}}^{2}d{{m}^{-}}^{3}\,at{{m}^{-}}^{1}\] mol, 606 \[d{{m}^{6}}\] \[at{{m}^{2}}\,mo{{l}^{-}}^{2}\]

    C) \[1,24.62\text{ }d{{m}^{3}}\text{ }atm\text{ }mo{{l}^{-}}^{1}\], \[1.65\times {{10}^{-3}}\] \[d{{m}^{-6}}\]\[at{{m}^{-}}^{2}\,mo{{l}^{2}}\]

    D) 1, 24.62 \[d{{m}^{3}}\] atm\[mo{{l}^{-}}^{1}\], 606.0 \[d{{m}^{6}}\] \[at{{m}^{2}}\]\[mo{{l}^{-}}^{2}\]

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  • question_answer45) Consider the given plots for a reaction obeying Arrhenius equation \[\left( 0{}^\circ C<T<300{}^\circ C \right)\]: (K and \[{{E}_{a}}\] are rate constant and activation energy, respectively) Choose the correct option:

    A) I is right but II is wrong

    B) Both I and II are correct

    C) Both I and II are wrong

    D) I is wrong but II is right

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  • question_answer46) If dichloromethane (DCM) and water \[({{H}^{2}}O)\]are used for differential extraction, which one of the following statements is correct?

    A) DCM and \[{{H}_{2}}O\] would stay as upper and lower layer respectively in the separating funnel (S.F.)

    B) DCM and \[{{H}_{2}}O\] will make turbid/ colloidal mixture

    C) DCM and \[{{H}_{2}}O\] would stay as lower and upper layer respectively in the S.F.

    D) DCM and \[{{H}_{2}}O\] will be miscible clearly

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  • question_answer47) Which, dicarboxylic acid in presence of a dehydrating agent is least reactive to give an anhydride?

    A)

    B)

    C)

    D)

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  • question_answer48) The major product of the following reaction is

    A)

    B)

    C)

    D)

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  • question_answer49) The major product 'X' formed in the following reaction is:

    A)                              

    B)  

    C)       

    D)  

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  • question_answer50) Two pi and half sigma bonds are present in:

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

    B) \[{{N}^{+}}_{2}\]

    C) \[{{O}^{+}}_{2}\]

    D) \[{{N}_{2}}\]

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  • question_answer51) The correct structure of product 'P' in the following reactions is: \[Asn-Ser+\underset{excess}{\mathop{{{\left( C{{H}_{3}}CO \right)}_{2}}O}}\,\text{ }\xrightarrow{NE{{t}_{3}}}\text{ }P\]

    A)

    B)  

    C)  

    D)

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  • question_answer52) Wilkinson catalyst is : \[\left( Et={{C}_{2}}{{H}_{5}} \right)\]

    A) \[\left[ {{\left( P{{h}_{3}}P \right)}_{3}}\text{ }RhCl \right]\]

    B) \[\left[ {{\left( E{{t}_{3}}P \right)}_{3}}RhCl \right]\]

    C) \[\left[ {{\left( E{{t}_{3}}P \right)}_{3}}IrCl \right]\]

    D) \[\left[ {{\left( P{{h}_{3}}P \right)}_{3}}IrCl \right]\]

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  • question_answer53) The chemical nature of hydrogen peroxide is:

    A) Oxidising agent in acidic medium, but not in basic medium

    B) Oxidising and reducing agent in both acidic and basic medium

    C) Reducing agent in basic medium, but not in acidic medium

    D) Oxidising and reducing agent in acidic medium, but not in basic medium.

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  • question_answer54) The major product of the following reaction is:

    A)

    B)

    C)

    D)

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  • question_answer55) The effect of lanthanoid contraction in the lanthanoid series of elements by and large means:

    A) increase in atomic radii and decrease in ionic radii

    B) increase in both atomic and ionic radii

    C) decrease in both atomic and ionic radii

    D) decrease in atomic radii and increase in ionic radii

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  • question_answer56) Water filled in two glasses A and B have BOD values of 10 and 20, respectively. The correct statement regarding them, is:

    A) B is more polluted than A

    B) A is suitable for drinking, whereas B is not

    C) Both A and B are suitable for drinking

    D) A is more polluted than B.

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  • question_answer57) The decreasing order of ease of alkaline hydrolysis for the following esters in

    (I)
    (II)
    (III)
    (IV)

    A) \[III>II>IV>I\]

    B) \[IV>II>III>I\]

    C) \[III>II>I>IV\]

    D) \[II>III>I>IV\]

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  • question_answer58) Liquids A and B form an ideal solution in the entire composition range. At 350 K, the vapor pressures of pure A and pure B are \[7\times {{10}^{3}}\]Pa and \[12\times {{10}^{3}}\] Pa, respectively. The composition of the vapor in equilibrium with a solution containing 40 mole percent of A at this temperature is:

    A) \[{{x}_{A}}=0.76;\,\,{{x}_{B}}=0.24\]

    B) \[{{x}_{A}}=0.28;\,\,{{x}_{B}}=0.72\]

    C) \[{{x}_{A}}=0.4;\,\,{{x}_{B}}=0.6\]

    D) \[{{x}_{A}}=0.37;\,\,{{x}_{B}}=0.63\]

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  • question_answer59) The total number of isomers for a square planar complex \[\left[ M\left( F \right)\left( Cl \right)\left( SCN \right)\left( N{{O}_{2}} \right) \right]\] is:

    A) 16

    B) 8

    C) 12

    D) 4

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  • question_answer60) Consider the following reduction processes:

    \[Z{{n}^{2}}+2{{e}^{-}}\to Zn\left( s \right);\text{ }E{}^\circ =-\,0.76V\]
    \[C{{a}^{2+}}+2{{e}^{-}}\to Ca\left( s \right);\text{ }E{}^\circ =-\,2.87\,V\]
    \[M{{g}^{2+}}+2{{e}^{-}}\to Mg\left( s \right);\text{ }E{}^\circ =-\,2.36\,V\]
    \[N{{i}^{2}}+2{{e}^{-}}\to Ni\left( s \right);\text{ }E{}^\circ =-\,0.25\,V\]
    The reducing power of the metals increases in the order:

    A) \[Ca<Mg<Zn<Ni\]

    B) \[Ni<Zn<Mg<Ca\]

    C) \[Zn<Mg<Ni<Ca\]

    D) \[Ca<Zn<Mg<Ni\]

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  • question_answer61) In a class of 140 student numbered 1 to 140, all even numbered students opted Mathematics course, those whose number is divisible by 3 opted Physics course and those whose number is divisible by 5 opted Chemistry course. Then the number of students who did not opt for any of the three courses is:

    A) 42

    B) 102

    C) 1

    D) 38

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  • question_answer62) Let \[\overrightarrow{a}=2\widehat{i}+{{\lambda }_{1}}\widehat{j}+3\widehat{k},\text{ }\overrightarrow{b}=4\widehat{i}+(3-{{\lambda }_{2}})\widehat{j}+6\widehat{k}\] and \[\overrightarrow{c}=3\widehat{i}+6\widehat{j}+({{\lambda }_{3}}-1)\widehat{k}\] be three vectors such that \[\overrightarrow{b}=2\overrightarrow{a}\] and \[\overrightarrow{a}\] is perpendicular to\[\overrightarrow{c}\]. Then a possible value of \[({{\lambda }_{1}},\,\,{{\lambda }_{2}},\,\,{{\lambda }_{3}})\] is -

    A) (1, 5, 1)

    B) (1, 3, 1)

    C) \[\left( -\frac{1}{2},\,\,4,\,\,0 \right)\]

    D) \[\left( \frac{1}{2},\,\,4,\,\,-2 \right)\]

    View Answer play_arrow
  • question_answer63) Consider the statement: \[''P\left( n \right):{{n}^{2}}-n+41\] is prime?. Then which one of the following is true?

    A) P(5) is false but P(3) is true

    B) Both P(3) and P(5) are true

    C) P(3) is false but P(5) is true

    D) Both P(3) and P(5) are false

    View Answer play_arrow
  • question_answer64) If a circle C passing through the point (4, 0) touches the circle \[{{x}^{2}}+{{y}^{2}}+4x-6y=12\] externally at the point \[\left( 1,\,\,-1 \right)\], then the radius of C is-

    A) 5

    B) \[2\sqrt{5}\]

    C) 4

    D) \[\sqrt{57}\]

    View Answer play_arrow
  • question_answer65) If the parabolas \[{{y}^{2}}=4b\left( x-c \right)\text{ }and\text{ }{{y}^{2}}=8\,ax\] have a common normal, then which on of the following is a valid choice for the ordered triad (a, b, c)?

    A) (1, 1, 3)

    B) (1, 1, 0)

    C) \[\left( \frac{1}{2},\,\,2,\,\,0 \right)\]

    D) \[\left( \frac{1}{2},\,\,2,\,\,3 \right)\]

    View Answer play_arrow
  • question_answer66) The plane passing through the point \[\left( 4,\,\,-1,\text{ }2 \right)\] and parallel to the lines \[\frac{x+2}{3}\,\,=\,\frac{y-2}{-1}\,\,=\,\,\frac{z+1}{2}\] and \[\frac{x-2}{1}\,\,=\,\frac{y-3}{2}\,\,=\,\,\frac{z-4}{3}\] also passes through

    A) (1, 1, -1)

    B) (1, 1, 1)

    C) (-1, -1, -I)

    D) (-1, -1, 1)

    View Answer play_arrow
  • question_answer67) Let \[n\ge 2\] be a natural number and \[0<\theta <\frac{\pi }{2}\]Then \[\int{\frac{(si{{n}^{n}}\,\theta \,-\,sin\,\theta ){{\,}^{1/n}}\,\cos \,\theta }{\sin {{\,}^{n+1}}\,\theta }}\,d\theta \] is equal to -(where C is a constant of integration)

    A) \[\frac{n}{{{n}^{2}}-1}\,{{\left( 1+\frac{1}{\sin {{\,}^{n-1}}\,\theta } \right)}^{\frac{n+1}{n}}}\,+C\]

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

    C) \[\frac{n}{{{n}^{2}}-1}\,{{\left( 1-\frac{1}{\sin {{\,}^{n-1}}\,\theta } \right)}^{\frac{n+1}{n}}}\,+C\]

    D) \[\frac{n}{{{n}^{2}}+1}\,{{\left( 1-\frac{1}{\sin {{\,}^{n-1}}\,\theta } \right)}^{\frac{n+1}{n}}}\,+C\]

    View Answer play_arrow
  • question_answer68) The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are 1, 3 and 8, then a ratio of other two observations is -

    A) 6 : 7

    B) 10 : 3

    C) 4 : 9

    D) 5 : 8

    View Answer play_arrow
  • question_answer69) If the system of equations

    \[x+y+z=5\] \[x+2y+3z=9\] \[x+3y+\alpha z=\beta \]
    has infinitely many solutions, then \[\beta -\alpha \] equals-

    A) 8

    B) 21

    C) 18

    D) 5

    View Answer play_arrow
  • question_answer70) If 5, 5r, \[5{{r}^{2}}\] are the lengths of the sides of a triangle, then r cannot be equal to -

    A) \[\frac{7}{4}\]

    B) \[\frac{5}{4}\]

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

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

    View Answer play_arrow
  • question_answer71) An unbiased coin is tossed. If the outcome is a head then a pair of unbiased dice is rolled and the sum of the numbers obtained on them is noted. If the toss of the coin results in tail then a card from a well- shuffled pack of nine cards numbered 1, 2, 3, ....... 9 is randomly picked and the number on the card is noted. The probability that the noted number is either 7 or 8 is -

    A) \[\frac{19}{36}\]

    B) \[\frac{15}{72}\]

    C) \[\frac{13}{36}\]

    D) \[\frac{19}{72}\]

    View Answer play_arrow
  • question_answer72) Let \[f:R\,\to R\] be a function such that\[f\left( x \right)={{x}^{3}}+{{x}^{2}}f\,\left( 1 \right)+xf\,\left( 2 \right)+f\text{ }\left( 3 \right),\] \[x\in R\]. Then f(2) equals-

    A) 30

    B) - 2

    C) - 4

    D) 8

    View Answer play_arrow
  • question_answer73) The equation of a tangent to the hyperbola \[4{{x}^{2}}-5{{y}^{2}}=20\] parallel to the line \[x-y=2\] is-

    A) \[x-y+9=0\]

    B) \[x-y-3=0\]

    C) \[x-y+1=0\]

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

    View Answer play_arrow
  • question_answer74) If \[\frac{dy}{dx}+\frac{3}{{{\cos }^{2}}x}y=\frac{1}{\cos {{\,}^{2}}\,x}\] \[x\in \left( \frac{-\pi }{3},\,\,\frac{\pi }{3} \right)\] and \[y\left( \frac{\pi }{4} \right)\,=\,\frac{4}{3}\] then \[y\left( -\frac{\pi }{4} \right)\,\] equals-

    A) \[\frac{1}{3}+{{e}^{6}}\]

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

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

    D) \[-\frac{4}{3}\]

    View Answer play_arrow
  • question_answer75) A point P moves on the line\[2x-3y+4=0\]. If Q(1, 4) and R (3, - 2) are fixed points, then the locus of the centroid of \[\Delta \,PQR\] is a line-

    A) parallel to y-axis

    B) with slope \[\frac{2}{3}\]

    C) parallel to x-axis

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

    View Answer play_arrow
  • question_answer76) The sum of all two digit positive numbers which when divided by 7 yield 2 or 5 as remainder is-

    A) 1356

    B) 1256

    C) 1365

    D) 1465

    View Answer play_arrow
  • question_answer77) If \[{{\sum\limits_{i\,=\,1}^{20}{\left( \frac{^{20}{{C}_{i-1}}}{^{20}{{C}_{i}}\,{{+}^{20}}{{C}_{i\,=\,1}}} \right)}}^{3}}\,\,=\,\,\frac{k}{21}\]then k is equal to

    A) 100

    B) 200

    C) 50

    D) 400

    View Answer play_arrow
  • question_answer78) Consider the quadratic equation

    \[(c-5){{x}^{2}}-2cx+(c-4)=0,c\ne 5\]. Let S be the set of all integral values of c for which one root of the equation lies in the integral values of c for which one root of the equation lies in the interval (0, 2) and its other root lies in the interval (2, 3). Then the number of elements in S is

    A) 12

    B) 18

    C) 10

    D) 11

    View Answer play_arrow
  • question_answer79) If the area enclosed between the curves \[y=k{{x}^{2}}\] and \[x=k{{y}^{2}},\text{ }\left( k>0 \right)\], is 1 square unit. Then k is-

    A) \[\sqrt{3}\]

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

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

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

    View Answer play_arrow
  • question_answer80) Consider a triangular plot ABC with sides\[AB=7\,m\], \[BC=5\,m\] and\[CA=6\,m\]. A vertical lamp-post at the mid-point D of AC subtends an angle \[30{}^\circ \] at B. The height (in m) of the lamp-post is-

    A) \[2\sqrt{21}\]

    B) \[\frac{3}{2}\sqrt{21}\]

    C) \[7\sqrt{3}\]

    D) \[\frac{2}{3}\sqrt{21}\]

    View Answer play_arrow
  • question_answer81) The shortest distance between the point \[\left( \frac{3}{2},\,\,0 \right)\] and the curve \[y=\sqrt{x},\,\,(x>0)\], is -

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

    B) \[\frac{5}{4}\]

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

    D) \[\frac{\sqrt{5}}{2}\]

    View Answer play_arrow
  • question_answer82) Let \[I=\int\limits_{a}^{b}{\left( {{x}^{4}}-2{{x}^{2}} \right)dx}\]. If I is minimum then the ordered pair (a, b) is -

    A) \[d\in R\]

    B) \[\,(0,\,\,\sqrt{2})\]

    C) \[(-\,\sqrt{2},\,\,\sqrt{2})\]

    D) \[\,(-\sqrt{2},\,\,0)\]

    View Answer play_arrow
  • question_answer83) For each \[t\in R\], let. [t] be the greatest integer less than or equal to t.

    Then \[\underset{x\to 1+}{\mathop{\lim }}\,\,\frac{1-\left| x \right|+\sin \left| 1-x \right|)sin\left( \frac{\pi }{2}[1-x] \right)}{\left| 1-x \right|\,.\,[1-x]\,}\]

    A) equals -1

    B) equals 1

    C) equals 0

    D) does not exist

    View Answer play_arrow
  • question_answer84) Let \[{{z}_{1}}\,and\text{ }{{z}_{2}}\] be any two non-zero complex numbers such that\[3\text{ }\left| {{z}_{1}} \right|=4\text{ }\left| {{z}_{2}} \right|\]. If \[z=\frac{3{{z}_{1}}}{2{{z}_{2}}}+\frac{2{{z}_{2}}}{3{{z}_{1}}}\] then-

    A) \[Im\left( z \right)=0\]

    B) \[\left| z \right|=\frac{\sqrt{5}}{2}\]

    C) \[\left| z \right|=\frac{1}{2}\frac{\sqrt{17}}{2}\]

    D) \[Re\left( z \right)=0\]

    E) None of these

    View Answer play_arrow
  • question_answer85) If the line \[3x+4y-24=0\] intersects the x-axis at the point A and the y-axis at the point B, then the in centre of the triangle OAB, where 0 is the origin, is-

    A) (3, 4)

    B) (2, 2)

    C) (4, 4)

    D) (4, 3)

    View Answer play_arrow
  • question_answer86) The sum of all values of \[\theta \in \left( 0,\,\,\frac{\pi }{2} \right)\] satisfying \[{{\sin }^{2}}2\theta \,\,+\,{{\cos }^{4}}2\theta =\frac{3}{4}\,\] is

    A) \[\frac{5\pi }{4}\]

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

    C) \[\pi \]

    D) \[\frac{3\,\pi }{8}\]

    View Answer play_arrow
  • question_answer87) Let A be a point on the line \[\overrightarrow{\text{r}}=\,\,\left( 1-3\mu \right)\widehat{i}+(\mu -1)\widehat{j}+\left( 2+5\mu \right)\widehat{k}\] and \[B(3,\,\,2,\,\,6)\]be a point in the space. Then the value of \[\mu \] for which the vector AB is parallel to the plane \[x-4y+3z=1\] is-

    A) \[\frac{1}{8}\]

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

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

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

    View Answer play_arrow
  • question_answer88) Let \[d\in R\], and

    \[A=\left[ \begin{matrix} -2 & 4+d & (sin\,\theta )-2 \\ 1 & (sin\,\theta )+2 & d \\ 5 & (2\,sin\,\theta )-d & (-sin\,\theta )+2+2d \\ \end{matrix} \right]\]
    \[\theta \in [0,\,\,2\,\pi ]\]. If the minimum value of det is 8, then a value of d is -

    A) -7

    B) \[2(\sqrt{2}+2)\]

    C) -5

    D) \[2(\sqrt{2}+1)\]

    View Answer play_arrow
  • question_answer89) Let \[f(x)\,=\,\,\left\{ \begin{matrix} \max \,\{\left| x \right|,\,{{x}^{2}}\} \\ 8-2\,\left| x \right| \\ \end{matrix} \right.\,\,\,\,\,\begin{matrix} \left| x \right|\,\le \,2 \\ 2<\left| x \right|\,\le \,4 \\ \end{matrix}\]

    Let S be the set of points in the interval (- 4, 4) at which f is not differentiable.
    Then S

    A) equals {-2, -1, 1, 2}

    B) equals {- 2, - 1, 0, 1, 2}

    C) equals {- 2, 2}

    D) is an empty set

    View Answer play_arrow
  • question_answer90) If the third term in the binomial expansion of \[{{\left( 1+{{x}^{{{\log }_{2}}x}} \right)}^{5}}\] equals 2560, then a possible value of x is-

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

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

    C) \[\frac{1}{8}\]

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

    View Answer play_arrow

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JEE Main Online Paper (Held On 10-Jan-2019 Morning)
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